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Parallelization, Amplification, and Exponential Time Simulation of Quantum Interactive Proof Systems
 In Proceedings of the 32nd ACM Symposium on Theory of Computing
, 2000
"... In this paper we consider quantum interactive proof systems, which are interactive proof systems in which the prover and verier may perform quantum computations and exchange quantum information. We prove that any polynomialround quantum interactive proof system with twosided bounded error can be p ..."
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Cited by 76 (19 self)
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In this paper we consider quantum interactive proof systems, which are interactive proof systems in which the prover and verier may perform quantum computations and exchange quantum information. We prove that any polynomialround quantum interactive proof system with twosided bounded error can be parallelized to a quantum interactive proof system with exponentially small onesided error in which the prover and verier exchange only 3 messages. This yields a simplied proof that PSPACE has 3message quantum interactive proof systems. We also prove that any language having a quantum interactive proof system can be decided in deterministic exponential time, implying that singleprover quantum interactive proof systems are strictly less powerful than multipleprover classical interactive proof systems unless EXP = NEXP. 1. INTRODUCTION Interactive proof systems were introduced by Babai [3] and Goldwasser, Micali, and Racko [17] in 1985. In the same year, Deutsch [10] gave the rst for...
The physical implementation of quantum computation
 Fortschr. Phys
, 2000
"... After a brief introduction to the principles and promise of quantum information processing, the requirements for the physical implementation of quantum computation are discussed. These five requirements, plus two relating to the communication of quantum information, are extensively explored and rela ..."
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Cited by 71 (0 self)
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After a brief introduction to the principles and promise of quantum information processing, the requirements for the physical implementation of quantum computation are discussed. These five requirements, plus two relating to the communication of quantum information, are extensively explored and related to the many schemes in atomic physics, quantum optics, nuclear and electron magnetic resonance spectroscopy, superconducting electronics, and quantumdot physics, for achieving quantum computing. 1.
Simulating quantum mechanics on a quantum computer
 PHYSICA D
, 1998
"... Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrödinger equation for interacting manybody systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quant ..."
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Cited by 51 (3 self)
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Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrödinger equation for interacting manybody systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quantum systems on a quantum computer with an exponential speedup compared to simulations on classical computers. Issues involved in simulating relativistic systems of Dirac or gauge particles are discussed.
Perfectly concealing quantum bit commitment from any quantum oneway permutation
, 2000
"... Abstract. We show that although unconditionally secure quantum bit commitment is impossible, it can be based upon any family of quantum oneway permutations. The resulting scheme is unconditionally concealing and computationally binding. Unlike the classical reduction of Naor, Ostrovski, Ventkatesen ..."
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Cited by 44 (8 self)
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Abstract. We show that although unconditionally secure quantum bit commitment is impossible, it can be based upon any family of quantum oneway permutations. The resulting scheme is unconditionally concealing and computationally binding. Unlike the classical reduction of Naor, Ostrovski, Ventkatesen and Young, our protocol is noninteractive and has communication complexity O(n) qubits for n a security parameter. 1
Approximation by Quantum Circuits
 and 68Q9529 at http://www.c3.lanl.gov/laces, Los Alamos National Laboratory
, 1995
"... In a recent preprint by Deutsch et al. [5] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on n qubits by 2qubit unitary operations. We address that comment by proving strong lower bounds on the approximation capabilities of gqubit unitary operati ..."
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Cited by 38 (4 self)
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In a recent preprint by Deutsch et al. [5] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on n qubits by 2qubit unitary operations. We address that comment by proving strong lower bounds on the approximation capabilities of gqubit unitary operations for fixed g. We consider approximation of unitary operations on subspaces as well as approximation of states and of density matrices by quantum circuits in several natural metrics. The ability of quantum circuits to probabilistically solve decision problem and guess checkable functions is discussed. We also address exact unitary representation by reducing the upper bound by a factor of n 2 and by formalizing the argument given by Barenco et al. [1] for the lower bound. The overall conclusion is that almost all problems are hard to solve with quantum circuits. 1 Introduction There has recently been great interest in the properties of quantum computation and quantum circuits, partly due...
Information and Computation: Classical and Quantum Aspects
 REVIEWS OF MODERN PHYSICS
, 2001
"... Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely ..."
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Cited by 36 (3 self)
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Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some outstanding aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as a few samples of the impact of quanta in the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement in information processing by a quantum computer. We provide finally some examples of current experimental
The Ion Trap Quantum Information Processor
 Appl. Phys. B
, 1997
"... An introductory review of the linear ion trap is given, with particular regard to its use for quantum information processing. The discussion aims to bring together ideas from information theory and experimental ion trapping, to provide a resource to workers unfamiliar with one or the other of these ..."
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Cited by 32 (2 self)
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An introductory review of the linear ion trap is given, with particular regard to its use for quantum information processing. The discussion aims to bring together ideas from information theory and experimental ion trapping, to provide a resource to workers unfamiliar with one or the other of these subjects. It is shown that information theory provides valuable concepts for the experimental use of ion traps, especially error correction, and conversely the ion trap provides a valuable link between information theory and physics, with attendant physical insights. Example parameters are given for the case of calcium ions. Passive stabilisation will allow about 200 computing operations on 10 ions; with error correction this can be greatly extended. 1
Prospects for Quantum Coherent Computation Using Superconducting Electronics
 IEEE Trans. Appl. Supercond
, 1997
"... We discuss the prospects and challenges for implementing a quantum computer using superconducting electronics. It appears that Josephson junction devices operating at milliKelvin temperatures can achieve a quantum dephasing time of milliseconds, allowing quantum coherent computations of 10 10 or ..."
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Cited by 32 (9 self)
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We discuss the prospects and challenges for implementing a quantum computer using superconducting electronics. It appears that Josephson junction devices operating at milliKelvin temperatures can achieve a quantum dephasing time of milliseconds, allowing quantum coherent computations of 10 10 or more steps. This figure of merit is comparable to that of atomic systems currently being studied for quantum computation. I. INTRODUCTION In quantum coherent computation information is coded not just as "1" and "0" but also as coherent superpositions of the "1" and "0" states of a quantum mechanical two state system. Recent experiments from atomic and optical physics have demonstrated the creation and manipulation of such quantum mechanical bits, socalled `qubits' [1][3], and consideration is being given to the prospects for constructing simple quantum computers. In this paper we will discuss the prospects for a superconducting electronics implementation of quantum computation. The great ...