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Physics Today

Two bits on qubits

Dave Bacon

Published Mar 1, 2008• 0 citations
Publisher

Abstract

I greatly enjoyed reading David Mermin’s last two Reference Frame columns on factoring and quantum computing (Physics Today, Physics Today 0031-9228 60 4 2007 8 https://doi.org/10.1063/1.2731953. April 2007, page 8 ; Physics Today 0031-9228 60 10 2007 10 https://doi.org/10.1063/1.2800253. October 2007, page 10 ). However, as the proud one-time owner of the California license plate QUBITS (which I had occasion to park beside a QUARKS license plate from New Mexico), I feel I must cheerfully disagree with Mermin’s choice to denote quantum bits as qbits. His slander of the traditional shortened spelling of quantum bit as “the vulgar spelling qubit “ lays down the gauntlet to the proud worldwide community of heterographic homophone lovers, many of whom I call friends.Mermin’s arguments are deceptively enticing: 1 1. N. D. Mermin, Am. J. Phys. 71, 23 (2003). https://doi.org/10.1119/1.1522741 that qubit violates the English rule that qu should be followed by a vowel, that no one would ever call the swab a Qutip, and that Paul Dirac with good reason called them q-numbers, not qunumbers. One reason might have been enough, but cube it and certainly no one will argue back at you.Let us rebut those arguments one by one. First, if Mermin is serious about his respelling of the shortened form of quantum bits, then certainly he should choose q-bit instead of qbit, because the only word with a consonant following a q in the Oxford English Dictionary is the crippling child of circumstance, qwerty, to describe a keyboard. And, having settled on q-bit, one faces a dilemma. Writing “q-bit” immediately conjures up Q-tip and, worse for those of us from the video game age, Q-Bert (or Q*Bert), the name of an addictive video game featuring an eponymous alien who hopped on a tricolored pyramidal staircase. Mermin may find no discomfort in hearing echoes of “Q-tip,” but I think the majority of physicists—not to mention computer scientists—would prefer not to be reminded of either ear infections or hopping aliens when they transcribe their serious scientific work.I note that q-number and Q-tip arose at the same time. (Originally called “Baby Gays,” Q-tips were renamed in 1926. The Q stood for quality.) With no disrespect to Dirac, who seemed to have a thing for full-letter initials, history, as measured by the success of q-number versus the ubiquity of Q-tip, has clearly decided that the q- prefix works better for brand names than for scientific terms. In short: Let us keep the corporate branding of science off our beloved quantum bits. Most importantly for the progress of science, the fact that qubit is an intentional homophone of cubit is not vulgar but rather a blessing in disguise. A cubit is an ancient unit of length, roughly equal to the length of a forearm. And that “roughly” should offend the heart of any physicist. Like the foot, the cubit is an imprecise unit whose lack of precision makes me think it deserves to die. Can you use cubit on your physics tests? No! And I can think of no better death than its replacement by qubit , a precise unit of quantum information. As an addendum to the beauty of this homophone, one should not overlook the fact that the cubit is most often associated with lengths in biblical texts. And despite Mermin’s claim to the contrary, qu followed by a consonant does appear in English words, albeit proper nouns, notably Qumran, the name of the settlement nearest where the Dead Sea scrolls were discovered.Long live qubits. And may qbits and their dirty cousins Q-bits only rear their heads in a future quantum computing company or in a medical journal describing bits of cotton swab lodged in the ear.REFERENCESSection:ChooseTop of pageREFERENCES <<1. N. D. Mermin, Am. J. Phys. 71, 23 (2003). https://doi.org/10.1119/1.1522741 , Google ScholarCrossref© 2008 American Institute of Physics.

DOI
10.1063/1.2897963

Related papers

Two bits on qubits

David Mermin

Mermin replies: The enticing arguments that Dave Bacon tries so well to refute were not in my Reference Frame columns, which I’m delighted he enjoyed. The point is put best in my new book, 1 1. N. D. Mermin, Quantum Computer Science: An Introduction, Cambridge U. Press, New York (2007), p. 3. where I also note that q-bit would indeed be better than Qbit, were it not that common expressions such as 2-Qbit gate fail to work when written in the form 2-q-bit gate. To solve the problem, I drop Dirac’s hyphen but put Q in uppercase (which the qbit Bacon wrongly attributes to me does not) to emphasize that it functions as the name of a letter and not as part of another grotesquely spelled word. Qbit for the quantum object parallels the equally important Cbit for the classical object (clbit would be ridiculous). The capitalization convention gives rise to the useful term Bit, which refers collectively to both kinds of physical objects, as opposed to bit, which refers only to a number that can be 0 or 1.I agree with Bacon that qubit has achieved its current status because of its spurious resemblance to cubit, 2 2. Ref. 1, p. 4. but I do not agree that the foot deserves to die. It should be redefined 5 millimeters downward to a light nanosecond 3 3. N. D. Mermin, It’s About Time: Understanding Einstein’s Relativity, Princeton U. Press, Princeton, NJ (2005), p. 22. a couple of years after our backward nation finally goes metric, which I confidently expect to happen in a century or two.Setting aside the fact that transliterations of foreign proper nouns notoriously violate all kinds of rules, I note that Qumran is pronounced k’mran. This class of examples would require qubit to be pronounced k’bit.It may be quixotic (but certainly not Qxotic) to try to correct the spelling of an entire community, but I owe it my best shot. What else is retirement good for?REFERENCESSection:ChooseTop of pageREFERENCES <<1. N. D. Mermin, Quantum Computer Science: An Introduction, Cambridge U. Press, New York (2007), p. 3. Google ScholarCrossref2. Ref. 1, p. 4. Google Scholar3. N. D. Mermin, It’s About Time: Understanding Einstein’s Relativity, Princeton U. Press, Princeton, NJ (2005), p. 22. Google Scholar© 2008 American Institute of Physics.

Physics Today•Mar 1, 2008•2 citations

Bits on Quantum Information

Gregg S. Jaeger

I was honored to see my book Quantum Information: An Overview (Springer, 2007) reviewed alongside David Mermin’s masterful new textbook ( Quantum Computer Science: An Introduction, Cambridge University Press, 2007). However, I was disappointed by reviewer Barbara Terhal’s facile and inappropriate approach (Physics Today, Physics Today 0031-9228 61 3 2008 54 https://doi.org/10.1063/1.2897953. March 2008, page 54 ).Terhal states, “The preface of the book speaks of his intentions: to write a text that provides an overview of the fundamentals of the field.” However, my intent, which was thoroughly laid out in the preface, goes far beyond that characterization. As a result, my necessary constraints on the book are misrepresented and underappreciated. In particular, I made it clear that the book was intended as “a handy reference … that also treats foundational aspects of quantum mechanics connected with quantum information science.” Unlike Mermin’s excellent monograph, mine was never intended to serve as an easily read introduction to the field or to provide unique insight. An overview such as mine cannot be the same thing as a textbook and should not be evaluated as one.Terhal further complains that the monograph contains little by way of personal insight, but that point was made clear both in the foreword by Tommaso Toffoli and in the preface. When presenting a subject as nascent and controversial as quantum information science, it is a good idea, particularly in the case of an overview, not to inject too much of oneself.More surprisingly, after recognizing that my book does provide a comprehensive overview of this rapidly expanding area, the reviewer questions “whether there is an audience for such encyclopedic texts, especially given the easy access to online sources of information such as the arXiv e-print server and Wikipedia.” That question is relatively easily answered: Yes, there is periodically a need for a concise and comprehensive monograph that is above the anarchy and distortions on Wikipedia and to a lesser extent the e-print servers and that can serve those with mathematical training and limited free time to cull accurate treatments from the Web.Moreover, because quantum information science is an area that transcends physics itself, the physics itself can sometimes be distorted, a situation more prevalent in online offerings such as Wikipedia and e-prints. Can one seriously rely on Wikipedia and e-print servers as clear and valid guides to the foundation and breadth of quantum information science? Are those the sources where researchers outside the area can obtain an organized overview of the subject? The unevenness and unreliable nature of the perspectives offered on free portions of the Web are reasons why I chose to write Quantum Information in the first place.Another aspect of my monograph, also clearly noted in its preface, is that the book discusses “a number of pertinent … results from earlier decades of the twentieth century … because they will likely prove important to future progress in both quantum mechanics and information theory.” Terhal’s only mention of that aspect was apparently her reference to the unspecified portion of the text she considered “mathematical and superfluous detail.” My reason for including that extra material is to show the extent to which quantum information science is grounded in fundamental physics and is capable of making great contributions to quantum foundations, provided the physics remains squarely in view.Like a standard quantum measurement, the effect of this lukewarm book review is, in all likelihood, irreversible. Fortunately, though, many who have carefully read the book’s preface and who, therefore, have understood the entirety of its purpose and constraints have expressed their satisfaction with the book over the 16 months since its publication. Those readers have been glad to have a reliable source to guide them into this exploding body of literature.© 2008 American Institute of Physics.

Physics Today•Jul 1, 2008•0 citations

Quantum information is exciting and important

Charles Day

For the March–April 2007 issue of Computing in Science & Engineering, I wrote an essay entitled “Quantum Computing Is Exciting and Important—Really!” The essay’s inspiration came from a sardonic disclaimer that Rolf Landauer (1927–99) proposed be added to papers about quantum computing: This proposal, like all proposals for quantum computation, relies on speculative technology, does not in current form take into account all possible sources of noise, unreliability and manufacturing error, and probably will not work. Fourteen years ago I argued that even if Landauer’s skepticism remained valid, the quest to build a quantum computer had already paid off. As supporting evidence, I cited the work of David Wineland and his collaborators at the NIST lab in Boulder, Colorado. Having developed logic gates based on trapped ions, they repurposed the technology to make new, entanglement-based clocks of unprecedented precision (see Physics Today, October 2005, page 24).I also cited the work of Princeton University’s Jason Petta. In developing quantum dots as a platform for quantum computing, he and his collaborators at Harvard University measured the puny fluctuating magnetic field of 106 gallium and arsenic nuclei inside a quantum dot (see Physics Today, March 2006, page 16).Theorists were just as productive, I noted. The work of Caltech’s Alexei Kitaev and others on topological quantum computation has spawned rich and fruitful explorations of the mathematical similarities of field theory, knots, and the fractional quantum Hall effect (see Physics Today, October 2005, page 21). Princeton’s Robert Calderbank applied the theory of quantum error correction to understand radar polarimetry.Physicists continue to advance the field of quantum information. Perhaps the most spectacular recent feat is that of Jian-Wei Pan of the University of Science and Technology of China (USTC) and his collaborators. In 2017 their experiment aboard the satellite Micius beamed down pairs of entangled photons to the Chinese cities of Delingha and Lijiang, which are 1200 km apart. “Never has the spooky action of quantum mechanics been observed at so great a distance,” wrote Ashley Smart in his news story (Physics Today, August 2017, page 14).This past summer, the team known as Google AI Quantum and collaborators reported the use of a quantum processor in combination with a classical computer to calculate the binding energy of chains of 6, 8, 10, and 12 atoms of hydrogen and the cis–trans isomerization energy of a diazene molecule, HNNH.The Google team’s calculations are not beyond the abilities of a classical computer. However, in October 2019 the Google team published a report in Nature that described achieving so-called quantum supremacy: Its 53-qubit device made of Josephson junctions took 200 seconds to solve a sampling problem that would take a classical system 104 years. This past December, USTC’s Pan and his collaborators reported a similar feat in Science: Their 76-qubit device based on entangled photons solved a sampling problem 1014 times faster than a classical device could.If Landauer were alive today, would he concede that a quantum computer probably will work? That’s hard to say. The sampling problems tackled by the Google and USTC teams were expressly devised as benchmarks of quantum supremacy. They fall short of a universal quantum computer capable of, say, proving that the Hubbard model is sufficient to account for high-Tc superconductivity or the particles that result when protons and antiprotons collide at 14 TeV in an upgraded LHC.Despite his skepticism about quantum computing, Landauer was a pioneer in investigating the quantum limits of information. One of his most cited papers is his 1961 derivation of the minimum about heat that is dissipated when one bit of information is erased: kT log 2. Section:ChooseTop of page <<© 2021 American Institute of Physics.

Physics Today•Mar 1, 2021•2 citations

Mermin habitually answers opinions, real and abstract

Rodney Brooks

I am that friend of David Mermin’s “who was enchanted by the revelation that quantum fields were the real stuff that makes up the world.” I plead guilty to reification and offer the following defense.I started out, as I think we all did, with the notion that there is a reality out there and that space and time are part of it—not just “an extremely effective way to represent relations between distinct events.” When I read Arthur Eddington’s The Nature of the Physical World (J. M. Dent & Sons, 1942) in high school, I learned that reality was not what it seemed—that Eddington’s solid writing desk, for example, was mostly empty space. The next step in my understanding of reality came in college when I found that the electromagnetic field offered a more satisfying picture of the world than action at a distance, which even Isaac Newton derided. 1 1. H. Boorse, L. Motz, eds., The World of the Atom, Basic Books, New York (1966), p. 319. When I encountered quantum mechanics, of course, everything became confusion. However, along with David, I was fortunate to attend Julian Schwinger’s courses at Harvard University just after he had perfected his treatment of quantum field theory. 2 2. J. Schwinger, Ann. Phys. 2, 407 (1957). https://doi.org/10.1016/0003-4916(57)90015-5 I sat enthralled throughout the three-year series (1956–59), in which Schwinger developed QFT as a seemingly inevitable consequence of the most basic assumptions.However, I came away with a different understanding of QFT than David’s. I understood that the fields are physical properties of space that are described by field strengths—just as in classical physics, except that in QFT the state of the field at each point is represented by a vector in Hilbert space rather than by a pure number. That use of Hilbert space, which followed naturally from Schwinger’s “measurement algebra,” allows superpositions of values. The operators in Hilbert space, as I understood it, are mathematical tools that describe the evolution of the state vectors, and they are not to be reified.When I saw how QFT resolves the paradoxes of modern physics, it became irresistible. The special relativity paradoxes—for example, Lorentz contraction and time dilation—are a natural result of the way fields behave. 3 3. J. Schwinger wrote a six-part series on the theory of quantized fields: Phys. Rev. 82, 914 (1951); 91, 713 (1953); https://doi.org/10.1103/PhysRev.82.914 91, 728 (1953); 92, 1283 (1953); 93, 615 (1954); 94, 1362 (1954). The spacetime curvature of general relativity, which I could never really visualize, does not exist in QFT; the gravitational field equations are equivalent to spacetime curvature for those who can visualize it, but equivalent is not the same as identical. 4 4. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972), pp. vii–147. Finally, the mysterious wave–particle duality of quantum mechanics vanishes; in QFT, reality consists of fields and only fields.Because QFT is so neglected by the public (and by many physicists), I am writing a book that presents it without equations. A draft copy of the work, The Theory That Escaped Einstein, can be found through an internet search. Feedback is appreciated.For those who can’t kick the reification habit, QFT is the way to go. It is the only theory that offers a consistent and visualizable picture of reality. Reifiers of the world, unite! You have nothing to lose but your abstractions.REFERENCESSection:ChooseTop of pageREFERENCES <<1. H. Boorse, L. Motz, eds., The World of the Atom, Basic Books, New York (1966), p. 319. Google Scholar2. J. Schwinger, Ann. Phys. 2, 407 (1957). https://doi.org/10.1016/0003-4916(57)90015-5 , Google ScholarCrossref, ISI3. J. Schwinger wrote a six-part series on the theory of quantized fields: Phys. Rev. 82, 914 (1951); 91, 713 (1953); https://doi.org/10.1103/PhysRev.82.914 , Google ScholarCrossref, ISI 91, 728 (1953); , Google Scholar 92, 1283 (1953); Google Scholar 93, 615 (1954); Google Scholar 94, 1362 (1954). Google Scholar4. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972), pp. vii–147. Google Scholar© 2009 American Institute of Physics.

Physics Today•Sep 1, 2009•0 citations

Architecture

Noson S. Yanofsky, Mirco A. Mannucci

From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician. Sir James Jeans, Mysterious Universe Now that we have the mathematical and physical preliminaries under our belt, we can move on to the nuts and bolts of quantum computing. At the heart of a classical computer is the notion of a bit and at the heart of quantum computer is a generalization of the concept of a bit called a qubit, which shall be discussed in Section 5.1. In Section 5.2, classical (logical) gates, which manipulate bits, are presented from a new and different perspective. From this angle, it is easy to formulate the notion of quantum gates, which manipulate qubits. As mentioned in Chapters 3 and 4, the evolution of a quantum system is reversible, i.e., manipulations that can be done must also be able to be undone. This “undoing” translates into reversible gates, which are discussed in Section 5.3. We move on to quantum gates in Section 5.4. Reader Tip . Discussion of the actual physical implementation of qubits and quantum gates is dealt with in Chapter 11. BITS AND QUBITS What is a bit ? Definition 5.1.1 A bit is a unit of information describing a two-dimensional classical system . There are many examples of bits: ▪ A bit is electricity traveling through a circuit or not (or high and low). ▪ A bit is a way of denoting “true” or “false.” […]

Cambridge University Press eBooks•Aug 11, 2008•0 citations

Qubits, Gates, and Circuits

Eduardo R. Mucciolo

Before we start to discuss quantum bits (“qubits” for short), let us spend some time reviewing classical bits, which we will simply call bits, and the types of operations one can perform with them.

CRC Press eBooks•Aug 6, 2025•0 citations
I greatly enjoyed reading David Mermin’s last two Reference Frame columns on factoring and quantum computing (Physics Today, Physics Today 0031-9228 60 4 2007 8 https://doi.org/10.1063/1.2731953. April 2007, page 8 ; Physics Today 0031-9228 60 10 2007 10 https://doi.org/10.1063/1.2800253. October 2007, page 10 ). However, as the proud one-time owner of the California license plate QUBITS (which I had occasion to park beside a QUARKS license plate from New Mexico), I feel I must cheerfully disagree with Mermin’s choice to denote quantum bits as qbits. His slander of the traditional shortened spelling of quantum bit as “the vulgar spelling qubit “ lays down the gauntlet to the proud worldwide community of heterographic homophone lovers, many of whom I call friends.Mermin’s arguments are deceptively enticing: 1 1. N. D. Mermin, Am. J. Phys. 71, 23 (2003). https://doi.org/10.1119/1.1522741 that qubit violates the English rule that qu should be followed by a vowel, that no one would ever call the swab a Qutip, and that Paul Dirac with good reason called them q-numbers, not qunumbers. One reason might have been enough, but cube it and certainly no one will argue back at you.Let us rebut those arguments one by one. First, if Mermin is serious about his respelling of the shortened form of quantum bits, then certainly he should choose q-bit instead of qbit, because the only word with a consonant following a q in the Oxford English Dictionary is the crippling child of circumstance, qwerty, to describe a keyboard. And, having settled on q-bit, one faces a dilemma. Writing “q-bit” immediately conjures up Q-tip and, worse for those of us from the video game age, Q-Bert (or Q*Bert), the name of an addictive video game featuring an eponymous alien who hopped on a tricolored pyramidal staircase. Mermin may find no discomfort in hearing echoes of “Q-tip,” but I think the majority of physicists—not to mention computer scientists—would prefer not to be reminded of either ear infections or hopping aliens when they transcribe their serious scientific work.I note that q-number and Q-tip arose at the same time. (Originally called “Baby Gays,” Q-tips were renamed in 1926. The Q stood for quality.) With no disrespect to Dirac, who seemed to have a thing for full-letter initials, history, as measured by the success of q-number versus the ubiquity of Q-tip, has clearly decided that the q- prefix works better for brand names than for scientific terms. In short: Let us keep the corporate branding of science off our beloved quantum bits. Most importantly for the progress of science, the fact that qubit is an intentional homophone of cubit is not vulgar but rather a blessing in disguise. A cubit is an ancient unit of length, roughly equal to the length of a forearm. And that “roughly” should offend the heart of any physicist. Like the foot, the cubit is an imprecise unit whose lack of precision makes me think it deserves to die. Can you use cubit on your physics tests? No! And I can think of no better death than its replacement by qubit , a precise unit of quantum information. As an addendum to the beauty of this homophone, one should not overlook the fact that the cubit is most often associated with lengths in biblical texts. And despite Mermin’s claim to the contrary, qu followed by a consonant does appear in English words, albeit proper nouns, notably Qumran, the name of the settlement nearest where the Dead Sea scrolls were discovered.Long live qubits. And may qbits and their dirty cousins Q-bits only rear their heads in a future quantum computing company or in a medical journal describing bits of cotton swab lodged in the ear.REFERENCESSection:ChooseTop of pageREFERENCES <<1. N. D. Mermin, Am. J. Phys. 71, 23 (2003). https://doi.org/10.1119/1.1522741 , Google ScholarCrossref© 2008 American Institute of Physics.
Mermin replies: The enticing arguments that Dave Bacon tries so well to refute were not in my Reference Frame columns, which I’m delighted he enjoyed. The point is put best in my new book, 1 1. N. D. Mermin, Quantum Computer Science: An Introduction, Cambridge U. Press, New York (2007), p. 3. where I also note that q-bit would indeed be better than Qbit, were it not that common expressions such as 2-Qbit gate fail to work when written in the form 2-q-bit gate. To solve the problem, I drop Dirac’s hyphen but put Q in uppercase (which the qbit Bacon wrongly attributes to me does not) to emphasize that it functions as the name of a letter and not as part of another grotesquely spelled word. Qbit for the quantum object parallels the equally important Cbit for the classical object (clbit would be ridiculous). The capitalization convention gives rise to the useful term Bit, which refers collectively to both kinds of physical objects, as opposed to bit, which refers only to a number that can be 0 or 1.I agree with Bacon that qubit has achieved its current status because of its spurious resemblance to cubit, 2 2. Ref. 1, p. 4. but I do not agree that the foot deserves to die. It should be redefined 5 millimeters downward to a light nanosecond 3 3. N. D. Mermin, It’s About Time: Understanding Einstein’s Relativity, Princeton U. Press, Princeton, NJ (2005), p. 22. a couple of years after our backward nation finally goes metric, which I confidently expect to happen in a century or two.Setting aside the fact that transliterations of foreign proper nouns notoriously violate all kinds of rules, I note that Qumran is pronounced k’mran. This class of examples would require qubit to be pronounced k’bit.It may be quixotic (but certainly not Qxotic) to try to correct the spelling of an entire community, but I owe it my best shot. What else is retirement good for?REFERENCESSection:ChooseTop of pageREFERENCES <<1. N. D. Mermin, Quantum Computer Science: An Introduction, Cambridge U. Press, New York (2007), p. 3. Google ScholarCrossref2. Ref. 1, p. 4. Google Scholar3. N. D. Mermin, It’s About Time: Understanding Einstein’s Relativity, Princeton U. Press, Princeton, NJ (2005), p. 22. Google Scholar© 2008 American Institute of Physics.
I was honored to see my book Quantum Information: An Overview (Springer, 2007) reviewed alongside David Mermin’s masterful new textbook ( Quantum Computer Science: An Introduction, Cambridge University Press, 2007). However, I was disappointed by reviewer Barbara Terhal’s facile and inappropriate approach (Physics Today, Physics Today 0031-9228 61 3 2008 54 https://doi.org/10.1063/1.2897953. March 2008, page 54 ).Terhal states, “The preface of the book speaks of his intentions: to write a text that provides an overview of the fundamentals of the field.” However, my intent, which was thoroughly laid out in the preface, goes far beyond that characterization. As a result, my necessary constraints on the book are misrepresented and underappreciated. In particular, I made it clear that the book was intended as “a handy reference … that also treats foundational aspects of quantum mechanics connected with quantum information science.” Unlike Mermin’s excellent monograph, mine was never intended to serve as an easily read introduction to the field or to provide unique insight. An overview such as mine cannot be the same thing as a textbook and should not be evaluated as one.Terhal further complains that the monograph contains little by way of personal insight, but that point was made clear both in the foreword by Tommaso Toffoli and in the preface. When presenting a subject as nascent and controversial as quantum information science, it is a good idea, particularly in the case of an overview, not to inject too much of oneself.More surprisingly, after recognizing that my book does provide a comprehensive overview of this rapidly expanding area, the reviewer questions “whether there is an audience for such encyclopedic texts, especially given the easy access to online sources of information such as the arXiv e-print server and Wikipedia.” That question is relatively easily answered: Yes, there is periodically a need for a concise and comprehensive monograph that is above the anarchy and distortions on Wikipedia and to a lesser extent the e-print servers and that can serve those with mathematical training and limited free time to cull accurate treatments from the Web.Moreover, because quantum information science is an area that transcends physics itself, the physics itself can sometimes be distorted, a situation more prevalent in online offerings such as Wikipedia and e-prints. Can one seriously rely on Wikipedia and e-print servers as clear and valid guides to the foundation and breadth of quantum information science? Are those the sources where researchers outside the area can obtain an organized overview of the subject? The unevenness and unreliable nature of the perspectives offered on free portions of the Web are reasons why I chose to write Quantum Information in the first place.Another aspect of my monograph, also clearly noted in its preface, is that the book discusses “a number of pertinent … results from earlier decades of the twentieth century … because they will likely prove important to future progress in both quantum mechanics and information theory.” Terhal’s only mention of that aspect was apparently her reference to the unspecified portion of the text she considered “mathematical and superfluous detail.” My reason for including that extra material is to show the extent to which quantum information science is grounded in fundamental physics and is capable of making great contributions to quantum foundations, provided the physics remains squarely in view.Like a standard quantum measurement, the effect of this lukewarm book review is, in all likelihood, irreversible. Fortunately, though, many who have carefully read the book’s preface and who, therefore, have understood the entirety of its purpose and constraints have expressed their satisfaction with the book over the 16 months since its publication. Those readers have been glad to have a reliable source to guide them into this exploding body of literature.© 2008 American Institute of Physics.
For the March–April 2007 issue of Computing in Science & Engineering, I wrote an essay entitled “Quantum Computing Is Exciting and Important—Really!” The essay’s inspiration came from a sardonic disclaimer that Rolf Landauer (1927–99) proposed be added to papers about quantum computing: This proposal, like all proposals for quantum computation, relies on speculative technology, does not in current form take into account all possible sources of noise, unreliability and manufacturing error, and probably will not work. Fourteen years ago I argued that even if Landauer’s skepticism remained valid, the quest to build a quantum computer had already paid off. As supporting evidence, I cited the work of David Wineland and his collaborators at the NIST lab in Boulder, Colorado. Having developed logic gates based on trapped ions, they repurposed the technology to make new, entanglement-based clocks of unprecedented precision (see Physics Today, October 2005, page 24).I also cited the work of Princeton University’s Jason Petta. In developing quantum dots as a platform for quantum computing, he and his collaborators at Harvard University measured the puny fluctuating magnetic field of 106 gallium and arsenic nuclei inside a quantum dot (see Physics Today, March 2006, page 16).Theorists were just as productive, I noted. The work of Caltech’s Alexei Kitaev and others on topological quantum computation has spawned rich and fruitful explorations of the mathematical similarities of field theory, knots, and the fractional quantum Hall effect (see Physics Today, October 2005, page 21). Princeton’s Robert Calderbank applied the theory of quantum error correction to understand radar polarimetry.Physicists continue to advance the field of quantum information. Perhaps the most spectacular recent feat is that of Jian-Wei Pan of the University of Science and Technology of China (USTC) and his collaborators. In 2017 their experiment aboard the satellite Micius beamed down pairs of entangled photons to the Chinese cities of Delingha and Lijiang, which are 1200 km apart. “Never has the spooky action of quantum mechanics been observed at so great a distance,” wrote Ashley Smart in his news story (Physics Today, August 2017, page 14).This past summer, the team known as Google AI Quantum and collaborators reported the use of a quantum processor in combination with a classical computer to calculate the binding energy of chains of 6, 8, 10, and 12 atoms of hydrogen and the cis–trans isomerization energy of a diazene molecule, HNNH.The Google team’s calculations are not beyond the abilities of a classical computer. However, in October 2019 the Google team published a report in Nature that described achieving so-called quantum supremacy: Its 53-qubit device made of Josephson junctions took 200 seconds to solve a sampling problem that would take a classical system 104 years. This past December, USTC’s Pan and his collaborators reported a similar feat in Science: Their 76-qubit device based on entangled photons solved a sampling problem 1014 times faster than a classical device could.If Landauer were alive today, would he concede that a quantum computer probably will work? That’s hard to say. The sampling problems tackled by the Google and USTC teams were expressly devised as benchmarks of quantum supremacy. They fall short of a universal quantum computer capable of, say, proving that the Hubbard model is sufficient to account for high-Tc superconductivity or the particles that result when protons and antiprotons collide at 14 TeV in an upgraded LHC.Despite his skepticism about quantum computing, Landauer was a pioneer in investigating the quantum limits of information. One of his most cited papers is his 1961 derivation of the minimum about heat that is dissipated when one bit of information is erased: kT log 2. Section:ChooseTop of page <<© 2021 American Institute of Physics.
I am that friend of David Mermin’s “who was enchanted by the revelation that quantum fields were the real stuff that makes up the world.” I plead guilty to reification and offer the following defense.I started out, as I think we all did, with the notion that there is a reality out there and that space and time are part of it—not just “an extremely effective way to represent relations between distinct events.” When I read Arthur Eddington’s The Nature of the Physical World (J. M. Dent & Sons, 1942) in high school, I learned that reality was not what it seemed—that Eddington’s solid writing desk, for example, was mostly empty space. The next step in my understanding of reality came in college when I found that the electromagnetic field offered a more satisfying picture of the world than action at a distance, which even Isaac Newton derided. 1 1. H. Boorse, L. Motz, eds., The World of the Atom, Basic Books, New York (1966), p. 319. When I encountered quantum mechanics, of course, everything became confusion. However, along with David, I was fortunate to attend Julian Schwinger’s courses at Harvard University just after he had perfected his treatment of quantum field theory. 2 2. J. Schwinger, Ann. Phys. 2, 407 (1957). https://doi.org/10.1016/0003-4916(57)90015-5 I sat enthralled throughout the three-year series (1956–59), in which Schwinger developed QFT as a seemingly inevitable consequence of the most basic assumptions.However, I came away with a different understanding of QFT than David’s. I understood that the fields are physical properties of space that are described by field strengths—just as in classical physics, except that in QFT the state of the field at each point is represented by a vector in Hilbert space rather than by a pure number. That use of Hilbert space, which followed naturally from Schwinger’s “measurement algebra,” allows superpositions of values. The operators in Hilbert space, as I understood it, are mathematical tools that describe the evolution of the state vectors, and they are not to be reified.When I saw how QFT resolves the paradoxes of modern physics, it became irresistible. The special relativity paradoxes—for example, Lorentz contraction and time dilation—are a natural result of the way fields behave. 3 3. J. Schwinger wrote a six-part series on the theory of quantized fields: Phys. Rev. 82, 914 (1951); 91, 713 (1953); https://doi.org/10.1103/PhysRev.82.914 91, 728 (1953); 92, 1283 (1953); 93, 615 (1954); 94, 1362 (1954). The spacetime curvature of general relativity, which I could never really visualize, does not exist in QFT; the gravitational field equations are equivalent to spacetime curvature for those who can visualize it, but equivalent is not the same as identical. 4 4. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972), pp. vii–147. Finally, the mysterious wave–particle duality of quantum mechanics vanishes; in QFT, reality consists of fields and only fields.Because QFT is so neglected by the public (and by many physicists), I am writing a book that presents it without equations. A draft copy of the work, The Theory That Escaped Einstein, can be found through an internet search. Feedback is appreciated.For those who can’t kick the reification habit, QFT is the way to go. It is the only theory that offers a consistent and visualizable picture of reality. Reifiers of the world, unite! You have nothing to lose but your abstractions.REFERENCESSection:ChooseTop of pageREFERENCES <<1. H. Boorse, L. Motz, eds., The World of the Atom, Basic Books, New York (1966), p. 319. Google Scholar2. J. Schwinger, Ann. Phys. 2, 407 (1957). https://doi.org/10.1016/0003-4916(57)90015-5 , Google ScholarCrossref, ISI3. J. Schwinger wrote a six-part series on the theory of quantized fields: Phys. Rev. 82, 914 (1951); 91, 713 (1953); https://doi.org/10.1103/PhysRev.82.914 , Google ScholarCrossref, ISI 91, 728 (1953); , Google Scholar 92, 1283 (1953); Google Scholar 93, 615 (1954); Google Scholar 94, 1362 (1954). Google Scholar4. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972), pp. vii–147. Google Scholar© 2009 American Institute of Physics.
From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician. Sir James Jeans, Mysterious Universe Now that we have the mathematical and physical preliminaries under our belt, we can move on to the nuts and bolts of quantum computing. At the heart of a classical computer is the notion of a bit and at the heart of quantum computer is a generalization of the concept of a bit called a qubit, which shall be discussed in Section 5.1. In Section 5.2, classical (logical) gates, which manipulate bits, are presented from a new and different perspective. From this angle, it is easy to formulate the notion of quantum gates, which manipulate qubits. As mentioned in Chapters 3 and 4, the evolution of a quantum system is reversible, i.e., manipulations that can be done must also be able to be undone. This “undoing” translates into reversible gates, which are discussed in Section 5.3. We move on to quantum gates in Section 5.4. Reader Tip . Discussion of the actual physical implementation of qubits and quantum gates is dealt with in Chapter 11. BITS AND QUBITS What is a bit ? Definition 5.1.1 A bit is a unit of information describing a two-dimensional classical system . There are many examples of bits: ▪ A bit is electricity traveling through a circuit or not (or high and low). ▪ A bit is a way of denoting “true” or “false.” […]