C. P. Williams and S. H. Clearwater, Explorations in quantum computing, TELOS (Springer-Verlag New York, 1998).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....have been sought to relate those algorithms. The hidden subgroup problem [25] has been seen as a conceptually unifying principle whilst multi particle interference [6] has been proposed as a unifying principle closer to implementation. More pragmatically, several simulations have been proposed [1, 26, 31] at various levels of applicability. Not surprisingly we take the formal methods or MPC view that a derivation is worth a thousand simulations (or more ) Thus in an area containing subtle algorithms formal reasoning can be expected to come into its own. One approach would be to perform ....

Colin P. Williams and Scott H. Clearwater. Explorations in Quantum Computing. Springer-Verlag, New York, 1998.

....surprising, since these problems can usually be cast as optimization problems. It has been claimed that quantum computers will be able to solve many optimization problems thought to be intractable on today s digital computers due to the parallelism inherent in the superposition of quantum states [18]. Are quantum computers somehow immune to the NFLTs We claim they are not, and our argument goes like this. Consider a deterministic optimization problem, where we are trying to optimize a specific column of the F matrix, but we have no knowledge about which columns are feasible or which column ....

C. P. Williams and S. H. Clearwater, Explorations in Quantum Computing. New York: Springer-Verlag, 1997.

....the selected encoding. Preparation of superposition of states is of great interest in order to exploit its inherent parallelism. An example is the preparation in many particle qubit systems of entangled states, which o#er information manipulation that is not possible with the classical binary bits [23]. The most e#ective strategies in classical control applications involve feedback control. The implementation of classical feedback control for quantum systems, however, poses severe challenges since quantum measurements tend to destroy the state of the system (wave packet reduction) 24, 25] ....

C. Williams and S. Clearwater, Exploration in Quantum Computing, Springer -- Verlag, New York (1998). 8

....for the gates. Surveys of QC. The following are reviews and surveys have been made of QC: Bennett [BD95a, BD95b] Barenco [Bar96] Brassard [Bra96,Bra97,Bra98] Haroche, Raimond [HR96] Preskill [Pre97a] Scarani [Sca98] Steane [Ste98] Vedral, Plenio [VP98] Also, Williams and Clearwater [WC97] is the first text book in QC. Reif [R99a] also gives an extensive survey emphasizing quantum compression and information processing. 1.2 Quantum Compression Shannon Entropy and the Limitations of Classical Methods for Noiseless Compression. Suppose n characters from a finite alphabet Sigma ....

C.P. Williams and S.H. Clearwater, Explorations in Quantum Computing, Springer-Verlag, Yew York, (1997).

....for constant cost every two years or so 6 . We are more interested in the closely related physical forms of Moore s law, which state, for example, that the number of atoms needed to represent one bit of information should halve every two years or so. This prediction has, indeed, been borne out [50, 192] over the past thirty years. Extrapolating this trend, it has been predicted [192] that around the year 2020, bits will be stored in individual atoms. At that level, we would certainly expect quantum mechanical effects to become very important. Techniques for quantum control 7 , motivated in ....

....related physical forms of Moore s law, which state, for example, that the number of atoms needed to represent one bit of information should halve every two years or so. This prediction has, indeed, been borne out [50, 192] over the past thirty years. Extrapolating this trend, it has been predicted [192] that around the year 2020, bits will be stored in individual atoms. At that level, we would certainly expect quantum mechanical effects to become very important. Techniques for quantum control 7 , motivated in part by potential applications to quantum information processing, will be necessary ....

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C. P. Williams and S. H. Clearwater. Explorations in quantum computing. Springer-Verlag, New York, 1998.

....of quantum algorithms has attracted widespread interest. For those new to quantum computing Steane provides a good overview [7] Braunstein provides an accessible on line tutorial [8] Williams and Clearwater provide a text with a CD ROM containing Mathematica code for simulating quantum computers [9], and Milburn provides an introduction for the general reader [10] The widespread application of quantum computation presupposes the existence of both quantum computer hardware and quantum software that solves practical problems. But the development of quantum algorithms is not trivial. Williams ....

C. P. Williams and S. H. Clearwater, Explorations in Quantum Computing, Springer-Verlag, TELOS, 1997.

....E k P i = P i h i h i x j l ss i ( x j G i G i = 116 Modeling the dissipation this way, describes the relaxation of the coherence vector towards . 5. 2 An application of the coherence vector formalism: Quantum computing with Quantum dot Cellular Automata Quantum computing [58 90] has attracted attention in the last two decades because it was found that computers exploiting quantum mechanics are able to outperform classical digital computers in certain areas (factoring integers [83] searching [64,86] Beside designing and analyzing new quantum computing algorithms, ....

C. P. Williams and Scott H. Clearwater, Explorations in Quantum Computing (Springer, 1998).

.... and computational feats that are widely believed to be classically impossible [5, 9, 19, 23, 40, 53] as shown for example by the polynomial time quantum algorithm for integer factorization due to Shor [45] As a result, the field has now been the subject of numerous popular accounts, including [1, 11, 37, 60]. But despite these remarkable theoretical advances, one outstanding question remains: Can a fully programmable quantum computer actually be built Most approaches to this problem (loc. cit. have attempted to isolate a single submicroscopic system completely from its environment, so that it can ....

.... demonstration of a quantum error correcting code [14] This extension of the classical theory of error correction to quantum systems was developed in order to control decoherence in quantum computations [44, 52] which would otherwise destroy the coherences on which quantum algorithms depend [11, 60]. Such codes rely upon the fact that the e#ects of environmental interactions on the system can be completely described by a discrete stochastic process of the form # # # m pm Um # Um , 1.68) where pm # 0 are the probabilities with which the unitary operators Um are applied to the ....

C. P. Williams and S. H. Clearwater, Explorations in Quantum Computing, Springer-Verlag, New York, NY, 1998.

....of QC. The following are reviews and surveys have been made of QC: Bennett [BD95a, BD95b] Barenco [Bar96] Benio [Ben96] Brassard [Bra96,Bra98] Haroche, Raimond [HR96] Brassard [Bra97] Preskill [Pre97a] Scarani [Sca98] Steane [Ste98] Vedral, Plenio [VP98] Also, Williams and Clearwater [WC97] is the first text book in QC. Also, Taubes [Tau96] and Gershenfeld, Chuang [GC98] give popular press descriptions of QC. 1.3 Organization of this Paper. In this Section 1 we have introduced BMC and QC. In Section 3 we discuss resource bounds for BMC and QC, including time, volume, and energy. ....

C.P. Williams and S.H. Clearwater, Explorations in Quantum Computing, Springer-Verlag, Yew York, (1997).

.... of QC The following are reviews and surveys have been made of QC: Bennett [BD95a, BD95b] Barenco [Bar96] Benio [Ben96] Brassard [Bra96,Bra98] Haroche, Raimond [HR96] Brassard [Bra97] Preskill [Pre97a] Scarani [Sca98] Steane [Ste98] Vedral, Plenio [VP98] Also, Williams and Clearwater [WC97] is the first text book in QC. Also, Taubes [Tau96] and Gershenfeld, Chuang [GC98] give popular press descriptions of QC. 1.4 Initial Work in QC Benioff [Ben82] and Feynman [Fey86] were the first to suggest the use of quantum mechanical principles for doing computation. Deutsch and Jozsa ....

C.P. Williams and S.H. Clearwater, Explorations in Quantum Computing, Springer-Verlag, Yew York, (1997).

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C. P. Williams and S. H. Clearwater, Explorations in quantum computing, TELOS (Springer-Verlag New York, 1998).

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C. P. Williams and S. H. Clearwater, Explorations in Quantum Computing. Berlin, Germany: Springer-Verlag, 1998.

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C. P. Williams and S. H. Clearwater, Explorations in Quantum Computing. Berlin: Springer-Verlag, 1998.

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Williams, C. P. and Clearwarter, S. H. 1998 Explorations in Quantum Computing. Springer-Verlag New York, Inc.

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Colin P. Williams and Scott H. Clearwater, Explorations in Quantum Computing, Springer-Telos, 1997. 89

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C. P. Williams and S. H. Clearwater, Explorations in Quantum Computing, New York: Springer, 1997.

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Williams, Colin P., and Scott H. Clearwater, "Explorations in Quantum Computing," Springer-Verlag, (1998).

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