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Journal of Optics B Quantum and Semiclassical Optics

Quantum Computing and the Feynman Festival

Howard E. Brandt, Young Shin Kim, Margarita A. Man’ko

Published Oct 16, 2003• 1 citation
Publisher

Abstract

The Feynman Festival is a new interdisciplinary conference developed for studying Richard Feynman and his physics. The first meeting of this new conference series was held at the University of Maryland on 23--28 August 2002 ( http://www.physics.umd.edu/robot/feynman.html ) and the second meeting is scheduled for August 2004 at the same venue. According to Feynman, the different aspects of nature are different aspects of the same thing. Therefore, the ultimate purpose of the conference is to find Feynman's same thing from all different theories. For this reason, the first meeting of the Festival did not begin with a fixed formula, but composed its scientific programme based on responses from the entire physics community. The conference drew the most enthusiastic response from the community of quantum computing, the field initiated by Feynman. Encouraged by the response, we decided to edit a special issue of Journal of Optics B: Quantum and Semiclassical Optics on quantum computing in connection with the first Feynman Festival. The authorship is not restricted to the participants of the Feynman Festival, and all interested parties were encouraged to submit their papers on this subject. Needless to say, all the papers were peer reviewed according to the well-established standards of the journal. The subject of quantum computing is not restricted to building and operating computers. It requires a deeper understanding of how quantum mechanics works in materials as well as in our minds. Indeed, it covers the basic foundations of quantum mechanics, measurement theory, information theory, quantum optics, atomic physics and condensed matter physics. It may be necessary to develop new mathematical tools to accommodate the language that nature speaks. It is gratifying to note that this special issue contains papers covering all these aspects of quantum computing. As Feynman noted, we could be discussing these diversified issues to study one problem. In our case, this `one problem' is to build quantum computers.

DOI
10.1088/1464-4266/5/6/e01

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The Feynman Festival is a new interdisciplinary conference developed for studying Richard Feynman and his physics. The first meeting of this new conference series was held at the University of Maryland on 23--28 August 2002 ( http://www.physics.umd.edu/robot/feynman.html ) and the second meeting is scheduled for August 2004 at the same venue. According to Feynman, the different aspects of nature are different aspects of the same thing. Therefore, the ultimate purpose of the conference is to find Feynman's same thing from all different theories. For this reason, the first meeting of the Festival did not begin with a fixed formula, but composed its scientific programme based on responses from the entire physics community. The conference drew the most enthusiastic response from the community of quantum computing, the field initiated by Feynman. Encouraged by the response, we decided to edit a special issue of Journal of Optics B: Quantum and Semiclassical Optics on quantum computing in connection with the first Feynman Festival. The authorship is not restricted to the participants of the Feynman Festival, and all interested parties were encouraged to submit their papers on this subject. Needless to say, all the papers were peer reviewed according to the well-established standards of the journal. The subject of quantum computing is not restricted to building and operating computers. It requires a deeper understanding of how quantum mechanics works in materials as well as in our minds. Indeed, it covers the basic foundations of quantum mechanics, measurement theory, information theory, quantum optics, atomic physics and condensed matter physics. It may be necessary to develop new mathematical tools to accommodate the language that nature speaks. It is gratifying to note that this special issue contains papers covering all these aspects of quantum computing. As Feynman noted, we could be discussing these diversified issues to study one problem. In our case, this `one problem' is to build quantum computers.
This Special Issue of Journal of Optics B: Quantum and Semiclassical Optics brings together contributions of various researchers working on theoretical and experimental aspects of quantum optics and quantum entanglement. The physics of quantum entangled states, an interdisciplinary field of research involving quantum optics, physics of quantum information and foundations of quantum theory, has been intensively exploited over the last decade in connection with quantum information processing, quantum communication and quantum computing. It was shown that the use of entangled states opens new horizons in such practical fields as cryptography, computing, information transmission, quantum imaging and precision measurements. Essential progress has also been achieved in the area of photon squeezing, generation of nonclassical states, including Schrödinger cats, trapped ions, Bose–Einstein condensates, cavity quantum electrodynamics, the Casimir effect, etc. These results have initiated applications in quantum information and communication, quantum imaging and quantum computing. This special issue is published in connection with the International Conference on Quantum Electronics (IQEC 2002) held on 26 June–1 July 2002, in Moscow, Russia, where the topics of quantum optics, generation and characterization of the entangled states and their applications were discussed in the framework of regular sections on quantum optics, quantum information and quantum computing, and during the special symposium on entangled states. We would like to express our gratitude to both authors and reviewers, for their efforts in preparing and ensuring the high scientific quality of the papers in this special issue. While the issue was in preparation for publication, one of the guest editors, Professor Anatoly Oraevski, suddenly passed away. He was a great scientist, recognized worldwide for his numerous important contributions to nonlinear and quantum optics, and to laser physics. Anatoly was always an enthusiastic advisor, mentor and collaborator. All of us remember numerous positive interactions with him, not only while organizing IQEC 2002 in Moscow last summer, but also throughout the years. He will be missed both for his scientific insight and because he was a good, kind and gentle man. Editing this special issue of Journal of Optics B: Quantum and Semiclassical Optics together with Professor Oraevski was our last joint effort and we would like to pay a tribute to him by dedicating this issue to his memory.
Quantum theory and quantum computing in recent years, has raised more and more increasing interest within the scientific community because of various reasons. First, the highly interdisciplinary nature of the subject which involves diverse topics such as, on the theoretical side, information theory and foundational issues of quantum mechanics and on the experimental side, the physics of quantum, optical, atomic and solid state systems. Secondly, the field is extremely promising for revolutionary technological implications in the near future. It is now perfectly clear that one can use quantum mechanics to process and transmit information in a way which does not have a classical analogue, and that using quantum techniques one can implement fully secure cryptographic systems. Recent breakthroughs, such as quantum teleportation, have led to extremely rapid progresses in a fascinating new field and, as a consequence, have attracted the interest of many scientists from varied disciplines. The purpose of this article is to provide a comprehensive overview about the deep involvement of quantum theory in quantum computation to young researchers and newcomers in the field.
The conference brings together researchers working on mathematical foundations of quantum physics, quantum computing, and related areas, with a focus on structural perspectives and the use of logical tools, ordered algebraic and category-theoretic structures, formal languages, semantically methods, and other computer science techniques applied to the study of physical behaviour in general. Work that applies structures and methods inspired by quantum theory to other fields (including computer science) is also welcome. With members from around the world focused on Quantum physics and Nuclear Engineering this is your best opportunity to reach the largest assemblage of participants from the universities, colleges, research centres, societies, institutions, labs, associations, communities and companies etc. We want to make a worldwide meet in which data between researchers from the different controls can be effectively traded. The explanation behind bringing the general population at the meetings together is to catalyse empowering trades and connections between experts in different fields, from physical science to engineering. It will make new interdisciplinary systems and permit members to trade know-how and data to accomplish speedier and better results.
The Wigner Centennial Conference was held in Pécs, Hungary, on 8–12 July 2002. Eugene Paul Wigner was born in Budapest on 17 November 1902 and left us on 1 January 1995 in Princeton, USA. Numerous other conferences and conference sessions were also held during 2002 to commemorate the centennial year of his birth, because so many wished to pay tribute to him. It would, of course, take a major international effort to review thoroughly all the contributions Wigner made in all branches of physics and for the cause of world peace. The purpose of the Wigner Centennial Conference was to enrich and enhance the research lines initiated by Wigner. The conference was particularly interested in assembling young researchers who will develop and expand those research lines in the future. Indeed, there were many papers of current interest, including symmetry problems in quantum mechanics and quantum field theory, group theoretical issues, foundations of quantum mechanics, nuclear physics, chemical physics, the phase-space formulation of quantum mechanics, as well as quantum computing, information and entanglement problems. In 1932 Wigner published a seminal paper entitled 'On the quantum correction for thermodynamic equations' ( Phys. Rev. 40 749--759) in which he introduced a fundamental tool for quantum mechanics known these days as the Wigner function. The Wigner function has a long history, but began to gain its major strength in quantum optics during the 1970s. Since then, it has become the primary scientific language for squeezed states of light dealing with multi-photon coherent states. The Wigner function is also the basic language for transition from classical to quantum mechanics through phase-space. It therefore plays a major role in detecting quantum effects in processes routinely regarded as classical. Indeed, most optical instruments have been based on classical optics; it is, however, a great challenge to find quantum effects in those devices. This itself is an important subject. Wigner initially formulated the Wigner function to understand thermodynamic effects in physical systems, and thus it plays an important role in studying entropy in measurement processes, statistical mechanics and chemical physics. Physicists do not seem to fully appreciate the fact that Wigner functions can be used for the purpose of group representations. For instance, the single-mode and two-mode squeezed states are isomorphic to the Lorentz groups O(2,1) and O(3,2), respectively. This can be done very cleanly within the framework of the Wigner phase-space approach. By combining two of Wigner's main research areas, namely group theory and the Wigner function, we can construct a very rich field of physics. This is a future possibility for today's young physicists. Turning to computing, a man or woman is born with ten fingers, which constitute a natural computer based on decimal numbers. Indeed, the Chinese developed an abacus for dealing with decimal numbers. Slide rules perform additions, but they can do multiplications in the logarithmic scale. In the 1940s, another Hungarian scientist named John von Neumann observed that vacuum tubes could perform 'yes or no' logic. His observation led to the computer age in which we live. It is interesting to note that both Wigner and von Neumann came from the same high school in Hungary, the Budapest Evangelikus Gimnazium. Likewise, Eugene Wigner began to worry about the language that atoms speak even before the present form of quantum mechanics was formulated. He published in 1929 a book entitled 'Group Theory and its Applications to Quantum Mechanics of Atomic Spectra'. This is, in fact, the first book on quantum computing. Physicists do not yet seem to appreciate this aspect of Wigner's contribution, but eventually they will. If we are seriously interested in building quantum computers, we should use atoms. We should then develop mathematical algorithms to use group theory of atomic spectra for numerical computation. This is what Wigner left to us as a homework. The Wigner Centennial Conference was dedicated to Wigner's future rather than to his past. Indeed, we are very happy to note that many young physicists presented their new research results at this conference. We regret that this special issue cannot include all the subjects covered at the Conference. We are, however, very fortunate to have so many excellent papers on Wigner functions, quantum optics and quantum information, as well as quantum computing. The special issue is not meant to be the conference proceedings. The papers included here have been refereed according to the standards of Journal of Optics B: Quantum and Semiclassical Optics and publication was not restricted to the participants of the Conference. This is indeed a special issue dedicated to the above-mentioned subjects.
In 1981, Richard Feynman proposed a device called a "quantum computer" to take advantage of the laws of quantum physics to achieve computational speed-ups over classical methods. Quantum computing promises to revolutionize how and what we compute. Over the course of three decades, quantum algorithms have been developed that offer fast solutions to problems in a variety of fields including number theory, optimization, chemistry, physics, and materials science. Quantum devices have also significantly advanced such that components of a scalable quantum computer have been demonstrated; the promise of implementing quantum algorithms is in our near future. I will attempt to explain some of the mysteries of this disruptive, revolutionary computational paradigm and how it will transform our digital age.