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QUANTUM FRONTIERS
The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations to watch The West Wing. PEEKING INTO THE WORLD OF QUANTUM INTELLIGENCE Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly. An illustration of receiving, processing, and storing information. Based on the processed information, one can make prediction about the future. We, as intelligent beings, receive, process, andQUANTUM FRONTIERS
Imagine a line of ions trapped by lasers. Each ion contains the physical manifestation of a qubit—a quantum two-level system, the basic unit of quantum information. You can think of a qubit as having a quantum analogue of angular momentum, called spin. The spin has three components, one per direction of space.LEARNING THEORY
It is natural to wonder what a world of quantum intelligence would be like. While we have never encountered such a strange creature in the real world (yet), the mathematics of quantum mechanics, machine learning, and information theory allow us THE GRAND TOUR OF QUANTUM THERMODYNAMICS The Grand Tour of quantum thermodynamics. Young noblemen used to undertake a “Grand Tour” during the 1600s and 1700s. Many of the tourists hailed from England, though well-to-do compatriots traveled from Scandinavia, Germany, and the United States. The men had just graduated from university—in many cases, Oxford or Cambridge.THE SIGN PROBLEM(S)
The sign problem (s) The thirteen-month-old had mastered the word “dada” by the time I met her. Her parents were teaching her to communicate other concepts through sign language. Picture her, dark-haired and bibbed, in a high chair. Banana and mango slices litter the tray in front of her. More fruit litters the floor in frontof the tray.
QUANTUM INFORMATION IN QUANTUM COGNITION Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care aboutprogress.
FERNANDO PASTAWSKI
TOP 10 QUESTIONS FOR YOUR POTENTIAL PHD ADVISER/GROUP Everyone in grad school has taken on the task of picking the perfect research group at some point. Then some among us had the dubious distinction of choosing the perfect research group twice. Luckily for me, a year of grad research taught me a lot and WE ARE ALL WILSONIANS NOW We are all Wilsonians now. Ken Wilson passed away on June 15 at age 77. He changed how we think about physics. Renormalization theory, first formulated systematically by Freeman Dyson in 1949, cured the flaws of quantum electrodynamics and turned it into a precise computational tool. But the subject seemed magical and mysterious.QUANTUM FRONTIERS
The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations to watch The West Wing. PEEKING INTO THE WORLD OF QUANTUM INTELLIGENCE Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly. An illustration of receiving, processing, and storing information. Based on the processed information, one can make prediction about the future. We, as intelligent beings, receive, process, andQUANTUM FRONTIERS
Imagine a line of ions trapped by lasers. Each ion contains the physical manifestation of a qubit—a quantum two-level system, the basic unit of quantum information. You can think of a qubit as having a quantum analogue of angular momentum, called spin. The spin has three components, one per direction of space.LEARNING THEORY
It is natural to wonder what a world of quantum intelligence would be like. While we have never encountered such a strange creature in the real world (yet), the mathematics of quantum mechanics, machine learning, and information theory allow us THE GRAND TOUR OF QUANTUM THERMODYNAMICS The Grand Tour of quantum thermodynamics. Young noblemen used to undertake a “Grand Tour” during the 1600s and 1700s. Many of the tourists hailed from England, though well-to-do compatriots traveled from Scandinavia, Germany, and the United States. The men had just graduated from university—in many cases, Oxford or Cambridge.THE SIGN PROBLEM(S)
The sign problem (s) The thirteen-month-old had mastered the word “dada” by the time I met her. Her parents were teaching her to communicate other concepts through sign language. Picture her, dark-haired and bibbed, in a high chair. Banana and mango slices litter the tray in front of her. More fruit litters the floor in frontof the tray.
QUANTUM INFORMATION IN QUANTUM COGNITION Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care aboutprogress.
FERNANDO PASTAWSKI
TOP 10 QUESTIONS FOR YOUR POTENTIAL PHD ADVISER/GROUP Everyone in grad school has taken on the task of picking the perfect research group at some point. Then some among us had the dubious distinction of choosing the perfect research group twice. Luckily for me, a year of grad research taught me a lot and WE ARE ALL WILSONIANS NOW We are all Wilsonians now. Ken Wilson passed away on June 15 at age 77. He changed how we think about physics. Renormalization theory, first formulated systematically by Freeman Dyson in 1949, cured the flaws of quantum electrodynamics and turned it into a precise computational tool. But the subject seemed magical and mysterious.QUANTUM FRONTIERS
Imagine a line of ions trapped by lasers. Each ion contains the physical manifestation of a qubit—a quantum two-level system, the basic unit of quantum information. You can think of a qubit as having a quantum analogue of angular momentum, called spin. The spin has three components, one per direction of space. LEARNING ABOUT LEARNING The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations towatch The West
LEARNING THEORY
It is natural to wonder what a world of quantum intelligence would be like. While we have never encountered such a strange creature in the real world (yet), the mathematics of quantum mechanics, machine learning, and information theory allow usALEKSANDER KUBICA
Posted on July 3, 2020 by Aleksander Kubica. 1. Have you ever wondered what can be done in 48 hours? For instance, our heart beats around 200 000 times. One of the biggest supercomputers crunches petabytes (peta = 10 15) of numbers to simulate an experiment that took Google’s quantum processor only 300 seconds to run. LIFE AMONG THE EXPERIMENTALISTS Life among the experimentalists. Posted on March 21, 2021 by Nicole Yunger Halpern. I used to catch lizards—brown anoles, as I learned to call them later—as a child. They were colored as their name suggests, were about as long as one of my hands, and resented my attention. But they frequented our back porch, and I had a butterflynet.
PRESKILL | QUANTUM FRONTIERS John Preskill – There are two main classes of attempts. One is just to come up with a cryptographic protocol not so different conceptually from what’s done now, but based on a problem that’s hard for quantum computers. Craig Cannon – There you go.SHAUNMAGUIRE
The Science that made Stephen Hawking famous. Posted on November 5, 2014 by shaunmaguire. 8. In anticipation of The Theory of Everything which comes out today, and in the spirit of continuing with Quantum Frontiers’ current movie theme, I wanted to provide an overview of Stephen Hawking’s pathbreaking research.QUANTUM CHESS
The Quantum Chess board begins in the same configuration as standard chess. All pawns move the same as they would in standard chess, but all other pieces get a choice of two movement types, standard or quantum. Standard moves act exactly as they would in standard chess. However, quantum moves, create superpositions. THIS VIDEO OF SCIENTISTS SPLITTING AN ELECTRON WILL SHOCK by Jorge Cham. Ok, this is where things get weird. If quantum computers, femtometer motions or laser alligators weren't enough, let's throw in fractionalized electrons, topological surfaces and strings that go to the end of time. To be honest, the idea that an electron can't be split hadn't even occurred to me before my conversation with Gil and SPIROS | QUANTUM FRONTIERS Posted on September 15, 2015 by spiros. 4. A blog on everything quantum is the perfect place to announce the launch of the 2015 Quantum Shorts competition. The contest encourages readers to create quantum-themed “flash fiction”: a short story of no more than 1000 words that is inspired by quantum physics.QUANTUM FRONTIERS
The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations to watch The West Wing. PEEKING INTO THE WORLD OF QUANTUM INTELLIGENCE Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly. An illustration of receiving, processing, and storing information. Based on the processed information, one can make prediction about the future. We, as intelligent beings, receive, process, and LEARNING ABOUT LEARNING The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations towatch The West
QUANTUM FRONTIERS
Imagine a line of ions trapped by lasers. Each ion contains the physical manifestation of a qubit—a quantum two-level system, the basic unit of quantum information. You can think of a qubit as having a quantum analogue of angular momentum, called spin. The spin has three components, one per direction of space. THE GRAND TOUR OF QUANTUM THERMODYNAMICS The Grand Tour of quantum thermodynamics. Young noblemen used to undertake a “Grand Tour” during the 1600s and 1700s. Many of the tourists hailed from England, though well-to-do compatriots traveled from Scandinavia, Germany, and the United States. The men had just graduated from university—in many cases, Oxford or Cambridge.LEARNING THEORY
Rigorously, one refers to a classical/quantum being as a classical/quantum model, algorithm, protocol, or procedure. This is because the actions of these classical/quantum beings are the center of the mathematical analysis. Formally, we consider the task of learning an unknown physical evolution described by a CPTP map thattakes in -qubit
QUANTUM INFORMATION IN QUANTUM COGNITION Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care aboutprogress.
THE SIGN PROBLEM(S)
The sign problem (s) The thirteen-month-old had mastered the word “dada” by the time I met her. Her parents were teaching her to communicate other concepts through sign language. Picture her, dark-haired and bibbed, in a high chair. Banana and mango slices litter the tray in front of her. More fruit litters the floor in frontof the tray.
HSIN-YUAN HUANG (ROBERT) About Hsin-Yuan Huang (Robert) I am a third-year Caltech Ph.D. student (advised by John Preskill and Thomas Vidick). I think about fundamental questions to understand how quantum machines can improve our capability to learn about the world around us. TOP 10 QUESTIONS FOR YOUR POTENTIAL PHD ADVISER/GROUP Everyone in grad school has taken on the task of picking the perfect research group at some point. Then some among us had the dubious distinction of choosing the perfect research group twice. Luckily for me, a year of grad research taught me a lot andQUANTUM FRONTIERS
The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations to watch The West Wing. PEEKING INTO THE WORLD OF QUANTUM INTELLIGENCE Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly. An illustration of receiving, processing, and storing information. Based on the processed information, one can make prediction about the future. We, as intelligent beings, receive, process, and LEARNING ABOUT LEARNING The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations towatch The West
QUANTUM FRONTIERS
Imagine a line of ions trapped by lasers. Each ion contains the physical manifestation of a qubit—a quantum two-level system, the basic unit of quantum information. You can think of a qubit as having a quantum analogue of angular momentum, called spin. The spin has three components, one per direction of space. THE GRAND TOUR OF QUANTUM THERMODYNAMICS The Grand Tour of quantum thermodynamics. Young noblemen used to undertake a “Grand Tour” during the 1600s and 1700s. Many of the tourists hailed from England, though well-to-do compatriots traveled from Scandinavia, Germany, and the United States. The men had just graduated from university—in many cases, Oxford or Cambridge.LEARNING THEORY
Rigorously, one refers to a classical/quantum being as a classical/quantum model, algorithm, protocol, or procedure. This is because the actions of these classical/quantum beings are the center of the mathematical analysis. Formally, we consider the task of learning an unknown physical evolution described by a CPTP map thattakes in -qubit
QUANTUM INFORMATION IN QUANTUM COGNITION Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care aboutprogress.
THE SIGN PROBLEM(S)
The sign problem (s) The thirteen-month-old had mastered the word “dada” by the time I met her. Her parents were teaching her to communicate other concepts through sign language. Picture her, dark-haired and bibbed, in a high chair. Banana and mango slices litter the tray in front of her. More fruit litters the floor in frontof the tray.
HSIN-YUAN HUANG (ROBERT) About Hsin-Yuan Huang (Robert) I am a third-year Caltech Ph.D. student (advised by John Preskill and Thomas Vidick). I think about fundamental questions to understand how quantum machines can improve our capability to learn about the world around us. TOP 10 QUESTIONS FOR YOUR POTENTIAL PHD ADVISER/GROUP Everyone in grad school has taken on the task of picking the perfect research group at some point. Then some among us had the dubious distinction of choosing the perfect research group twice. Luckily for me, a year of grad research taught me a lot andQUANTUM FRONTIERS
Imagine a line of ions trapped by lasers. Each ion contains the physical manifestation of a qubit—a quantum two-level system, the basic unit of quantum information. You can think of a qubit as having a quantum analogue of angular momentum, called spin. The spin has three components, one per direction of space. LIFE AMONG THE EXPERIMENTALISTS Life among the experimentalists. Posted on March 21, 2021 by Nicole Yunger Halpern. I used to catch lizards—brown anoles, as I learned to call them later—as a child. They were colored as their name suggests, were about as long as one of my hands, and resented my attention. But they frequented our back porch, and I had a butterflynet.
PRESKILL | QUANTUM FRONTIERS John Preskill – There are two main classes of attempts. One is just to come up with a cryptographic protocol not so different conceptually from what’s done now, but based on a problem that’s hard for quantum computers. Craig Cannon – There you go. ONE IF BY LAND MINUS TWO IF BY SEA, OVER THE SQUARE-ROOT While laying plans, Revere instructs Newman: He said to his friend, “If the British march By land or sea from the town to-night, Hang a lantern aloft in the belfry-arch Of the North-Church-tower, as a signal light. Then comes one of the poem’s most famous lines: “One if by land, and two if by sea.”. The British could have left Bostonby
IN THE HOUR OF DARKNESS AND PERIL AND NEED A cry of defiance, and not of fear, A voice in the darkness, a knock at the door, And a word that shall echo forevermore! For, borne on the night-wind of the Past, Through all our history, to the last, In the hour of darkness and peril and need, The people will waken and listento hear.
SHAUNMAGUIRE
The Science that made Stephen Hawking famous. Posted on November 5, 2014 by shaunmaguire. 8. In anticipation of The Theory of Everything which comes out today, and in the spirit of continuing with Quantum Frontiers’ current movie theme, I wanted to provide an overview of Stephen Hawking’s pathbreaking research. THE 10 BIGGEST BREAKTHROUGHS IN PHYSICS OVER THE PAST 25 The biggest breakthroughs of the past 25 years: *Neutrino Mass: surprisingly, neutrinos have a nonzero mass, which provides a window into particle physics beyond the standard model. THE STANDARD MODEL has been getting a lot of attention recently. This is well deserved in my opinion, considering that the vast majority of its predictions have come true, most of which were made by theFERNANDO PASTAWSKI
Roughly speaking, tensor networks are ingenious ways of encoding (quantum) inputs into (quantum) outputs. In particular, if you enter some input at the boundary of your tensor network, the tensors do the work of processing that information throughout the network so that if you ask for an output at any one of the nodes in the bulk of the tensor network, you get the right encoded answer. WE ARE ALL WILSONIANS NOW We are all Wilsonians now. Ken Wilson passed away on June 15 at age 77. He changed how we think about physics. Renormalization theory, first formulated systematically by Freeman Dyson in 1949, cured the flaws of quantum electrodynamics and turned it into a precise computational tool. But the subject seemed magical and mysterious. THIS VIDEO OF SCIENTISTS SPLITTING AN ELECTRON WILL SHOCK by Jorge Cham. Ok, this is where things get weird. If quantum computers, femtometer motions or laser alligators weren't enough, let's throw in fractionalized electrons, topological surfaces and strings that go to the end of time. To be honest, the idea that an electron can't be split hadn't even occurred to me before my conversation with Gil andQUANTUM FRONTIERS
The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations to watch The West Wing. PEEKING INTO THE WORLD OF QUANTUM INTELLIGENCE Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly. An illustration of receiving, processing, and storing information. Based on the processed information, one can make prediction about the future. We, as intelligent beings, receive, process, andQUANTUM FRONTIERS
Imagine a line of ions trapped by lasers. Each ion contains the physical manifestation of a qubit—a quantum two-level system, the basic unit of quantum information. You can think of a qubit as having a quantum analogue of angular momentum, called spin. The spin has three components, one per direction of space. LEARNING ABOUT LEARNING The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations towatch The West
LEARNING THEORY
Rigorously, one refers to a classical/quantum being as a classical/quantum model, algorithm, protocol, or procedure. This is because the actions of these classical/quantum beings are the center of the mathematical analysis. Formally, we consider the task of learning an unknown physical evolution described by a CPTP map thattakes in -qubit
THE GRAND TOUR OF QUANTUM THERMODYNAMICS The Grand Tour of quantum thermodynamics. Young noblemen used to undertake a “Grand Tour” during the 1600s and 1700s. Many of the tourists hailed from England, though well-to-do compatriots traveled from Scandinavia, Germany, and the United States. The men had just graduated from university—in many cases, Oxford or Cambridge.THE SIGN PROBLEM(S)
The sign problem (s) The thirteen-month-old had mastered the word “dada” by the time I met her. Her parents were teaching her to communicate other concepts through sign language. Picture her, dark-haired and bibbed, in a high chair. Banana and mango slices litter the tray in front of her. More fruit litters the floor in frontof the tray.
QUANTUM INFORMATION IN QUANTUM COGNITION Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care aboutprogress.
HSIN-YUAN HUANG (ROBERT) About Hsin-Yuan Huang (Robert) I am a third-year Caltech Ph.D. student (advised by John Preskill and Thomas Vidick). I think about fundamental questions to understand how quantum machines can improve our capability to learn about the world around us. TOP 10 QUESTIONS FOR YOUR POTENTIAL PHD ADVISER/GROUP Everyone in grad school has taken on the task of picking the perfect research group at some point. Then some among us had the dubious distinction of choosing the perfect research group twice. Luckily for me, a year of grad research taught me a lot andQUANTUM FRONTIERS
The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations to watch The West Wing. PEEKING INTO THE WORLD OF QUANTUM INTELLIGENCE Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly. An illustration of receiving, processing, and storing information. Based on the processed information, one can make prediction about the future. We, as intelligent beings, receive, process, andQUANTUM FRONTIERS
Imagine a line of ions trapped by lasers. Each ion contains the physical manifestation of a qubit—a quantum two-level system, the basic unit of quantum information. You can think of a qubit as having a quantum analogue of angular momentum, called spin. The spin has three components, one per direction of space. LEARNING ABOUT LEARNING The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations towatch The West
LEARNING THEORY
Rigorously, one refers to a classical/quantum being as a classical/quantum model, algorithm, protocol, or procedure. This is because the actions of these classical/quantum beings are the center of the mathematical analysis. Formally, we consider the task of learning an unknown physical evolution described by a CPTP map thattakes in -qubit
THE GRAND TOUR OF QUANTUM THERMODYNAMICS The Grand Tour of quantum thermodynamics. Young noblemen used to undertake a “Grand Tour” during the 1600s and 1700s. Many of the tourists hailed from England, though well-to-do compatriots traveled from Scandinavia, Germany, and the United States. The men had just graduated from university—in many cases, Oxford or Cambridge.THE SIGN PROBLEM(S)
The sign problem (s) The thirteen-month-old had mastered the word “dada” by the time I met her. Her parents were teaching her to communicate other concepts through sign language. Picture her, dark-haired and bibbed, in a high chair. Banana and mango slices litter the tray in front of her. More fruit litters the floor in frontof the tray.
QUANTUM INFORMATION IN QUANTUM COGNITION Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care aboutprogress.
HSIN-YUAN HUANG (ROBERT) About Hsin-Yuan Huang (Robert) I am a third-year Caltech Ph.D. student (advised by John Preskill and Thomas Vidick). I think about fundamental questions to understand how quantum machines can improve our capability to learn about the world around us. TOP 10 QUESTIONS FOR YOUR POTENTIAL PHD ADVISER/GROUP Everyone in grad school has taken on the task of picking the perfect research group at some point. Then some among us had the dubious distinction of choosing the perfect research group twice. Luckily for me, a year of grad research taught me a lot andQUANTUM FRONTIERS
Imagine a line of ions trapped by lasers. Each ion contains the physical manifestation of a qubit—a quantum two-level system, the basic unit of quantum information. You can think of a qubit as having a quantum analogue of angular momentum, called spin. The spin has three components, one per direction of space.PROJECT ANT-MAN
Project Ant-Man. The craziest challenge I’ve undertaken hasn’t been skydiving; sailing the Amazon on a homemade raft; scaling Mt. Everest; or digging for artifacts atop a hill in a Middle Eastern desert, near midday, during high summer. 1 The craziest challenge has been to study the possibility that quantum phenomena affect cognition LIFE AMONG THE EXPERIMENTALISTS Life among the experimentalists. Posted on March 21, 2021 by Nicole Yunger Halpern. I used to catch lizards—brown anoles, as I learned to call them later—as a child. They were colored as their name suggests, were about as long as one of my hands, and resented my attention. But they frequented our back porch, and I had a butterflynet.
PRESKILL | QUANTUM FRONTIERS John Preskill – There are two main classes of attempts. One is just to come up with a cryptographic protocol not so different conceptually from what’s done now, but based on a problem that’s hard for quantum computers. Craig Cannon – There you go. ONE IF BY LAND MINUS TWO IF BY SEA, OVER THE SQUARE-ROOT While laying plans, Revere instructs Newman: He said to his friend, “If the British march By land or sea from the town to-night, Hang a lantern aloft in the belfry-arch Of the North-Church-tower, as a signal light. Then comes one of the poem’s most famous lines: “One if by land, and two if by sea.”. The British could have left Bostonby
SHAUNMAGUIRE
The Science that made Stephen Hawking famous. Posted on November 5, 2014 by shaunmaguire. 8. In anticipation of The Theory of Everything which comes out today, and in the spirit of continuing with Quantum Frontiers’ current movie theme, I wanted to provide an overview of Stephen Hawking’s pathbreaking research. THE 10 BIGGEST BREAKTHROUGHS IN PHYSICS OVER THE PAST 25 The biggest breakthroughs of the past 25 years: *Neutrino Mass: surprisingly, neutrinos have a nonzero mass, which provides a window into particle physics beyond the standard model. THE STANDARD MODEL has been getting a lot of attention recently. This is well deserved in my opinion, considering that the vast majority of its predictions have come true, most of which were made by theFERNANDO PASTAWSKI
Roughly speaking, tensor networks are ingenious ways of encoding (quantum) inputs into (quantum) outputs. In particular, if you enter some input at the boundary of your tensor network, the tensors do the work of processing that information throughout the network so that if you ask for an output at any one of the nodes in the bulk of the tensor network, you get the right encoded answer. THIS VIDEO OF SCIENTISTS SPLITTING AN ELECTRON WILL SHOCK by Jorge Cham. Ok, this is where things get weird. If quantum computers, femtometer motions or laser alligators weren't enough, let's throw in fractionalized electrons, topological surfaces and strings that go to the end of time. To be honest, the idea that an electron can't be split hadn't even occurred to me before my conversation with Gil and WE ARE ALL WILSONIANS NOW We are all Wilsonians now. Ken Wilson passed away on June 15 at age 77. He changed how we think about physics. Renormalization theory, first formulated systematically by Freeman Dyson in 1949, cured the flaws of quantum electrodynamics and turned it into a precise computational tool. But the subject seemed magical and mysterious.QUANTUM FRONTIERS
The United States salutes word and whimsy in April, and Quantum Frontiers is continuing its tradition of celebrating. As a resident of Cambridge, Massachusetts and as a quantum information scientist, I have trouble avoiding the poem “Paul Revere’s Ride.”. Henry Wadsworth Longfellow wrote the poem, as well as others in the Americancanon
PEEKING INTO THE WORLD OF QUANTUM INTELLIGENCE Peeking into the world of quantum intelligence. Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly. An illustration of receiving, processing, and storing information. Based on the processed information, one can make LEARNING ABOUT LEARNING The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations towatch The West
THE GRAND TOUR OF QUANTUM THERMODYNAMICS The Grand Tour of quantum thermodynamics. Young noblemen used to undertake a “Grand Tour” during the 1600s and 1700s. Many of the tourists hailed from England, though well-to-do compatriots traveled from Scandinavia, Germany, and the United States. The men had just graduated from university—in many cases, Oxford or Cambridge.THE SIGN PROBLEM(S)
The sign problem (s) The thirteen-month-old had mastered the word “dada” by the time I met her. Her parents were teaching her to communicate other concepts through sign language. Picture her, dark-haired and bibbed, in a high chair. Banana and mango slices litter the tray in front of her. More fruit litters the floor in frontof the tray.
QUANTUM INFORMATION IN QUANTUM COGNITION Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care aboutprogress.
MERMIN SQUARE
Before telling you why quantum mechanics is contextual, let me give you an experiment that admits a simple non-contextual explanation. This story takes place in Flatland, a two-dimensional world inhabited by polygons.Our protagonist is a square who became famous after claiming that he met a TOP 10 QUESTIONS FOR YOUR POTENTIAL PHD ADVISER/GROUPQUESTIONS TO ASKPHD FACULTY
Everyone in grad school has taken on the task of picking the perfect research group at some point. Then some among us had the dubious distinction of choosing the perfect research group twice. Luckily for me, a year of grad research taught me a lot and WE ARE ALL WILSONIANS NOW We are all Wilsonians now. Ken Wilson passed away on June 15 at age 77. He changed how we think about physics. Renormalization theory, first formulated systematically by Freeman Dyson in 1949, cured the flaws of quantum electrodynamics and turned it into a precise computational tool. But the subject seemed magical and mysterious. PAUL DIRAC AND POETRY Paul Dirac and poetry. In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in the case of poetry, it’s the exact opposite! I tacked Dirac’s quote onto the bulletin board above my desk,QUANTUM FRONTIERS
The United States salutes word and whimsy in April, and Quantum Frontiers is continuing its tradition of celebrating. As a resident of Cambridge, Massachusetts and as a quantum information scientist, I have trouble avoiding the poem “Paul Revere’s Ride.”. Henry Wadsworth Longfellow wrote the poem, as well as others in the Americancanon
PEEKING INTO THE WORLD OF QUANTUM INTELLIGENCE Peeking into the world of quantum intelligence. Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly. An illustration of receiving, processing, and storing information. Based on the processed information, one can make LEARNING ABOUT LEARNING The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations towatch The West
THE GRAND TOUR OF QUANTUM THERMODYNAMICS The Grand Tour of quantum thermodynamics. Young noblemen used to undertake a “Grand Tour” during the 1600s and 1700s. Many of the tourists hailed from England, though well-to-do compatriots traveled from Scandinavia, Germany, and the United States. The men had just graduated from university—in many cases, Oxford or Cambridge.THE SIGN PROBLEM(S)
The sign problem (s) The thirteen-month-old had mastered the word “dada” by the time I met her. Her parents were teaching her to communicate other concepts through sign language. Picture her, dark-haired and bibbed, in a high chair. Banana and mango slices litter the tray in front of her. More fruit litters the floor in frontof the tray.
QUANTUM INFORMATION IN QUANTUM COGNITION Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care aboutprogress.
MERMIN SQUARE
Before telling you why quantum mechanics is contextual, let me give you an experiment that admits a simple non-contextual explanation. This story takes place in Flatland, a two-dimensional world inhabited by polygons.Our protagonist is a square who became famous after claiming that he met a TOP 10 QUESTIONS FOR YOUR POTENTIAL PHD ADVISER/GROUPQUESTIONS TO ASKPHD FACULTY
Everyone in grad school has taken on the task of picking the perfect research group at some point. Then some among us had the dubious distinction of choosing the perfect research group twice. Luckily for me, a year of grad research taught me a lot and WE ARE ALL WILSONIANS NOW We are all Wilsonians now. Ken Wilson passed away on June 15 at age 77. He changed how we think about physics. Renormalization theory, first formulated systematically by Freeman Dyson in 1949, cured the flaws of quantum electrodynamics and turned it into a precise computational tool. But the subject seemed magical and mysterious. PAUL DIRAC AND POETRY Paul Dirac and poetry. In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in the case of poetry, it’s the exact opposite! I tacked Dirac’s quote onto the bulletin board above my desk,QUANTUM FRONTIERS
Imagine a line of ions trapped by lasers. Each ion contains the physical manifestation of a qubit—a quantum two-level system, the basic unit of quantum information. You can think of a qubit as having a quantum analogue of angular momentum, called spin. The spin has three components, one per direction of space.LEARNING THEORY
Rigorously, one refers to a classical/quantum being as a classical/quantum model, algorithm, protocol, or procedure. This is because the actions of these classical/quantum beings are the center of the mathematical analysis. Formally, we consider the task of learning an unknown physical evolution described by a CPTP map thattakes in -qubit
PEEKING INTO THE WORLD OF QUANTUM INTELLIGENCE Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly. An illustration of receiving, processing, and storing information. Based on the processed information, one can make prediction about the future. We, as intelligent beings, receive, process, and PRESKILL | QUANTUM FRONTIERS John Preskill – There are two main classes of attempts. One is just to come up with a cryptographic protocol not so different conceptually from what’s done now, but based on a problem that’s hard for quantum computers. Craig Cannon – There you go. LIFE AMONG THE EXPERIMENTALISTS Life among the experimentalists. Posted on March 21, 2021 by Nicole Yunger Halpern. I used to catch lizards—brown anoles, as I learned to call them later—as a child. They were colored as their name suggests, were about as long as one of my hands, and resented my attention. But they frequented our back porch, and I had a butterflynet.
SEVEN REASONS WHY I CHOSE TO DO SCIENCE IN THE GOVERNMENT When I was in college, people asked me what I wanted to do with my life. I’d answer, “I want to be of use and to learn always.” The question resurfaced in grad school and at the beginning of my postdoc. I answered that I wanted to do extraordinary science that I’d steer.Academia attracted
WE ARE ALL WILSONIANS NOW We are all Wilsonians now. Ken Wilson passed away on June 15 at age 77. He changed how we think about physics. Renormalization theory, first formulated systematically by Freeman Dyson in 1949, cured the flaws of quantum electrodynamics and turned it into a precise computational tool. But the subject seemed magical and mysterious. MODERN PHYSICS EDUCATION? Being the physics department executive officer (on top of being a quantum physicist) makes me think a lot about our physics college program. It is exciting. We start with mechanics, and then go to electromagnetism (E&M) and relativity, then to quantum and statistical mechanics, and then to advanced mathematical methods, analytical mechanics and more E&M.MATTHEW FISHER
Matthew Fisher is only 55, but reluctance to be seen as a crazy old guy might partially explain why he has kept pretty quiet about his passionate pursuit of neuroscience over the past three years. That changed two months ago when he posted a paper on the arXiv aboutQuantum Cognition.
ALWAYS LOOK ON THE BRIGHT SIDE…OF CPTP MAPS. CPTP maps represent processes undergone by quantum systems. Imagine preparing some system—an electron, a photon, a superconductor, etc.—in a state I’ll call “ “. Imagine turning on a magnetic field, or coupling one electron to another, or letting the superconductor sit untouched. A CPTP map, labeled as , represents every such evolution.QUANTUM FRONTIERS
The United States salutes word and whimsy in April, and Quantum Frontiers is continuing its tradition of celebrating. As a resident of Cambridge, Massachusetts and as a quantum information scientist, I have trouble avoiding the poem “Paul Revere’s Ride.”. Henry Wadsworth Longfellow wrote the poem, as well as others in the Americancanon
PEEKING INTO THE WORLD OF QUANTUM INTELLIGENCE Peeking into the world of quantum intelligence. Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly. An illustration of receiving, processing, and storing information. Based on the processed information, one can makeTHE SIGN PROBLEM(S)
The sign problem (s) The thirteen-month-old had mastered the word “dada” by the time I met her. Her parents were teaching her to communicate other concepts through sign language. Picture her, dark-haired and bibbed, in a high chair. Banana and mango slices litter the tray in front of her. More fruit litters the floor in frontof the tray.
THE GRAND TOUR OF QUANTUM THERMODYNAMICS The Grand Tour of quantum thermodynamics. Young noblemen used to undertake a “Grand Tour” during the 1600s and 1700s. Many of the tourists hailed from England, though well-to-do compatriots traveled from Scandinavia, Germany, and the United States. The men had just graduated from university—in many cases, Oxford or Cambridge. QUANTUM INFORMATION IN QUANTUM COGNITION Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care aboutprogress.
RANDOM WALKS
On average, five minutes after arriving at the lamppost, he’s back at the lamppost. But, if we wait for a time , we have a decent chance of finding him a distance away. These characteristic typify a simple random walk. Random walks crop up across statistical physics. For instance, consider a grain of pollen dropped onto a thin film ofwater.
PRESKILL | QUANTUM FRONTIERS John Preskill – There are two main classes of attempts. One is just to come up with a cryptographic protocol not so different conceptually from what’s done now, but based on a problem that’s hard for quantum computers. Craig Cannon – There you go.FERNANDO PASTAWSKI
TOP 10 QUESTIONS FOR YOUR POTENTIAL PHD ADVISER/GROUPQUESTIONS TO ASKPHD FACULTY
Everyone in grad school has taken on the task of picking the perfect research group at some point. Then some among us had the dubious distinction of choosing the perfect research group twice. Luckily for me, a year of grad research taught me a lot and MODERN PHYSICS EDUCATION? Being the physics department executive officer (on top of being a quantum physicist) makes me think a lot about our physics college program. It is exciting. We start with mechanics, and then go to electromagnetism (E&M) and relativity, then to quantum and statistical mechanics, and then to advanced mathematical methods, analytical mechanics and more E&M.QUANTUM FRONTIERS
The United States salutes word and whimsy in April, and Quantum Frontiers is continuing its tradition of celebrating. As a resident of Cambridge, Massachusetts and as a quantum information scientist, I have trouble avoiding the poem “Paul Revere’s Ride.”. Henry Wadsworth Longfellow wrote the poem, as well as others in the Americancanon
PEEKING INTO THE WORLD OF QUANTUM INTELLIGENCE Peeking into the world of quantum intelligence. Intelligent beings have the ability to receive, process, store information, and based on the processed information, predict what would happen in the future and act accordingly. An illustration of receiving, processing, and storing information. Based on the processed information, one can makeTHE SIGN PROBLEM(S)
The sign problem (s) The thirteen-month-old had mastered the word “dada” by the time I met her. Her parents were teaching her to communicate other concepts through sign language. Picture her, dark-haired and bibbed, in a high chair. Banana and mango slices litter the tray in front of her. More fruit litters the floor in frontof the tray.
THE GRAND TOUR OF QUANTUM THERMODYNAMICS The Grand Tour of quantum thermodynamics. Young noblemen used to undertake a “Grand Tour” during the 1600s and 1700s. Many of the tourists hailed from England, though well-to-do compatriots traveled from Scandinavia, Germany, and the United States. The men had just graduated from university—in many cases, Oxford or Cambridge. QUANTUM INFORMATION IN QUANTUM COGNITION Some research topics, says conventional wisdom, a physics PhD student shouldn’t touch with an iron-tipped medieval lance: sinkholes in the foundations of quantum theory. Problems so hard, you’d have a snowball’s chance of achieving progress. Problems so obscure, you’d have a snowball’s chance of convincing anyone to care aboutprogress.
RANDOM WALKS
On average, five minutes after arriving at the lamppost, he’s back at the lamppost. But, if we wait for a time , we have a decent chance of finding him a distance away. These characteristic typify a simple random walk. Random walks crop up across statistical physics. For instance, consider a grain of pollen dropped onto a thin film ofwater.
PRESKILL | QUANTUM FRONTIERS John Preskill – There are two main classes of attempts. One is just to come up with a cryptographic protocol not so different conceptually from what’s done now, but based on a problem that’s hard for quantum computers. Craig Cannon – There you go.FERNANDO PASTAWSKI
TOP 10 QUESTIONS FOR YOUR POTENTIAL PHD ADVISER/GROUPQUESTIONS TO ASKPHD FACULTY
Everyone in grad school has taken on the task of picking the perfect research group at some point. Then some among us had the dubious distinction of choosing the perfect research group twice. Luckily for me, a year of grad research taught me a lot and MODERN PHYSICS EDUCATION? Being the physics department executive officer (on top of being a quantum physicist) makes me think a lot about our physics college program. It is exciting. We start with mechanics, and then go to electromagnetism (E&M) and relativity, then to quantum and statistical mechanics, and then to advanced mathematical methods, analytical mechanics and more E&M.QUANTUM FRONTIERS
The United States salutes word and whimsy in April, and Quantum Frontiers is continuing its tradition of celebrating. As a resident of Cambridge, Massachusetts and as a quantum information scientist, I have trouble avoiding the poem “Paul Revere’s Ride.”. Henry Wadsworth Longfellow wrote the poem, as well as others in the Americancanon
ABOUT | QUANTUM FRONTIERS The Institute for Quantum Information and Matter (IQIM) at Caltech is the newest Physics Frontiers Center supported by the National Science Foundation and the Gordon and Betty Moore Foundation.Here at IQIM, we study physical systems in which the weirdness of the quantum world becomes manifest on macroscopic scales. Our work spans a wide range of cutting edge research, from superconductivity LEARNING ABOUT LEARNING The autumn of my sophomore year of college was mildly hellish. I took the equivalent of three semester-long computer-science and physics courses, atop other classwork; co-led a public-speaking self-help group; and coordinated a celebrity visit to campus. I lived at my desk and in office hours, always declining my flatmates’ invitations towatch The West
LEARNING THEORY
Rigorously, one refers to a classical/quantum being as a classical/quantum model, algorithm, protocol, or procedure. This is because the actions of these classical/quantum beings are the center of the mathematical analysis. Formally, we consider the task of learning an unknown physical evolution described by a CPTP map thattakes in -qubit
SEVEN REASONS WHY I CHOSE TO DO SCIENCE IN THE GOVERNMENT When I was in college, people asked me what I wanted to do with my life. I’d answer, “I want to be of use and to learn always.” The question resurfaced in grad school and at the beginning of my postdoc. I answered that I wanted to do extraordinary science that I’d steer.Academia attracted
LIFE AMONG THE EXPERIMENTALISTS Life among the experimentalists. Posted on March 21, 2021 by Nicole Yunger Halpern. I used to catch lizards—brown anoles, as I learned to call them later—as a child. They were colored as their name suggests, were about as long as one of my hands, and resented my attention. But they frequented our back porch, and I had a butterflynet.
SHAUNMAGUIRE
The Science that made Stephen Hawking famous. Posted on November 5, 2014 by shaunmaguire. 8. In anticipation of The Theory of Everything which comes out today, and in the spirit of continuing with Quantum Frontiers’ current movie theme, I wanted to provide an overview of Stephen Hawking’s pathbreaking research. IN THE HOUR OF DARKNESS AND PERIL AND NEED A cry of defiance, and not of fear, A voice in the darkness, a knock at the door, And a word that shall echo forevermore! For, borne on the night-wind of the Past, Through all our history, to the last, In the hour of darkness and peril and need, The people will waken and listento hear.
QUANTUM CHESS
The Quantum Chess board begins in the same configuration as standard chess. All pawns move the same as they would in standard chess, but all other pieces get a choice of two movement types, standard or quantum. Standard moves act exactly as they would in standard chess. However, quantum moves, create superpositions. PAUL DIRAC AND POETRY Paul Dirac and poetry. In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in the case of poetry, it’s the exact opposite! I tacked Dirac’s quote onto the bulletin board above my desk,QUANTUM FRONTIERS
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ACHIEVING SUPERLUBRICITY WITH GRAPHENE Posted on March 24, 2020by benphysics
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Sometimes, experimental results spark enormous curiosity inspiring a myriad of questions and ideas for further experimentation. In 2004, Geim and Novoselov, from The University of Manchester, isolated a single layer of graphene from bulk graphite with the “Scotch Tape Method” for which they were awarded the 2010 Nobel Prize in Physics. This one experimental result has branched out countless times serving as a source of inspiration in as many different fields. We are now in the midst of an array of branching-out in graphene research, and one of those branches gaining attention is ultra low friction observed between graphene and other surfacematerials.
Much has been learned about graphene in the past 15 years through an immense amount of research, most of which, in non-mechanical realms (e.g., electron transport measurements, thermal conductivity, pseudo magnetic fields in strain engineering). However, superlubricity, a mechanical phenomenon, has become the focus among many research groups. Mechanical measurements have famously shown graphene’s tensile strength to be hundreds of times that of the strongest steel, indisputably placing it atop the list of construction materials best for a superhero suit. Superlubricity is a tribological property of graphene and is, arguably, as equally impressive as graphene’stensile strength.
Tribology is the study of interacting surfaces during relative motion including sources of friction and methods for its reduction. It’s not a recent discovery that coating a surface with graphite (many layers of graphene) can lower friction between two sliding surfaces. Current research studies the precise mechanisms and surfaces for which to minimize friction with single or several layers of graphene. Research published in _Nature Materials_ in 2018
measures friction between surfaces under constant load and velocity. The experiment includes two groups; one consisting of two graphene surfaces (homogeneous junction), and another consisting of graphene and hexagonal boron nitride (heterogeneous junction). The research group measures friction using Atomic Force Microscopy (AFM). The hexagonal boron nitride (or graphene for a homogeneous junction) is fixed to the stage of the AFM while the graphene slides atop. Loads are held constant at 20 𝜇N and sliding velocity constant at 200 nm/s. Ultra low friction is observed for homogeneous junctions when the underlying crystalline lattice structures of the surfaces are at a relative angle of 30 degrees. However, this ultra low friction state is very unstable and upon sliding, the surfaces rotate towards a locked-in lattice alignment. Friction varies with respect to the relative angle between the two surface’s crystalline lattice structures. Minimum (ultra low) friction occurs at a relative angle of 30 degrees reaching a maximum when locked-in lattice alignment is realized upon sliding. While in a state of lattice alignment, shearing is rendered impossible with the experimental setup due to the relatively large amount offriction.
Friction varies with respect to the relative angle of the crystalline lattice structures and is, therefore, anisotropic. For example, the fact it takes less force to split wood when an axe blade is applied parallel to its grains than when applied perpendicularly illustrates the anisotropic nature of wood, as the force to split wood is dependent upon the direction along which the force is applied. Frictional anisotropy is greater in homogeneous junctions because the tendency to orient into a stuck, maximum friction alignment, is greater than with heterojunctions. In fact, heterogeneous junctions experience frictional anisotropy three orders of magnitude less than homogeneous junctions. Heterogenous junctions display much less frictional anisotropy due to a lattice misalignment when the angle between the lattice vectors is at a minimum. In other words, the graphene and hBN crystalline lattice structures are never parallel because the materials differ, therefore, never experience the impact of lattice alignment as do homogenous junctions. Hence, heterogeneous junctions do not become stuck in a high friction state that characterizes homogeneous ones, and experience ultra low friction during sliding at all relative crystalline lattice structure angles. Presumably, to increase applicability, upscaling to much larger loads will be necessary. A large scale cost effective method to dramatically reduce friction would undoubtedly have an enormous impact on a great number of industries. Cost efficiency is a key component to the realization of graphene’s potential impact, not only as it applies to superlubricity, but in all areas of application. As access to large amounts of affordable graphene increases, so will experiments in fabricating devices exploiting the extraordinary characteristics which have placed graphene and graphene based materials on the front lines of material research the past couple decades.SHARE THIS:
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IN THE HOUR OF DARKNESS AND PERIL AND NEED Posted on March 15, 2020 by Nicole Yunger Halpern1
I recited the poem “Paul Revere’s Ride” to myself while walking across campus last week. A few hours earlier, I’d cancelled the seminar that I’d been slated to cohost two days later. In a few hours, I’d cancel the rest of the seminars in the series. Undergraduates would begin vacating their dorms within a day. Labs would shut down, and postdocs would receive instructions to work from home. I memorized “Paul Revere’s Ride” after moving to Cambridge, following tradition: As a research assistant at Lancaster University in the UK, I memorized e. e. cummings’s “anyone lived in a pretty how town.”At
Caltech, I memorized “Kubla Khan.”Another
home called for another poem. “Paul Revere’s Ride” brooked no competition: Campus’s red bricks run into Boston, where Revere’s story began during the 1700s. Henry Wadsworth Longfellow, who lived a few blocks from Harvard, composed the poem. It centers on the British assault against the American colonies, at Lexington and Concord, on the eve of the Revolutionary War. A patriot learned of the British troops’ movements one night. He communicated the information to faraway colleagues by hanging lamps in a church’s belfry. His colleagues rode throughout the night, to “spread the alarm / through every Middlesex village and farm.” The riders included Paul Revere, aBoston silversmith.
The Boston-area bricks share their color with Harvard’s crest, crimson. So do the protrusions on the coronavirus’s surface incolored pictures.
I couldn’t have designed a virus to suit Harvard’s website better. The yard that I was crossing was about to “de-densify,” the red-brick buildings were about to empty, and my home was about to lock its doors. I’d watch regulations multiply, emails keep pace, and masks appear. Revere’s messenger friend, too, stood back andobserved his home:
he climbed to the tower of the church, Up the wooden stairs, with stealthy tread, To the belfry-chamber overhead, By the trembling ladder, steep and tall, To the highest window in the wall, Where he paused to listen and look down A moment on the roofs of the town, And the moonlight flowing over all. I commiserated also with Revere, waiting on tenterhooks for hismessage:
Meanwhile, impatient to mount and ride, Booted and spurred, with a heavy stride, On the opposite shore walked Paul Revere. Now he patted his horse’s side, Now gazed on the landscape far and near, Then impetuous stamped the earth, And turned and tightened his saddle-girth… The lamps ended the wait, and Revere rode off. His mission carried a sense of urgency, yet led him to serenity that I hadn’t expected: He has left the village and mounted the steep, And beneath him, tranquil and broad and deep, Is the Mystic, meeting the ocean tides… The poem’s final stanza kicks. Its message carries as much relevance to the 21st century as Longfellow, writing about the 1700s during the 1800s, could have dreamed: So through the night rode Paul Revere; And so through the night went his cry of alarm To every Middlesex village and farm,— A cry of defiance, and not of fear, A voice in the darkness, a knock at the door, And a word that shall echo forevermore! For, borne on the night-wind of the Past, Through all our history, to the last, In the hour of darkness and peril and need, The people will waken and listen to hear The hurrying hoof-beats of that steed, And the midnight message of Paul Revere. Reciting poetry clears my head. I can recite on autopilot, while processing other information or admiring my surroundings. But the poem usually wins my attention at last. The rhythm and rhyme sweep me along, narrowing my focus. Reciting “Paul Revere’s Ride” takes me 5-10 minutes. After finishing that morning, I repeated the poem, and began repeating it again, until arriving at my institute on the edge of Harvard’s campus. Isolation can benefit theorists. Many of us need quiet to study, capture proofs, and disentangle ideas. Many of us need collaboration; but email, Skype, Google hangouts, and Zoom connect us. Many of us share and gain ideas through travel; but I can forfeit a little car sickness, air turbulence, and waiting in lines. Many of us need results from experimentalist collaborators, but experimental results often take long to gather in the absence of pandemics.Many
of us are introverts who enjoy a little self-isolation. https://xkcd.com/2276 April is National Poetry Month in the United States. I often celebrateby intertwining
physics with poetry
in my April blog post. Next month, though, I’ll have other news to report. Besides, my walk demonstrated, we need poetry now. Paul Revere found tranquility on the eve of a storm. Maybe, when the night clears and doors reopen, science born of the quiet will flood journals. Aren’t we fortunate, as physicists, to lead lives steeped in a kind of poetry?SHARE THIS:
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THE SHAPE OF MIP* = RE Posted on March 1, 2020by
Henry Yuen
6
There’s a famous parable about a group of blind men encountering an elephant for the very first time. The first blind man, who had his hand on the elephant’s side, said that it was like an enormous wall. The second blind man, wrapping his arms around the elephant’s leg, exclaimed that surely it was a gigantic tree trunk. The third, feeling the elephant’s tail, declared that it must be a thick rope. Vehement disagreement ensues, but after a while the blind men eventually come to realize that, while each person was partially correct, there is much more to the elephant than initially thought. Last month, Zhengfeng, Anand, Thomas, John and I posted _MIP* = RE _ to arXiv. The paper feels very much like the elephant of the fable — and not just because of the number of pages! To a computer scientist, the paper is ostensibly about the complexity of interactive proofs. To a quantum physicist, it is talking about mathematical models of quantum entanglement. To the mathematician, there is a claimed resolution to a long-standing problem in operator algebras. Like the blind men of the parable, each are feeling a small part of a new phenomenon. How do the wall, the tree trunk, and the rope all fit together? I’ll try to trace the outline of the elephant: it starts with a mystery in quantum complexity theory, curves through the mathematical foundations of quantum mechanics, and arrives at a deep question aboutoperator algebras.
THE ROPE: THE COMPLEXITY OF NONLOCAL GAMES In 2004, computer scientists Cleve, Hoyer, Toner, and Watrous were thinking about a funny thing called nonlocal games. A nonlocal game involves three parties: two cooperating players named Alice and Bob, and someone called the verifier. The verifier samples a pair of random questions and sends to Alice (who responds with answer ), and to Bob (who responds with answer ). The verifier then uses some function that tells her whether the players win, based on their questions and answers. All three parties know the rules of the game before it starts, and Alice and Bob’s goal is to _maximize_ their probability of winning the game. The players aren’t allowed to communicate with each other during the game, so it’s a nontrivial task for them to coordinate an optimal strategy (i.e., how they should individually respond to the verifier’s questions) before the game starts. The most famous example of a nonlocal game is the CHSH game (which has made several appearances on this blog already): in this game, the verifier sends a uniformly random bit to Alice (who responds with a bit ) and a uniformly random bit to Bob (who responds with a bit ). The players win if (in other words, the sum of their answer bits is equal to the product of the input bits modulo ). What is Alice’s and Bob’s maximum winning probability? Well, it depends on what type of strategy they use. If they use a strategy that can be modeled by _classical_ physics, then their winning probability cannot exceed (we call this the _classical value_ of CHSH). On the other hand, if they use a strategy based on _quantum_ physics, Alice and Bob can do better by sharing two quantum bits (qubits) that are _entangled_. During the game each player measures their own qubit (where the measurement depends on their received question) to obtain answers that win the CHSH game with probability (we call this the _quantum value_ of CHSH). So even though the entangled qubits don’t allow Alice and Bob to communicate with each other, entanglement gives them a way to win with higher probability! In technical terms, their responses are _more correlated_ than what is possible classically. The CHSH game comes from physics, and was originally formulated not as a game involving Alice and Bob, but rather as an experiment involving two spatially separated devices to test whether stronger-than-classical correlations exist in nature. These experiments are known as _Bell tests_, named after John Bell. In 1964, he proved that correlations from quantum entanglement cannot be explained by any “local hidden variable theory” — in other words, a classical theory of physics.1 He then showed that a Bell test, like the CHSH game, gives a simple statistical test for the presence of nonlocal correlations between separated systems. Since the 1960s, numerous Bell testshave been
conducted experimentally, and the verdict is clear: nature does notbehave classically.
Cleve, Hoyer, Toner and Watrous noticed that nonlocal games/Bell tests can be viewed as a kind of _multiprover interactive proof_. In complexity theory, interactive proofs are protocols where some _provers_ are trying to convince a _verifier_ of a solution to a long, difficult computation, and the verifier is trying to efficiently determine if the solution is correct. In a Bell test, one can think of the provers as instead trying to convince the verifier of a _physical statement_: that they possess quantum entanglement. With the computational lens trained firmly on nonlocal games, it then becomes natural to ask about their _complexity_. Specifically, what is the complexity of approximating the optimal winning probability in a given nonlocal game ? In complexity-speak, this is phrased as a question about characterizing the class _MIP*_ (pronounced “M-I-P star”). This is also a well-motivated question for an experimentalist conducting Bell tests: at the very least, they’d want to determine if (a) quantum players can do better than classical players, and (b) what can the best possible quantum strategy achieve? Studying this question in the case of classical players led to some of the most important results in complexity theory, such as _MIP = NEXP_ and the PCP
Theorem . Indeed, the PCP Theorem says that it is _NP_-hard to approximate the classical value of a nonlocal game (i.e. the maximum winning probability of classical players) to within constant additive accuracy (say ). Thus, assuming that _P_ is not equal to _NP_, we shouldn’t expect a polynomial-time algorithm for this. However it is easy to see that there is a “brute force” algorithm for this problem: by taking _exponential time_ to enumerate over all possible deterministic player strategies, one can exactly compute the classical value of nonlocal games. When considering games with entangled players, however, it’s not even clear if there’s a similar “brute force” algorithm that solves this in _any_ amount of time — forget polynomial time; even if we allow ourselves exponential, doubly-exponential, Ackermann function amount of time, we still don’t know how to solve this quantum value approximation problem. The problem is that there is no known upper bound on the _amount_ of entanglement that is needed for players to play a nonlocal game. For example, for a given game , does an optimal quantum strategy require one qubit, ten qubits, or qubits of entanglement? Without any upper bound, a “brute force” algorithm wouldn’t know how big of a quantum strategy to search for — it would keep enumerating over bigger and bigger strategies in hopes of finding a better one. Thus approximating the quantum value may not even be solvable in principle! But could it _really_ be uncomputable? Perhaps we just haven’t found the right mathematical tool to give an upper bound on the dimension — maybe we just need to come up with some clever variant of, say, Johnson-Lindenstraussor
some other dimension reduction technique.2 In 2008, there was promising progress towards an algorithmic solution for this problem. Two papers (appearing on arXiv on the same day!) showed that an algorithm based on semidefinite programming can produce a sequence of numbers that converge to something called the _commuting operator value_ of a nonlocal game.3 If one could show that the commuting operator value and the quantum value of a nonlocal game coincide, then this would yield an algorithm for solving this approximation problem! Asking whether this commuting operator and quantum values are the same, however, immediately brings us to the precipice of some deep mysteries in mathematical physics and operator algebras, far removed from computer science and complexity theory. This takes us to the next part of the elephant. THE TREE: MATHEMATICAL FOUNDATIONS OF LOCALITY The mystery about the quantum value versus the commuting operator value of nonlocal games has to do with two different ways of modeling Alice and Bob in quantum mechanics. As I mentioned earlier, quantum physics predicts that the maximum winning probability in, say, the CHSH game when Alice and Bob share entanglement is approximately 85%. As with any physical theory, these predictions are made using some mathematical framework — formal rules for modeling physical experiments like the CHSH game. In a typical quantum information theory textbook , players in the CHSH game are usually modelled in the following way: Alice’s device is described a _state space_ (all the possible states the device could be in), a particular _state_ from , and a set of _measurement operators_ (operations that can be performed by the device). It’s not necessary to know what these things are formally; the important feature is that these three things are enough to make any prediction about Alice’s device — when treated in isolation, at least. Similarly, Bob’s device can be described using its own state space , state , and measurement operators . In the CHSH game though, one wants to make predictions about Alice’s and Bob’s devices _together_. Here the textbooks say that Alice and Bob are jointly described by the _tensor product_ formalism, which is a natural mathematical way of “putting separate spaces together”. Their state space is denoted by . The joint state describing the devices comes from this tensor product space. When Alice and Bob independently make their local measurements, this is described by a measurement operator from the tensor product of operators from and . The strange correlations of quantum mechanics arise when their joint state is _entangled_, i.e. it cannot be written as a well-defined state on Alice’s side combined with a well-defined state on Bob’s side (even though the state space itself is two independent spaces combined together!) The tensor product model works well; it satisfies natural properties you’d want from the CHSH experiment, such as the constraint that Alice and Bob can’t instantaneously signal to each other. Furthermore, predictions made in this model match up very accurately with experimental results! This is the not the whole story, though. The tensor product formalism works very well in _non-relativistic quantum mechanics_, where things move slowly and energies are low. To describe more extreme physical scenarios — like when particles are being smashed together at near-light speeds in the Large Hadron Collider — physicists turn to the more powerful _quantum field theory_. However, the notion of spatiotemporal separation in relativistic settings gets especiallytricky
. In particular, when trying to describe quantum mechanical systems, it is no longer evident how to assign Alice and Bob their own independent state spaces, and thus it’s not clear how to put relativistic Alice and Bob in the tensor product framework! In quantum field theory, locality is instead described using the _commuting operator model_. Instead of assigning Alice and Bob their own individual state spaces and then tensoring them together to get a combined space, the commuting operator model stipulates that there is just a _single_ monolithic space for both Alice and Bob. Their joint state is described using a vector from , and Alice and Bob’s measurement operators both act on . The constraint that they can’t communicate is captured by the fact that Alice’s measurement operators _commute_ with Bob’s operators. In other words, the order in which the players perform their measurements on the system does not matter: Alice measuring before Bob, or Bob measuring before Alice, both yield the same statistical outcomes. Locality is enforced through commutativity. The commuting operator framework contains the tensor product framework as a special case4, so it’s more general. Could the commuting operator model allow for correlations that can’t be captured by the tensor product model, even approximately56? This question is known as _Tsirelson’s problem _, named after the late mathematician Boris Tsirelson.
There is a simple but useful way to phrase this question using nonlocal games. What we call the “quantum value” of a nonlocal game (denoted by ) really refers to the supremum of success probabilities over tensor product strategies for Alice and Bob. If they use strategies from the more general commuting operator model, then we call their maximum success probability the _commuting operator value_ of (denoted by ). Since tensor product strategies are a special case of commuting operator strategies, we have the relation for all nonlocal games . Could there be a nonlocal game whose tensor product value is _different_ from its commuting operator value? With tongue-in-cheek: is there a game that Alice and Bob could succeed at better if they were using quantum entanglement at near-light speeds? It is difficult to find even a plausible candidate game for which the quantum and commuting operator values may differ. The CHSH game, for example, has the same quantum and commuting operator value; this was provedby Tsirelson.
If the tensor product and the commuting operator models are the same (i.e., the “positive” resolution of Tsirelson’s problem), then as I mentioned earlier, this has unexpected ramifications: there would be an algorithm for approximating the quantum value of nonlocal games. How does this algorithm work? It comes in two parts: a procedure to _search from below_, and one to _search from above_. The “search from below” algorithm computes a sequence of numberswhere is
(approximately) the best winning probability when Alice and Bob use a -qubit tensor product strategy. For fixed , the number can be computed by enumerating over (a discretization of) the space of all possible -qubit strategies. This takes a _doubly-exponential_ amount of time in — but at least this is still a finite time! This naive “brute force” algorithm will slowly plod along, computing a sequence of better and better winning probabilities. We’re guaranteed that in the limit as goes to infinity, the sequence converges to the quantum value . Of course the issue is that the “search from below” procedure never knows how close it is to the true quantumvalue.
This is where the “search from above” comes in. This is an algorithm that computes a different sequence of numbers where each is an _upper bound_ on the commuting operator value , and furthermore as goes to infinity, eventually converges to . Furthermore, each can be computed by a technique known as semidefinite optimization; this was
shown by the two papersI mentioned.
Let’s put the pieces together. If the quantum and commuting operator values of a game coincide (i.e. ), then we can run the “search from below” and “search from above” procedures in parallel, interleaving the computation of the and . Since both are guaranteed to converge to the quantum value, at some point the upper bound will come within some to the lower bound , and thus we would have homed in on (an approximation of) . There we have it: an algorithm to approximate the quantum value ofgames.
All that remains to do, surely, is to solve Tsirelson’s problem in the affirmative (that commuting operator correlations can be approximated by tensor product correlations), and then we could put this pesky question about the quantum value to rest. Right? THE WALL: CONNES’ EMBEDDING PROBLEM At the end of the 1920s, polymath extraordinaire John von Neumann formulated the first rigorous mathematical framework for the recently developed quantum mechanics. This framework, now familiar to physicists and quantum information theorists everywhere, posits that quantum states are vectors in a Hilbert space, and measurements are linear operators acting on those spaces. It didn’t take long for von Neumann to realize that there was a much deeper theory of operators on Hilbert spaces waiting to be discovered. With Francis Murray, in the 1930s he started to develop a theory of “rings of operators” — today these are called von Neumannalgebras .
The theory of operator algebras has since flourished into a rich and beautiful area of mathematics. It remains inseparable from mathematical physics, but has established deep connections with subjects such as knot theory and group theory. One of the most important goals in operator algebras has been to provide a classification of von Neumann algebras. In their series of papers on the subject, Murray and von Neumann first showed that classifying von Neumann algebras reduces to understanding their _factors_, the atoms out of which all von Neumann algebras are built. Then, they showed that factors of von Neumann algebras come in one of three species: type , type , and type . Type factors were completely classified by Murray and von Neumann, and they made much progress on characterizing certain type factors. However progress stalled until the 1970s, when Alain Connes provided a classification of type factors (work for which he would later receive the Fields Medal). In the same 1976 classification paper, Connes makes a casual remark about something called type factors7: > We now construct an embedding of into . Apparently > such an embedding ought to exist for all factors. This line, written in almost a throwaway manner, eventually came to be called “Connes’ embedding problem”: does every
separable factor embed into an ultrapower of the hyperfinite factor? It seems that Connes surmises that it does (and thus this is also called “Connes’ embedding _conjecture_“). Since 1976, this problem has grown into a central question of operator algebras, with numerous equivalent formulationsand
consequences across mathematics. In 2010, two papers (again appearing on the arXiv on the same day!) showed that the reach of Connes’ embedding conjecture extends back to the foundations of quantum mechanics. If Connes’ embedding problem has a positive answer (i.e. an embedding exists), then Tsirelson’s problem (i.e. whether commuting operator can be approximated by tensor product correlations) _also_ has a positive answer! Later it was shown by Ozawa that Connes’ embedding problem is in fact _equivalent_ to Tsirelson’s problem. Remember that our approach to compute the value of nonlocal games hinged on obtaining a positive answer to Tsirelson’s problem. The sequence of papers together show that resolving — one way or another — whether this search-from-below, search-from-above algorithm works would essentially settle Connes’ embedding conjecture. What started as a funny question at the periphery of computer science and quantum information theory has morphed into an attack on one of the central problems in operatoralgebras.
_MIP* = RE_
We’ve now ended back where we started: the complexity of nonlocal games. Let’s take a step back and try to make sense of the elephant. Even to a complexity theorist, “_MIP* = RE_” may appear esoteric. The complexity classes _MIP*_ and
_RE _ refer to
a bewildering grabbag of concepts: there’s Alice, Bob, Turing machines, verifiers, interactive proofs, quantum entanglement. What is the meaning of the equality of these two classes? First, it says that the _Halting problem has an interactive proof involving quantum entangled provers_. In the Halting problem, you want to decide whether a Turing machine , if you started running it, would eventually terminate with a well-defined answer, or if it would get stuck in an infinite loop. Alan Turing showed that this problem is _undecidable_: there is no algorithm that can solve this problem in general. Loosely speaking, the best thing you can do is to just flick on the power switch to , and wait to see if it eventually stops. If gets stuck in an infinite loop — well, you’re going to bewaiting forever.
_MIP* = RE_ shows with the help of all-powerful Alice and Bob, a time-limited verifier can run an interactive proof to “shortcut” the waiting. Given the Turing machine ‘s description (its “source code”), the verifier can efficiently compute a description of a nonlocal game whose behavior reflects that of . If does eventually halt (which could happen after a million years), then there is a strategy for Alice and Bob that causes the verifier to accept with probability . In other words, . If gets stuck in an infinite loop, then no matter what strategy Alice and Bob use, the verifier always rejects with high probability, sois close to .
By playing this nonlocal game, the verifier can obtain _statistical evidence_ that is a Turing machine that eventually terminates. If the verifier plays and the provers win, then the verifier should believe that it is likely that halts. If they lose, then the verifier concludes there isn’t enough evidence that halts8. The verifier never actually runs in this game; she has offloaded the task to Alice and Bob, who we can assume are computational godscapable of
performing million-year-long computations instantly. For them, the challenge is instead to _convince_ the verifier that if she _were_ to wait millions of years, she would witness the termination of . Incredibly, the amount of work put in by the verifier in the interactive proof is _independent_ of the time it takes for tohalt!
The fact that the Halting problem has an interactive proof seems borderline absurd: if the Halting problem is unsolvable, why should we expect it to be _verifiable_? Although complexity theory has taught us that there can be a large gap between the complexity of verification versus search, it has always been a difference of _efficiency_: if solutions to a problem can be efficiently verified, then solutions can also be found (albeit at drastically higher computational cost). _MIP* = RE_ shows that, with quantum entanglement, there can be a chasm of _computability_ between verifying solutions and finding them. Now let’s turn to the non-complexity consequences of _MIP* = RE_. The fact that we can encode the Halting problem into nonlocal games also immediately tells us that there is no algorithm whatsoever to approximate the quantum value. Suppose there was an algorithm that could approximate . Then, using the transformation from Turing machines to nonlocal games mentioned above, we could use this algorithm to solve the Halting problem, which is impossible. Now the dominoes start to fall. This means that, in particular, the proposed “search-from-below”/”search-from-above” algorithm _cannot_ succeed in approximating . There must be a game , then, for which the quantum value is different from the commuting operator value. But this implies Tsirelson’s problem has a negative answer, and therefore Connes’ embedding conjecture is false. We’ve only sketched the barest of outlines of this elephant, and yet it is quite challenging to hold it in the mind’s eye all at once9. This story is intertwined with some of the most fundamental developments in the past century: modern quantum mechanics, operator algebras, and computability theory were birthed in the 1930s. Einstein, Podolsky and Rosen wrote their landmark paper questioning the nature of quantum entanglement in 1935, and John Bell discovered his famous test and inequality in 1964. Connes’ formulated his conjecture in the ’70s, Tsirelson made his contributions to the foundations of quantum mechanics in the ’80s, and about the same time computer scientists were inventing the theory of interactive proofs and probabilistically checkable proofs (PCPs). We haven’t said anything about the proof of _MIP* = RE_ yet (this may be the subject of future blog posts), but it is undeniably a product of complexity theory. The language of interactive proofs and Turing machines is not just convenient but necessary: at its heart _MIP* = RE_ is the classical PCP Theorem, with the help of quantum entanglement, recursed to infinity. What is going on in this proof? What parts of it are fundamental, and which parts are unnecessary? What is the core of it that relates to Connes’ embedding conjecture? Are there other consequences of this uncomputability result? These are questions to be explored in the coming days and months, and the answers we find will be fascinating. ACKNOWLEDGMENTS. Thanks to William Slofstra and Thomas Vidick for helpful feedback on this post. ------------------------- * This is why quantum correlations are called “nonlocal”, and why we call the CHSH game a “nonlocal game”: it is a test fornonlocal behavior.
* A reasonable hope would be that, for every nonlocal game , there is a generic upper bound on the number of qubits needed to approximate the optimal quantum strategy (e.g., a game with possible questions and possible answers would require at most, say, qubits to play optimally). * In those papers, they called it the _field theoreticvalue_.
* The space can be broken down into the tensor product , and Alice’s measurements only act on the space and Bob’s measurements only act on the space. In this case, Alice’s measurements clearly commute with Bob’s. * In a breakthrough work in 2017, Slofstra showed that the tensor product framework is _not_ exactly the same as the commuting operator framework; he shows that there is a nonlocal game where players using commuting operator strategies can win with probability , but when they use a tensor-product strategy they can only win with probability strictly less than . However the perfect commuting operator strategy can be approximated by tensor-product strategies arbitrarily well, so the quantum values and the commuting operator values of are thesame.
* The commuting operator model is motivated by attempts to develop a rigorous mathematical framework for quantum field theory from first principles (see, for example algebraic quantum field theory (AQFT)). In the
“vanilla” version of AQFT, tensor product decompositions between casually independent systems do not exist _a priori_, but mathematical physicists often consider AQFTs augmented with an additional “split property”, which _does_ imply tensor product decompositions. Thus in such AQFTs, Tsirelson’s problem has an affirmative answer. * Type is pronounced “type two one”. * This is _not_ the same as evidence that loops forever! * At least, speaking for myself.SHARE THIS:
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SENSE, SENSIBILITY, AND SUPERCONDUCTORS Posted on February 23, 2020 by Nicole Yunger Halpern1
Jonathan Monroe disagreed with his PhD supervisor—with respect. They needed to measure a superconducting qubit,
a tiny circuit in which current can flow forever. The qubit emits light, which carries information about the qubit’s state. Jonathan and Kater intensify the light using an amplifier. They’d fabricated many amplifiers, but none had worked. Jonathan suggested changing their strategy—with a politeness to which Emily Post couldn’t have objected. Jonathan’s supervisor, Kater Murch , suggested repeating the protocol they’d performed many times. “That’s the definition of insanity,” Kater admitted, “but I think experiment needs to involve some of that.” I watched the exchange via Skype, with more interest than I’d have watched the Oscars with. Someday, I hope, I’ll be able to weigh in on such a debate, despite working as a theorist. Someday, I’ll have partnered with enough experimentaliststo develop insight.
I’m partnering with Jonathan and Kater on an experiment that coauthors and I proposed in a paperblogged about here
. The
experiment centers on an uncertainty relation, an inequality of the sort immortalized by Werner Heisenberg in 1927. Uncertainty relations imply that, if you measure a quantum particle’s position, the particle’s momentum ceases to have a well-defined value. If you measure the momentum, the particle ceases to have a well-defined position. Our uncertainty relation involves _weak measurements_. Weakly
measuring a particle’s position doesn’t disturb the momentum much and vice versa. We can interpret the uncertainty in information-processing terms, because we cast the inequality in terms of entropies. _Entropies_, described here, are
functions that quantify how efficiently we can process information, such as by compressing data. Jonathan and Kater are checking our inequality, and exploring its implications, with a superconductingqubit.
I had too little experience to side with Jonathan or with Kater. So I watched, and I contemplated how their opinions would sound if expressed about theory. Do I try one strategy again and again, hoping to change my results without changing my approach? At the Perimeter Institute for Theoretical Physics, Masters students had to swallow half-a-year of course material in weeks. I questioned whether I’d ever understand some of the material. But some of that material resurfaced during my PhD. Again, I attended lectures about Einstein’s theory of general relativity. Again, I worked problems about observers in free-fall. Again, I calculated covariant derivatives. The material sank in. I decided never to question, again, whether I could understand a concept. I might not understand a concept today, or tomorrow, or next week. But if I dedicate enough time and effort, I chose to believe, I’ll learn. My decision rested on experience and on classes, taught by educational psychologists, that I’d taken in college. I’d studied how brains change during learning and how breaks enhance the changes. Sense, I thought, underlay my decision—though expecting outcomes to change, while strategies remain static, sounds insane. Does sense underlie Kater’s suggestion, likened to insanity, to keep fabricating amplifiers as before? He’s expressed cynicism many times during our collaboration: _Experiment needs to involve some insanity._ _The experiment probably won’t work for a long time. Plenty more things will likely break._ Jonathan and I agree with him. Experiments have a reputation for breaking, and Kater has a reputation for knowing experiments. Yet Jonathan—with professionalism and politeness—remains optimistic that other methods will prevail, that we’ll meet our goals early. I hope that Jonathan remains optimistic, and I fancy that Kater hopes, too. He prophesies gloom with a quarter of a smile, and his record speaks against him: A few months ago, I met a theorist who’d collaborated with Kater years before. The theorist marveled at the speed with which Kater had operated. A theorist would propose an experiment, and _boom_—the proposal would work. Perhaps luck smiled upon the implementation. But luck dovetails with the sense that underlies Kater’s opinion: Experiments involve factors that you can’t control. Implement a protocol once, and it might fail because the temperature has risen too high. Implement the protocol again, and it might fail because a truck drove by your building, vibrating the tabletop. Implement the protocol again, and it might fail because you bumped into a knob. Implement the protocol a fourth time, and it might succeed. If you repeat a protocol many times, your environment might change, changing your results. Sense underlies also Jonathan’s objections to Kater’s opinions. We boost our chances of succeeding if we keep trying. We derive energy to keep trying from creativity and optimism. So rebelling against our PhD supervisors’ sense is sensible. I wondered, watching the Skype conversation, whether Kater the student had objected to prophesies of doom as Jonathan did. Kater exudes the soberness of a tenured professor but the irreverence of a Californian who wears his hair slightly long and who tattooed his wedding band on. Science thrives on the soberness and the irreverence. Who won Jonathan and Kater’s argument? Both, I think. Last week, they reported having fabricated amplifiers that work. The lab followed a protocol similar to their old one, but with moreconscientiousness.
I’m looking forward to watching who wins the debate about how long the rest of the experiment takes. Either way, check out Jonathan’s talk about our experimentif you attend
the American Physical Society’s March Meeting. Jonathan will speak on Thursday, March 5, at 12:03, in room 106. Also, keep an eye out for our paper—which will debut once Jonathan coaxes the amplifier into synching with his qubit.SHARE THIS:
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INTERACTION + ENTANGLEMENT = EFFICIENT PROOFS OF HALTING Posted on January 30, 2020by Thomas
4
A couple weeks ago my co-authors Zhengfeng Ji (UTS Sydney), Heny Yuen (University of Toronto) and Anand Natarajan and John Wright (both at Caltech’s IQIM, with John soon moving to UT Austin) & I posted a manuscript on the arXiv preprintserver entitled
> MIP*=RE
The magic of the single-letter formula quickly made its effect, and our posting received some attention on the blogosphere (see links below). Within computer science, complexity theory is at an advantage in its ability to capture powerful statements in few letters: who has not head of P, NP, and, for readers of this blog, BQP and QMA? (In contrast, I am under no illusion that my vague attempt at a more descriptive title has, by the time you reach this line, all but vanished from the reader’s memory.) Even accounting for this popularity however, it is a safe bet that fewer of our readers have heard of MIP* or RE. Yet we are promised that the above-stated equality has great consequences for physics (“Tsirelson’s problem” in the study of nonlocality) and mathematics (“Connes’ embedding problem” in the theory of von Neumann algebras). How so — how can complexity-theoretic alphabet soup have any consequence for, on the one hand, physical reality, and on the other, abstract mathematics? The goal of this post and the next one is to help the interested reader grasp the significance of interactive proofs (that lie between the symbols MIP*) and undecidability (that lies behind RE) for quantummechanics.
The bulk of the present post is an almost identical copy of a post I wrote for my personal blog . To avoid accusations of self-plagiarism, I will substantiate it with a little picture and a story, see below. The post gives a very personal take on the research that led to the aforementioned result. In the next post, my co-author Henry Yuen has offered to give a more scientific introduction to the result and its significance. Before proceeding, it is important to make it clear that the research described in this post and the next has not been refereed or thoroughly vetted by the community. This process will take place over the coming months, and we should wait until it is completed before placing too much weight on the results. As an author, I am proud of my work; yet I am aware that there is due process to be made before the claims can be officialised. As such, these posts only represent my opinion (and Henry’s) and not necessarily that of the wider scientific community. For more popular introductions to our result, see the blog posts of Scott Aaronson , DickLipton
,
and Gil Kalai
and reporting by Davide Castelvecchifor Nature and
Emily Conover
for Science.
Now for the personal post…and the promised picture. Isn’t it beautiful? The design is courtesy of Tony Metger and Alexandru Gheorghiu, the first a visiting student and the second a postdoctoral scholar at Caltech’s IQIM. While Tony and Andru came up with the idea, the execution is courtesy of the bakery store employee, who graciously implemented the custom design (apparently writing equations on top of cakes is not common enough to be part of the standard offerings, so they had to go for the custom option). Although it is unclear if the executioner grasped the full depth of the signs they were copying, note how perfect the execution: not a single letter is out of place! Thanks to Tony, Andru, and the anonymous chef for thetasty souvenir.
Now for the story. In an earlier post on my personal research blog, I had reported on the beautiful recent result by Natarajan and Wright showing the astounding power of multi-prover interactive proofs with quantum provers sharing entanglement: in letters, . In the remainder of this post I will describe our follow-up work with Ji, Natarajan, Wright, and Yuen. In this post I will tell the story from a personal point of view, with all the caveats that this implies: the “hard science” will be limited (but there could be a hint as to how “science”, to use a big word, “progresses”, to use an ill-defined one; see also the upcoming post by Henry Yuen for more), the story is far too long, and it might be mostly of interest to me only. It’s a one-sided story, but that has to be. (In particular below I may at times attribute credit in the form “X had this idea”. This is my recollection only, and it is likely to be inaccurate. Certainly I am ignoring a lot of important threads.) I wrote this because I enjoyed recollecting some of the best moments in the story just as much as some the hardest; it is fun to look back and find meanings in ideas that initially appeared disconnected. Think of it as an example of how different lines of work can come together in unexpected ways; a case for open-ended research. It’s also an antidote against despair that I am preparing for myself: whenever I feel I’ve been stuck on a project for far too long, I’ll come back to this post and ask myself if it’s been 14 years yet — if not, then press on. It likely comes as a surprise to me only that I am no longer fresh out of the cradle. My academic life started in earnest some 14 years ago, when in the Spring of 2006 I completed my Masters thesis in Computer Science under the supervision of Julia Kempe, at Orsay in France. I had met Julia the previous term: her class on quantum computing was, by far, the best-taught and most exciting course in the Masters program I was attending, and she had gotten me instantly hooked. Julia agreed to supervise my thesis, and suggested that I look into some interesting recent result by Stephanie Wehner that linked the study of entanglement and nonlocality in quantum mechanics to complexity-theoretic questions about interactive proof systems (specifically, this was Stephanie’s papershowing that
).
At the time the topic was very new. It had been initiated the previous year with a beautiful paper by Cleve et al. (that I have recommended to many a student since!) It was a perfect fit for me: the mathematical aspects of complexity theory and quantum computing connected to my undergraduate background, while the relative concreteness of quantum mechanics (it is a physical theory after all) spoke to my desire for real-world connection (not “impact” or even “application” — just “connection”). Once I got myself up to speed in the area (which consisted of three papers: the two I already mentioned, together with a paper by Kobayashi and Matsumoto where they studied interactive proofs with quantum messages), Julia suggested looking into the “entangled-prover” class introduced in the aforementioned paper by Cleve et al. Nothing was known about this class! Nothing besides the trivial inclusion of single-prover interactive proofs, IP, and the containment in…ALL, the trivial class that contains all languages. Yet the characterization MIP=NEXP of its classical counterpart by Babai et al. in the 1990s had led to one of the most productive lines of work in complexity of the past few decades, through the PCP theorem and its use from hardness of approximation to efficient cryptographic schemes. Surely, studying had to be a productive direction? In spite of its well-established connection to classical complexity theory, via the formalism of interactive proofs, this was a real gamble. The study of entanglement from the complexity-theoretic perspective was entirely new, and bound to be fraught with difficulty; very few results were available and the existing lines of works, from the foundations of non-locality to more recent endeavors in device-independent cryptography, provided little other starting point than strong evidence that even the simplest examples came with many unanswered questions. But my mentor was fearless, and far from a novice in terms of defraying new areas, having done pioneering work in areas ranging from quantum random walks to Hamiltonian complexity through adiabatic computation. Surely this would lead to something? It certainly did. More sleepless nights than papers, clearly, but then the opposite would only indicate dullness. Julia’s question led to far more unexpected consequences than I, or I believe she, could have imagined at the time. I am writing this post to celebrate, in a personal way, the latest step in 15 years of research by dozens of researchers: today my co-authors and I uploaded to the quant-ph arXiv what we consider a complete characterization of the power of entangled-prover interactive proof systems by proving the equality , the class of all recursively enumerable languages (a complete problem for RE is the halting problem). Without going too much into the result itself (if you’re interested, look for an upcoming post here that goes into the proof a bit more), and since this is a more personal post, I will continue on with some personal thoughts about the path that got us there. When Julia & I started working on the question, our main source of inspiration were the results by Cleve et al. showing that the non-local correlations of entanglement had interesting consequences when seen through the lens of interactive proof systems in complexity theory. Since the EPR paper, a lot of work in understanding entanglement had already been accomplished in the Physics community, most notably by Mermin, Peres, Bell, and more recently the works in device-independent quantum cryptography by Acin, Pironio, Scarani and many others, stimulated by Ekert’s proposal for quantum key distribution and Mayers and Yao’s idea for “device-independent cryptography”. By then we certainly knew that “spooky action-at-a-distance” did not entail any faster-than-light communication, and indeed was not really “action-at-a-distance” in the first place but merely “correlation-at-a-distance”. What Cleve et al. recognized is that these “spooky correlations-at-a-distance” were sufficiently special so as to not only give numerically different values in “Bell inequalities”, the tool invented by Bell to evidence non-locality in quantum mechanics, but also have some potentially profound consequences in complexitytheory.
In particular, examples such as the “Magic Square game” demonstrated that enough correlation could be gained from entanglement so as to defeat basic proof systems whose soundness relied only on the absence of communication between the provers, an assumption that until then had been wrongly equated with the assumption that any computation performed by the provers could be modeled entirely locally. I think that the fallacy of this implicit assumption came as a surprise to complexity theorists, who may still not have entirely internalized it. Yet the perfect quantum strategy for the Magic Square game provides a very concrete “counter-example” to the soundness of the “clause-vs-variable” game for 3SAT. Indeed this game, a reformulation by Aravind and Cleve-Mermin of a Bell Inequality discovered by Mermin and Peres in 1990, can be easily re-framed as a 3SAT system of equations that is not satisfiable, and yet is such that the associated two-player clause-vs-variable game has a perfect quantum strategy. It is this observation, made in the paper by Cleve et al., that gave the first strong hint that the use of entanglement in interactive proof systems could make many classical results in thearea go awry.
By importing the study of non-locality into complexity theory Cleve et al. immediately brought it into the realm of asymptotic analysis. Complexity theorists don’t study fixed objects, they study families of objects that tend to have a uniform underlying structure and whose interesting properties manifest themselves “in the limit”. As a result of this new perspective focus shifted from the study of single games or correlations to infinite families thereof. Some of the early successes of this translation include the “unbounded violations” that arose from translating asymptotic separations in communication complexity to the language of Bell inequalities and correlations (e.g. this paper ). These early successes attracted the attention of some physicists working in foundations as well as some mathematical physicists, leading to a productive exploration that combined tools from quantum information, functional analysis and complexity theory. The initial observations made by Cleve et al. had pointed to as a possibly interesting complexity class to study. Rather amazingly, nothing was known about it! They had shown that under strong restrictions on the verifier’s predicate (it should be an XOR of two answer bits), a collapse took place: by the work of Hastad, XOR-MIP equals NEXP, but is included in EXP. This seemed very fortuitous (the inclusion is proved via a connection with semidefinite programming that seems tied to the structure of XOR-MIP protocols): could entanglement induce a collapse of the entire, unrestricted class? We thought (at this point mostly Julia thought, because I had no clue) that this ought not to be the case, and so we set ourselves to show that the equality , that would directly parallel Babai et al.’s characterization MIP=NEXP, holds. We tried to show this by introducing techniques to “immunize” games against entanglement: modify an interactive proof system so that its structure makes it “resistant” to the kind of “nonlocal powers” that can be used to defeat the clause-vs-variable game (witness the Magic Square). This was partially successful, and led to one of the papers I am most proud of — I am proud of it because I think it introduced elementary techniques (such as the use of the Cauchy-Schwarz inequality — inside joke — more seriously, basic things such as “prover-switching”, “commutation tests”, etc.) that are now routine manipulations in the area. The paper was a hard sell! It’s good to remember the first rejections we received. They were not unjustified: the main point of criticism was that we were only able to establish a hardness result for exponentially small completeness-soundness gap. A result for such a small gap in the classical setting follows directly from a very elementary analysis based on the Cook-Levin theorem. So then why did we have to write so many pages (and so many applications of Cauchy-Schwarz!) to arrive at basically the same result (with a )? Eventually we got lucky and the paper was accepted to a conference. But the real problem, of establishing any non-trivial lower bound on the class with constant (or, in the absence of any parallel repetition theorem, inverse-polynomial) completeness-soundness gap, remained. By that time I had transitioned from a Masters student in France to a graduate student in Berkeley, and the problem (pre-)occupied me during some of the most difficult years of my Ph.D. I fully remember spending my first year entirely thinking about this (oh and sure, that systems class I had to pass to satisfy the Berkeley requirements), and then my second year — yet, getting nowhere. (I checked the arXiv to make sure I’m not making this up: two full years, no posts.) I am forever grateful to my fellow student Anindya De for having taken me out of the cycle of torture by knocking on my door with one of the most interesting questions I have studied, that led me into quantum cryptography and quickly resulted in an enjoyable paper . It was good to feel productive again! (Though the paper had fun reactions as well: after putting it on the arXiv we quickly heard from experts in the area that we had solved an irrelevant problem, and that we better learn about information theory — which we did, eventually leading to another paper , etc.) The project had distracted me and I set interactive proofs aside; clearly, I wasstuck.
About a year later I visited IQC in Waterloo. I don’t remember in what context the visit took place. What I do remember is a meeting in the office of Tsuyoshi Ito, at the time a postdoctoral scholar at IQC. Tsuyoshi asked me to explain our result with Julia. He then asked a very pointed question: the bedrock for the classical analysis of interactive proof systems is the “linearity test” of Blum-Luby-Rubinfeld (BLR). Is there any sense in which we could devise a quantum version of that test? What a question! This was great. At first it seemed fruitless: in what sense could one argue that quantum provers apply a “linear function”? Sure, quantum mechanics is linear, but that is besides the point. The linearity is a property of the prover’s answers as a function of their question. So what to make of the quantum state, the inherent randomness, etc.? It took us a few months to figure it out. Once we got there however, the answer was relatively simple — the prover should be making a question-independent measurement that returns a linear function that it applies to its question in order to obtain the answer returned to the verifier — and it opened the path to our subsequent paper showing that the inclusion of NEXP in indeed holds. Tsuyoshi’s question about linearity testing had allowed us to make the connection with PCP techniques; from there to MIP=NEXP there was only one step to make, which is to analyze multi-linearity testing. That step was suggested by my Ph.D. advisor, Umesh Vazirani, who was well aware of the many pathways towards the classical PCP theorem, since the theorem had been obtained in great part by his former student Sanjeev Arora. It took a lot of technical work, yet conceptually a single question from my co-author had sufficed to take me out of a 3-year slumber. This was in 2012, and I thought we were done. For some reason the converse inclusion, of in NEXP, seemed to resist our efforts, but surely it couldn’t resist much longer. Navascues et al. had introduced a hierarchy of semidefinite programs that seemed to give the right answer (technically they could only show convergence to a relaxation, the commuting value, but that seemed like a technicality; in particular, the values coincide when restricted to finite-dimensional strategies, which is all we computer scientists cared about). There were no convergence bounds on the hierarchy, yet at the same time commutative SDP hierarchies were being used to obtain very strong results in combinatorial optimization, and it seemed like it would only be a matter of time before someone came up with an analysis of the quantum case. (I had been trying to solve a related “dimension reduction problem” with Oded Regev for years, and we were making no progress; yet it seemed someone ought to!) In Spring 2014 during an open questions session at a workshopat the Simons
Institute in Berkeley Dorit Aharonov suggested that I ask the question of the possible inclusion of QMA-EXP, the exponential-sized-proofs analogue of QMA, in . A stronger result than the inclusion of NEXP (under assumptions), wouldn’t it be a more natural “fully quantum” analogue of MIP=NEXP? Dorit’s suggestion was motivated by research on the “quantum PCP theorem”, that aims to establish similar hardness results in the realm of the local Hamiltonian problem; see e.g. this post for the connection. I had no idea how to approach the question — I also didn’t really believe the answer could be positive — but what can you do, if Dorit asks you something… So I reluctantly went to the board and asked the question. Joe Fitzsimons was in the audience, and he immediately picked it up! Joe had the fantastic ideas of using quantum error-correction, or more specifically secret-sharing, to distribute a quantum proof among the provers. His enthusiasm overcame my skepticism, and we eventually showed the desired inclusion. Maybe was bigger than after all. Our result, however, had a similar deficiency as the one with Julia, in that the completeness-soundness gap was exponentially small. Obtaining a result with a constant gap took 3 years of couple more years of work and the fantastic energy and insights of a Ph.D. student at MIT, Anand Natarajan. Anand is the first person I know of to have had the courage to dive into the most technical aspects of the analysis of the aforementioned results, while also bringing in the insights of a “true quantum information theorist” that were supported by Anand’s background in Physics and upbringing in the group of Aram Harrow at MIT. (In contrast I think of myself more as a “raw” mathematician; I don’t really understand quantum states other than as positive-semidefinite matrices…not that I understand math either of course; I suppose I’m some kind of a half-baked mish-mash.) Anand had many ideas but one of the most beautiful ones led to what he poetically called the “Pauli braiding test”, a “truly quantum” analogue of the BLR linearity test that amounts to doing two linearity tests in conjugate bases and piecing the results together into a robust test for {n}-qubit entanglement (I wrote about our work on this here).
At approximately the same time, Zhengfeng Ji had another wonderful idea that was in some sense orthogonal to our work. (My interpretation of) Zhengfeng’s idea is that one can see an interactive proof system as a computation (verifier-prover-verifier) and use Kitaev’s circuit-to-Hamiltonian construction to transform the entire computation into a “quantum CSP” (in the same sense that the local Hamiltonian problem is a quantum analogue of classical constraint satisfaction problems (CSP)) that could then itself be verified by a quantum multi-prover interactive proof system…with exponential gains in efficiency! Zhengfeng’s result implied an exponential improvement in complexity compared to the result by Julia and myself, showing inclusion of NEEXP, instead of NEXP, in . However, Zhengfeng’s technique suffered from the same exponentially small completeness-soundness gap as we had, so that the best lower bound on per se remained NEXP. Both works led to follow-ups. With Natarajan we promoted the Pauli braiding test into a “quantum low-degree test ” that allowed us to show the inclusion of QMA-EXP into , with constant gap, thereby finally answering the question posed by Aharonov 4 years after it was asked. (I should also say that by then all results on started relying on a sequence of parallel repetition results shown by Bavarian, Yuen, and others; I am skipping this part.) In parallel, with Ji, Fitzsimons, and Yuen we showed that Ji’s compression technique could be “iterated” an arbitrary number of times. In fact, by going back to “first principles” and representing verifiers uniformly as Turing machines we realized that the compression technique could be used iteratively to (up to small caveats) give a new proof of the fact (first shown by Slofstra using an embedding theorem for finitely presented group) that the zero-gap version of contains the halting problem. In particular, the entangled value is uncomputable! This was not the first time that uncomputability crops in to a natural problem in quantum computing (e.g. the spectral gap paper ), yet it still surprises when it shows up. Uncomputable! How can anything beuncomputable!
As we were wrapping up our paper Henry Yuen realized that our “iterated compression of interactive proof systems” was likely optimal, in the following sense. Even a mild improvement of the technique, in the form of a slower closing of the completeness-soundness gap through compression, would yield a much stronger result: undecidability of the constant-gap class . It was already known by work of Navascues et al., Fritz, and others, that such a result would have, if not surprising, certainly consequences that seemed like they would be taking us out of our depth. In particular, undecidability of any language in would imply a negative resolution to a series of equivalent conjectures in functional analysis, from Tsirelson’s problem to Connes’ Embedding Conjecture through Kirchberg’s QWEP conjecture. While we liked our result, I don’t think that we believed it could resolve any conjecture(s) in functional analysis. So we moved on. At least I moved on, I did some cryptography for a change. But Anand Natarajan and his co-author John Wright did not stop there. They had the last major insight in this story, which underlies their recent STOC best paper described in the previous post. Briefly, they were able to combine the two lines of work, by Natarajan & myself on low-degree testing and by Ji et al. on compression, to obtain a compression that is specially tailored to the existing protocol for NEXP and compresses that protocol without reducing its completeness-soundness gap. This then let them show Ji’s result that contains NEEXP, but this time with constant gap! The result received well-deserved attention. In particular, it is the first in this line of works to not suffer from any caveats (such as a closing gap, or randomized reductions, or some kind of “unfair” tweak on the model that one could attribute the gain in power to), and it implies an unconditional separationbetween MIP and .
As they were putting the last touches on their result, suddenly something happened, which is that a path towards a much bigger result opened up. What Natarajan & Wright had achieved is a one-step gapless compression. In our iterated compression paper we had observed that iterated gapless compression would lead to , implying negative answers to the aforementioned conjectures. So then? I suppose it took some more work, but in some way all the ideas had been laid out in the previous 15 years of work in the complexity of quantum interactive proof systems; we just had to put it together. And so a decade after the characterization QIP = PSPACE of single-prover quantum interactive proof systems, we have arrived at a characterization of quantum multiprover interactive proof systems, . With one author in common between the two papers: congratulationsZhengfeng!
Even though we just posted a paper, in a sense there is much more left to do. I am hopeful that our complexity-theoretic result will attract enough interest from the mathematicians’ community, and especially operator algebraists, for whom CEP is a central problem, that some of them will be willing to devote time to understanding the result. I also recognize that much effort is needed on our own side to make it accessible in the first place! I don’t doubt that eventually complexity theory will not be needed to obtain the purely mathematical consequences; yet I am hopeful that some of the ideas may eventually find their way into the construction of interesting mathematical objects (such as, who knows, a non-hyperlinear group). That was a good Masters project…thanks Julia!SHARE THIS:
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ON THE MERITS OF FLATWORM REPRODUCTION Posted on January 26, 2020 by Nicole Yunger Halpern1
On my right sat a quantum engineer. She was facing a melanoma specialist who works at a medical school. Leftward of us sat a networks expert, a flatworm enthusiast, and a condensed-mattertheorist.
Farther down sat a woman who slices up mouse brains. Welcome to “Coherent Spins in Biology,”a
conference that took place at the University of California, Los Angeles (UCLA) this past December. Two southern Californians organized the workshop: Clarice Aielloheads UCLA’s
Quantum Biology Tech lab. Thorsten Ritz , of the University of California, Irvine, cofounded a branch of quantum biology. Quantum biology served as the conference’s backdrop. According to conventional wisdom, quantum phenomena can’t influence biology significantly: Biological systems have high temperatures, many particles, and fluids. Quantum phenomena, such as entanglement (a relationship that quantum particles can share), die quickly under suchconditions.
Yet perhaps some survive. Quantum biologists search for biological systems that might use quantum resources. Then, they model and measure the uses and resources. Three settings (at least) have held out promise during the past few decades: avian navigation, photosynthesis, and olfaction. You can read about them in this book, cowritten by a conference participant for the general public. I’ll give you a taste (or a possibly quantum smell?) by sketching the avian-navigation proposal,
developed by Thorsten and colleagues. Birds migrate southward during the autumn and northward during the spring. How do they know where to fly? At least partially by sensing the Earth’s magnetic field, which leads compass needles to point northward. How do birds sense the field? Possibly with a protein called “cryptochrome.” A photon (a particle of light) could knock an electron out of part of the protein and into another part. Each part would have one electron that lacked a partner. The electrons would share entanglement. One electron would interact with the Earth’s magnetic field differently than its partner, because its surroundings would differ. (Experts: The electrons would form a radical pair. One electron would neighbor different atoms than the other, so the electron would experience a different local magnetic field. The discrepancy would change the relative phase between the electrons’ spins.) The discrepancy could affect the rate at which the chemical system could undergo certain reactions. Which reactions occur could snowball into large and larger effects, eventually signaling the brain about where the bird shouldfly.
Quantum mechanics and life rank amongst the universe’s mysteries. How could a young researcher resist the combination? A postdoc warned me away, one lunchtime at the start of my PhD. Quantum biology had enjoyed attention several years earlier, he said, but noise the obscured experimental data. Controversy marred the field. I ate lunch with that postdoc in 2013. Interest in quantum biology is reviving, as evidenced in the conference. Two reasons suggested themselves: new technologies and new research avenues. For example, Thorsten described the disabling and deletion of genes that code for cryptochrome. Such studies require years’ more work but might illuminate whether cryptochrome affects navigation. The keynote speaker, Harvard’s Misha Lukin, illustrated new technologies and new research avenues. Misha’s lab has diamonds that contain quantum defects, which serve as artificial atoms. The defects sense tiny magnetic fields and temperatures. Misha’s group applies these quantum sensors to biology problems. For example, different cells in an embryo divide at different times. Imagine reversing the order in which the cells divide. Would the reversal harm the organism? You could find out by manipulating the temperatures in different parts of the embryo: Temperature controls the rate at which cells divide. Misha’s team injected nanoscale diamonds into a worm embryo. (See this paper for a related study.) The diamonds reported the temperature at various points in the worm. This information guided experimentalists who heated the embryo with lasers. The manipulated embryos grew into fairly normal adults. But their cells, and their descendants’ cells, cycled through the stages of life slowly. This study exemplified, to me, one of the most meaningful opportunities for quantum physicists interested in biology: to develop technologies and analyses that can answer biology questions. I mentioned, in an earlier blog post,
another avenue emerging in quantum biology: Physicist Matthew Fisher proposed a mechanism by which entanglement might enhance coordinated neuron firing. My collaborator Elizabeth Crosson and I analyzed how the molecules in Matthew’s proposal—Posner clusters—could process quantum information. The field of Posner quantum biology had a population of about two, when Elizabeth and I entered, and I wondered whether anyone would join us. The conference helped resolve my uncertainty. Three speakers (including me) presented work based on Matthew’s; two other participants were tilling the Posner soil; and another speaker mentioned Matthew’s proposal. The other two Posner talks related data from three experiments. The experimentalists haven’t finished their papers, so I won’t share details. But stay tuned. Posner molecule (image by Swift _et al._)
Clarice and Thorsten’s conference reminded me of a conference I’d participated in at the end of my PhD: Last month, I moonlighted as a quantum biologist. In 2017, I moonlighted as a quantum-gravitytheorist
. Two
years earlier, I’d been dreaming about black holes and space-time. At UCLA, I was finishing the first paper I’ve coauthored with biophysicists . What a toolkit quantum information theory and thermodynamics provide, that it can unite such disparate fields. The contrast—on top of what I learned at UCLA—filled my mind for weeks. And reminded me of the description of asexual reproduction that we heard from the conference’s flatworm enthusiast. According to Western Michigan University’s Wendy Beane , a flatworm “glues its butt down, pops its head off, and grows a new one. Y’know. As onedoes.”
I hope I never flinch from popping my head off and growing a new one—on my quantum-information-thermodynamics spine—whenever new science calls for figuring out. _With thanks to Clarice, Thorsten, and UCLA for their invitation andhospitality._
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AN EQUATION FIT FOR A NOVEL Posted on December 22, 2019 by Nicole Yunger Halpern3
Archana Kamal was hunting for an apartment in Cambridge, Massachusetts. She was moving MIT, to work as a postdoc in physics. The first apartment she toured had housed John Updike, during his undergraduate career at Harvard. No other apartment could compete; Archana signed the lease. The apartment occupied the basement of a red-brick building covered in vines. The rooms spanned no more than 350 square feet. Yet her window opened onto the neighbors’ garden, whose leaves she tracked across the seasons. And Archana cohabited with history. She’s now studying the universe’s history, as an assistant professor of physics at the University of Massachusetts Lowell. The
cosmic microwave background (CMB) pervades the universe. The CMB consists of electromagnetic radiation, or light. Light has particle-like properties and wavelike properties. The wavelike properties include wavelength, the distance between successive peaks. Long-wavelength light includes red light, infrared light, and radio waves. Short-wavelength light includes blue light, ultraviolet light, and X-rays. Light of one wavelength and light of another wavelength are said to belong to different _modes_. Does the CMB have nonclassical properties, impossible to predict with classical physics but (perhaps) predictable with quantum theory? The CMB does according to the theory of inflation. According
to the theory, during a short time interval after the Big Bang, the universe expanded very quickly: Spacetime stretched. Inflation explains features of our universe, though we don’t know what mechanism would have effected the expansion. According to inflation, around the Big Bang time, all the light in the universe crowded together. The photons (particles of light) interacted, entangling (developing strong quantum correlations). Spacetime then expanded, and the photons separated. But they might retain entanglement. Detecting that putative entanglement poses challenges. For
instance, the particles that you’d need to measure could produce a signal too weak to observe. Cosmologists have been scratching their heads about how to observe nonclassicality in the CMB. One team—Nishant Agarwal at UMass Lowell and Sarah Shandera at Pennsylvania State University—turned to Archana for help. Archana studies the theory of open quantum systems, quantum systems that interact with their environments. She thinks most about systems such as superconducting qubits, tiny
circuits with which labs are building quantum computers. But the visible universe constitutes an open quantum system. We can see only part of the universe—or, rather, only part of what we believe is the whole universe. Why? We can see only stuff that’s emitted light that has reached us, and light has had only so long to travel. But the visible universe interacts (we believe) with stuff we haven’t seen. For instance, according to the theory of inflation, that rapid expansion stretched some light modes’ wavelengths. Those wavelengths grew longer than the visible universe. We can’t see those modes’ peak-to-peak variations or otherwise observe the modes, often called “frozen.” But the frozen modes act as an environment that exchanges information and energy with the visible universe. We describe an open quantum system’s evolution with a quantum master equation, which I blogged about four-and-a-half years ago. Archana
and collaborators constructed a quantum master equation for thevisible universe
. The
frozen modes, they found, retain memories of the visible universe. (Experts: the bath is non-Markovian.) Next, they need to solve the equation. Then, they’ll try to use their solution to identify quantum observables that could reveal nonclassicality in the CMB.Frozen modes
Archana’s project caught my fancy for two reasons. First, when I visited her in October, I was collaborating on a related project. My coauthors and I were concocting a scheme for detecting nonclassical correlations in many-particle systems by measuring large-scale properties. Our paper debuted last month. It might—with thought and a dash of craziness—be applied to detect nonclassicality in the CMB. Archana’s explanation improved my understanding of our scheme’s potential. Second, Archana and collaborators formulated a quantum master equation for the visible universe. _A quantum master equation for the visible universe._ The phrase sounded romantic to me.1 It merited a coauthor who’d seized on an apartment lived in by a Pulitzer Prize-winningnovelist.
Archana’s cosmology and Updike stories reminded me of one reason why I appreciate living in the Boston area: History envelops us here. Last month, while walking to a grocery, I found a sign that marks the building in which the poet e. e. cummings was born. My walking partner then generously tolerated a recitation of cummings’s “anyone lived in a pretty how town.”History
enriches our lives—and some of it might contain entanglement. 1It might sound like gobbledygook to you, if I’ve botched my explanations of the terminology. _With thanks to Archana and the UMass Lowell Department of Physics and Applied Physics for their hospitality and seminar invitation._SHARE THIS:
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