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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 23 (2 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
Quantum Computation
 In Annual Review of Computational Physics VI, D. Stauffer, Ed., World Scientific
, 1999
"... In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically powerful computational tool, capable of performing tasks which seem ..."
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Cited by 17 (0 self)
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In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically powerful computational tool, capable of performing tasks which seem intractable for classical computers. This review is about to tell the story of theoretical quantum computation. I left out the developing topic of experimental realizations of the model, and neglected other closely related topics which are quantum information and quantum communication. As a result of narrowing the scope of this paper, I hope it has gained the benefit of being an almost self contained introduction to the exciting field of quantum computation. The review begins with background on theoretical computer science, Turing machines and Boolean circuits. In light of these models, I define quantum computers, and discuss the issue of universal quantum gates. Quantum algorithms, including Shor’s factorization algorithm and Grover’s algorithm for searching databases, are explained. I will devote much attention to understanding what the origins of the quantum computational power are, and what the limits of this power are. Finally, I describe the recent theoretical results which show that quantum computers maintain their complexity power even in the presence of noise, inaccuracies and finite precision. This question cannot be separated from that of quantum complexity, because any realistic model will inevitably be subject to such inaccuracies. I tried to put all results in their context, asking what the implications to other issues in computer science and physics are. In the end of this review I make these connections explicit, discussing the possible implications of quantum computation on fundamental physical questions, such as the transition from quantum to classical physics. 1
Twoqubit projective measurements are universal for quantum computation
"... Nielsen showed in quantph/0108020 that universal quantum computation can be performed using projective measurements, quantum memory, and preparation of the 0 〉 state. Furthermore, 4qubit measurements are sufficient. Fenner and Zhang showed in quantph/0111077 that 3qubit measurements are suffici ..."
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Cited by 16 (0 self)
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Nielsen showed in quantph/0108020 that universal quantum computation can be performed using projective measurements, quantum memory, and preparation of the 0 〉 state. Furthermore, 4qubit measurements are sufficient. Fenner and Zhang showed in quantph/0111077 that 3qubit measurements are sufficient. We prove that 2qubit measurements are sufficient, closing the gap between the upper and lower bound of the number of qubits to be measured jointly. We conclude with some open questions. 1 Introduction and previous work Studying the resources required for universal quantum computation is important not only for its realization but also for our theoretical understanding of what makes it so powerful. In the predominant standard quantum circuit model [1], it suffices to prepare the 0 〉 state, to measure individual qubits in the computation basis, and to well approximate any unitary gate. Any unitary gate
A simple proof that Toffoli and Hadamard are quantum universal
 IN QUANTPH/0301040
, 2003
"... Recently Shi [15] proved that Toffoli and Hadamard are universal for quantum computation. This is perhaps the simplest universal set of gates that one can hope for, conceptually; It shows that one only needs to add the Hadamard gate to make a ’classical ’ set of gates quantum universal. In this note ..."
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Cited by 13 (1 self)
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Recently Shi [15] proved that Toffoli and Hadamard are universal for quantum computation. This is perhaps the simplest universal set of gates that one can hope for, conceptually; It shows that one only needs to add the Hadamard gate to make a ’classical ’ set of gates quantum universal. In this note we give a few lines proof of this fact relying on Kitaev’s universal set of gates [11], and discuss the meaning of the result.
New Trends in Quantum Computation
 in Proceedings of the 13 th Annual Symposium on Theoretical Aspects of Computer Science
, 1996
"... Abstract. Classical and quantum information are very different. Together they can perform feats that neither could achieve alone, such as quantum computing, quantum cryptography and quantum teleportation. Some of the applications range from helping to preventing spies from reading private communicat ..."
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Cited by 7 (3 self)
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Abstract. Classical and quantum information are very different. Together they can perform feats that neither could achieve alone, such as quantum computing, quantum cryptography and quantum teleportation. Some of the applications range from helping to preventing spies from reading private communications. Among the tools that will facilitate their implementation, we note quantum purification and quantum error correction. Although some of these ideas are still beyond the grasp of current technology, quantum cryptography has been implemented and the prospects are encouraging for smallscale prototypes of quantum computation devices before the end of the millennium. 1
Quantum information processing: cryptography, computation, and teleportation
 Proceedings of the IEEE
, 1996
"... Present information technology is based on the laws of classical physics. However, advances in quantum physics have stimulated interest in its potential impact on such technology. This article is a reasonably introductory review of three aspects of quantum information processing, cryptography, compu ..."
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Cited by 7 (0 self)
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Present information technology is based on the laws of classical physics. However, advances in quantum physics have stimulated interest in its potential impact on such technology. This article is a reasonably introductory review of three aspects of quantum information processing, cryptography, computation, and feleportation. In order to give a level of selfcontainment, I serve up hors d ' oeuvres on the relevant parts of quantum physics and the sorts of quantum systems which might form the building blocks for quantum processors. Quantum cryptography utilizes states of individual quantum systems for the transfer of conventional classical bits of information. The impossibility of measuring quantum systems without disturbing them guarantees the detection of eavesdropping and hence secure information transfer is possible. In a sense, tdeportation is the inverse of cryptography, using more robust classical bits to faithfully transfer a quantum state through a noisy environment. Quantum computation utilizes the evolving quantum state of a complex system. which consists of many interacting individuals. If such a machine could be built, it would be capable of solving some problems which are intractable on any conventional computer; I illustrate this with Shor's quantum factoring algorithm. I give some details of the current experimental achievements, proposals, and prospects for the future and of the patents granted to date. L
Encoded universality in physical implementations of a quantum computer
 in Proceedings of the 1st International Conference on Experimental Implementations of Quantum Computation
, 2001
"... We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., singlequbit operations and CNOT), we focus on the intrinsic ability of a system to act as a universal quantum computer ..."
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Cited by 5 (3 self)
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We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., singlequbit operations and CNOT), we focus on the intrinsic ability of a system to act as a universal quantum computer using only its naturally
SELFTESTING OF UNIVERSAL AND FAULTTOLERANT SETS OF QUANTUM GATES
, 2007
"... We consider the design of selftesters for quantum gates. A selftester for the gates F 1,...,F m is a procedure that, given any gates G1,...,Gm, decides with high probability if each Gi is close to F i. This decision has to rely only on measuring in the computational basis the effect of iterating ..."
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Cited by 4 (2 self)
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We consider the design of selftesters for quantum gates. A selftester for the gates F 1,...,F m is a procedure that, given any gates G1,...,Gm, decides with high probability if each Gi is close to F i. This decision has to rely only on measuring in the computational basis the effect of iterating the gates on the classical states. It turns out that, instead of individual gates, we can design only procedures for families of gates. To achieve our goal we borrow some elegant ideas of the theory of program testing: We characterize the gate families by specific properties, develop a theory of robustness for them, and show that they lead to selftesters. In particular we prove that the universal and faulttolerant set of gates consisting of a Hadamard gate, a cNOT gate, and a phase rotation gate of angle π/4 is selftestable.