W. G. Unruh, "Maintaining coherence in quantum computers", Phys. Rev. A 51, 992 (1995).  Home/Search   Document Not in Database   Summary   APS   Related Articles   Check

....a laboratory will necessarily be subject to the combined in uence of environmental noise and unavoidable imprecisions in the preparation, manipulation, and measurement of quantum mechanical states, reliable storage of quantum information will prove to be a daunting challenge. Indeed, some authors [95, 139] found that circuit based quantum computation (i.e. a temporal sequence of local unitary transformations, or quantum gates [8] is extremely vulnerable to noisy perturbations. The same noisy perturbations will also adversely a ect information stored in quantum registers (e.g. between successive ....

W.G. Unruh, \Maintaining coherence in quantum computers," Phys. Rev. A 51, 992 (1995).

.... to be more powerful than classical computation, due to oracle results[64, 9] and Shor s algorithm[61] It is yet unclear whether and how quantum computers will be physically realizable, 49, 25, 18] but as any physical system, they in principle will be subjected to noise, such as decoherence[75, 71, 53], and inaccuracies. Without error corrections, the e ect of noise can accumulate and ruin the entire computation[71, 16] hence the computation must be protected. Even the simpler question of protecting quantum information is harder than the classical analog because one must also protect the ....

....whether and how quantum computers will be physically realizable, 49, 25, 18] but as any physical system, they in principle will be subjected to noise, such as decoherence[75, 71, 53] and inaccuracies. Without error corrections, the e ect of noise can accumulate and ruin the entire computation[71, 16], hence the computation must be protected. Even the simpler question of protecting quantum information is harder than the classical analog because one must also protect the quantum correlations between the quantum bits (qubits) However, it was shown [12, 67] that good quantum error correcting ....

Unruh W G, Maintaining coherence in quantum computers, Phys. Rev. A, 51:992{ 997, 1995.

....9] but as any physical system, they in principle will not be ideally isolated, and will to some extant interact with their environment. Such interaction causes the state of the computer to be interwound, or entangled, with the state of the environment, a process called decoherence [18, 17, 14]. A real challenge to the polynomial church thesis would come from decohered quantum computers. Early works[5] showed that the effects of decoherence on the quantum computation can not be ignored, and that decoherence may limit the applicability of quantum algorithms. Thus, understanding the ....

....medium claims to compute a function fault tolerantly, it is supposed to compute it when subjected to any fault. The second, and maybe more significant reason, is that it is reasonable to assume that every physical realization of quantum computers will be subjected to some extent to collapses[17]. We present a simulation of a quantum medium subjected to single qubit collapses, on a classical probabilistic Turing machine. The simulation chooses, with the appropriate probability, a fault path. Then it keeps track of the development in time of the density matrix of the medium according to ....

W. G. Unruh. Maintaining coherence in quantum computers. Technical report, University of Vancouver, 1994. quant-ph/9406058.

....each other and the universe, a phenomenon called decoherence, see for example [27] The larger the scale of the coherent superposition the faster decoherence. Of course, the gain one hopes to make with quantum computing over classical computing must come out of the scale of the superposition. In [21] it is calculated that that CQC calculations using physical realizations based on spin lattices will have to be finished in an extremely short time. For example, factoring a 1000 bit number in square quantum factoring time we have to perform 10 6 steps in less than the thermal time scale h=kT ....

Unruh, W. G., Maintaining coherence in quantum computers, Physical Review A, 51(1995), 992--.

....Park, CA, 1987) W97] Wetmur, J. G. Physical Chemistry of Nucleic Acid Hybridize, 3rd DIMACS Meeting on DNA Based Computers, Univ. of Penns. June, 1997) WW95] Williams, R.M. and David H. Wood, Computational algebras for RNA processes, Gene Finding and Gene Structure Prediction Workshop, Unrefereed poster presentation, 1995). WW96] Williams, R.M. and David H. Wood, Exascale Computer Algebra Problems Interconnect with Molecular Reactions and Complexity Theory, The 2nd Annual Workshop on DNA Based Computers, American Mathematical Society, June, 1996. W95] Winfree, E. Complexity of Restricted and Unrestricted ....

W.G. Unruh. Maintaining coherence in quantum computers, Physical Review Letters A, 51:992-997, 1995.

....that if the errors are not corrected during quantum computation, they soon accumulate and ruin the entire computation[57, 58, 17, 149] Hence, a method to correct the effect of quantum noise is necessary. Physicists were pessimistic about the question of whether such a correction method exists[135, 189]. The reason is that quantum information in general cannot be cloned[83, 200, 20] and so the information cannot be simply protected by redundancy, as is done classically. Another problem is that in contrast to the discreteness of digital computers, a quantum system can be in a superposition of ....

....we understand some of the limitations and advantages of the quantum model, let us go on to the subject of quantum noise. 11 Worries about Decoherence, Precision and Inaccuracies Learning about the possibilities which lie in quantum computation gave rise to a lot of enthusiasm, but many physicist[135, 189, 57, 19] were at the same time very sceptic about the entire field. The reason was that all quantum algorithms achieve their advantage over classical algorithms when assuming that the gates and wires operate without any inaccuracies or errors. Unfortunately, in reality we cannot expect any system to be ....

Unruh W G, Maintaining coherence in quantum computers, Phys. Rev. A, 51:992--997, 1995.

.... have been made as to possible designs for such computers [Teich et al. 1988, Lloyd 1993, 1994a, Cirac and Zoller 1995, DiVincenzo 1995, Sleator and Weinfurter 1995, Barenco et al. 1995b, Chuang and Yamomoto 1995] but there will be substantial difficulty in building any of these [Landauer 1995, Unruh 1995, Chuang et al. 1995, Palma et al. 1995] The most difficult obstacles appear to involve the decoherence of quantum superpositions through the interaction of the computer with the environment, and the implementation of quantum state transformations with enough precision to give accurate results ....

....completing t steps of computation successfully. This holds not only for the simple model of decoherence where each bit has a fixed probability of decohering at each time step, but also for more complicated models of decoherence which are derived from fundamental quantum mechanical considerations [Unruh 1995, However, building quantum computers with high enough precision and low enough decoherence to accurately perform long computations may present formidable difficulties to experimental physicists. In classical computers, error probabilities can be reduced not only though hardware but also ....

W. G. Unruh (1995) "Maintaining coherence in quantum computers," Phys. Rev. A 51, 992--997.

....gate constructions. Some of the results presented here have no obvious connection with previous gate assembly schemes. We will not touch at all on the great difficulties attendant on the actual physical realization of a quantum computer the problems of error correction[36] and quantum coherence[37, 38] are very serious ones. We refer the reader to [39] for a comprehensive discussion of these difficulties. 2 Introduction We begin by introducing some basic ideas and notation. For any unitary U = u 00 u 01 u 10 u 11 ; and m 2 f0; 1; 2; g, define the (m 1) bit (2 (m 1) ....

W. G. Unruh, "Maintaining coherence in quantum computers", Phys. Rev. A 51, 992 (1995).

.... out a computation are very sensitive to the imperfections of the hardware, and above all, to the decoherence[6] caused by interaction with the environment (by environment we mean all the degrees of freedom which can have unwanted interactions with the computer) This fragility of a quantum computer[7, 8, 9] is closely tied to its function: it acts as a sophisticated, nonlinear interferometer. The coherent interference pattern between the multitude of superpositions is essential for taking advantage of quantum parallelism, which is the key feature allowing one to explore aspects of an exponentially ....

W. G. Unruh. Maintaining coherence in Quantum Computers. hepth /9406058; Phys. Rev. A, 51:992, 1995.

....to realize because long range interactions have to be implemented on a submicroscopical level. The power of quantum computers with only local interactions is investigated in [Pe85, Fe85, Ma86, GZ88, Ma90, Bi93, Gr94, Gr95] For a critical discussion about the realizability of quantum computers see [Zu84, La86, La92, Un94a, Un94b, CZ95]. 2 The Feynman computer Consider a deterministic classical computer that consists of k gates, connected in a serial way, as depicted in figure 1. It passes through a number k of computational states until it displays a final result at the output of the last gate. We now want to model the same ....

W.G.Unruh (1994): "Maintaining coherence in quantum computers", submitted to Physical Review A.

....in polynomial time, Shor, 1994] with preliminary work in [Deutsch, 1985 1992, Bernstein and Vazirani, 1993, Simon, 1994] This result opened the vista of a veritable breakthrough in computing. There are apparently formidable obstacles to surmount before a workable technology can be obtained, [Unruh, 1995]. The QCC approach as first advocated in [Benioff, 1980 1986] is currently aimed to exploit the accepted theory that quantum evolution of an appropriate system consists in a superposition of many (potentially infinitely many) simultaneous computation paths. It is theoretically possible that ....

....to effect a high probability of eventually observing a desired outcome. Physical realizations of QCC will have to struggle with the fact that the coherent states of the superposition will tend to deteriorate by interaction with each other and the universe, a phenomenon called decoherence. In [Unruh, 1995] it is calculated that that QCC calculations using physical realizations based on spin lattices will have to be finished in an extremely short time. For example, factoring a 1000 bit number in square quantum factoring time we have to perform 10 6 steps in less than the thermal time scale h=kT ....

Unruh, W. G., Maintaining coherence in quantum computers, Physical Review A, 51(1995), 992-.

....depend on details of actual implementations, such as any additional operations required for controlling errors that cannot themselves be performed in parallel with the higher level steps of the algorithm. These remain significant issues in the development of quantum computation (Landauer, 1994; Unruh, 1995; Haroche Raimond, 1996; Monroe Wineland, 1996) but at this point seem unlikely to be fundamental difficulties (Berthiaume, Deutsch, Jozsa, 1994; Shor, 1995; Knill, Laflamme, Zurek, 1998) In particular, because the algorithm requires only a single step, decoherence is likely to be less ....

Unruh, W. G. (1995). Maintaining coherence in quantum computers. Physical Review A, 51, 992--997.

....the bit level routines needed for performing the steps in the high level program. Appendix A discusses how these bit level routines may be made highly space efficient, with only a modest increase in running time (these latter routines result in a smaller time space product, which may be desirable [7,8]) Appendix B provides other ways of economizing in the bit level implementation of these codes, by using some of the phase freedom coming from the quantum mechanical nature of the computation. II. COMBINATORIAL EXPRESSION FOR SCHUMACHER CODING As Bennett [6] has described, a specific ....

.... are used instead, the execution time is increased to 8 3 n 3 O(n 2:5 ) but the total number of qubits is reduced to n 2 p n O(log n) If the relevant figure of merit for the tractability of the quantum computation is the product of time and space, as it is in certain physical models [7,8], then the space efficient procedures we have introduced would be preferred. A final note about these operation counts: they are all in terms of the primitive operations listed at the beginning of Section IV, which includes both two and three bit primitives. It is known [10,18] that all three bit ....

W. G. Unruh, "Maintaining coherence in quantum computers", Phys. Rev. A 51, 992 (1995).

....which it operates. In the best cases, coherence is kept for some 10 4 seconds and in the worst cases, hardly 10 Gamma10 seconds. And these figures are for a single qubit only; some decoherence models show the decoherence time dropping exponentially as the number of qubits increases (see [Unr95] 28 Andr e Berthiaume and [MSE95] But keeping a qubit in quantum superposition is only part of the problem. A quantum computer will have to perform operations on that qubit. The time needed to perform an operation also depends on the medium used for a qubit and the conditions under which it ....

W. G. Unruh. Maintaining coherence in quantum computers. Physical Review Letters A, 51:992--997, 1995.

....quantum computers is maintaining coherence of the superposition of states long enough to complete the computation. Environmental noise gradually couples to the state of the device, reducing the coherence and eventually limiting the time over which a superposition can perform useful computations (Unruh, 1995; Chuang, Laflamme, Shor, Zurek, 1995) In effect, the coupling to the environment can be viewed as performing a measurement on the quantum system, destroying the superposition of states. This problem is particularly severe for proposed universal quantum computers that need to maintain ....

Unruh, W. G. (1995). Maintaining coherence in quantum computers. Physical Review A, 41, 992.

....nobody knows how to build a quantum computer, although it seems as though it could be possible within the laws of quantum mechanics. Some suggestions have been made as to possible designs for such computers [30, 22, 23, 12] but there will be substantial difficulty in building any of these [18, 32]. Even if it is possible to build small quantum computers, scaling up to machines large enough to do interesting computations could present fundamental difficulties. It is hoped that this paper will stimulate research on whether it is feasible to actually construct a quantum computer. Even if no ....

W. G. Unruh, "Maintaining coherence in quantum computers," Phys. Rev. A, Vol. 51, pp. 992--997 (1995).

....gate constructions. Some of the results presented here have no obvious connection with previous gate assembly schemes. We will not touch at all on the great difficulties attendant on the actual physical realization of a quantum computer the problems of error correction[33] and quantum coherence[34, 35] are very serious ones. We refer the reader to [36] for a comprehensive discussion of these difficulties. 2 Introduction We begin by introducing some basic ideas and notation. For any unitary U = u 00 u 01 u 10 u 11 ; and m 2 f0; 1; 2; g, define the (m 1) bit (2 (m 1) ....

W. G. Unruh, "Maintaining coherence in quantum computers", Phys. Rev. A 51, 992 (1995). (hep-th/9406058)

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W. G. Unruh, "Maintaining coherence in quantum computers", Phys. Rev. A 51, 992 (1995).

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W. G. Unruh, "Maintaining coherence in quantum computers", Phys. Rev. A 51, 992 (1995).

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Unruh W G, Maintaining coherence in quantum computers, Phys. Rev. A, 51:992--997, 1995.

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Unruh, W., Maintaining coherence in quantum computers, Phys. Rev. A, 51(1995), p. 992.

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W. G. Unruh. Maintaining coherence in Quantum Computers. hep-th/9406058; Phys. Rev. A, 51:992, 1995.

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W.G. Unruh. Maintaining coherence in quantum computers, Physical Review Letters A, 51:992-997, 1995.

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