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Reliable quantum computers
 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
, 1998
"... The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mist ..."
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Cited by 127 (3 self)
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The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantum computer storing about 106 qubits, with a probability of error per quantum gate of order 106, would be a formidable factoring engine. Even a smaller lessaccurate quantum computer would be able to perform many useful tasks. This paper is based on a talk presented at the ITP Conference on Quantum Coherence
A functional quantum programming language
 In: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
, 2005
"... This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are inte ..."
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Cited by 47 (12 self)
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This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive operational semantics of irreversible quantum computations, realisable as quantum circuits. The quantum circuit model is also given a formal categorical definition via the category FQC. QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings, which may lead to the collapse of the quantum wavefunction, explicit. Strict programs are free from measurement, and hence preserve superpositions and entanglement. A denotational semantics of QML programs is presented, which maps QML terms
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 42 (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.
Quantum Mechanics Of Lattice Gas Automata I. One Particle Plane Waves And Potentials
, 1996
"... Classical lattice gas automata effectively simulate physical processes such as diffusion and fluid flow (in certain parameter regimes) despite their simplicity at the microscale. Motivated by current interest in quantum computation we recently defined quantum lattice gas automata; in this paper we i ..."
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Cited by 35 (10 self)
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Classical lattice gas automata effectively simulate physical processes such as diffusion and fluid flow (in certain parameter regimes) despite their simplicity at the microscale. Motivated by current interest in quantum computation we recently defined quantum lattice gas automata; in this paper we initiate a project to analyze which physical processes these models can effectively simulate. Studying the single particle sector of a one dimensional quantum lattice gas we find discrete analogues of plane waves and wave packets, and then investigate their behaviour in the presence of inhomogeneous potentials.
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 24 (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 ...
Building quantum wires: the long and the short of it
 In Proc. International Symposium on Computer Architecture (ISCA 2003
, 2003
"... As quantum computing moves closer to reality the need for basic architectural studies becomes more pressing. Quantum wires, which transport quantum data, will be a fundamental component in all anticipated silicon quantum architectures. In this paper, we introduce a quantum wire architecture based up ..."
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Cited by 22 (8 self)
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As quantum computing moves closer to reality the need for basic architectural studies becomes more pressing. Quantum wires, which transport quantum data, will be a fundamental component in all anticipated silicon quantum architectures. In this paper, we introduce a quantum wire architecture based upon quantum teleportation. We compare this teleportation channel with the traditional approach to transporting quantum data, which we refer to as the swapping channel. We characterize the latency and bandwidth of these two alternatives in a deviceindependent way and describe how the advanced architecture of the teleportation channel overcomes a basic limit to the maximum communication distance of the swapping channel. In addition, we discover a fundamental tension between the scale of quantum effects and the scale of the classical logic needed to control them. This “pitchmatching ” problem imposes constraints on minimum wire lengths and wire intersections, which in turn imply a sparsely connected architecture of coarsegrained quantum computational elements. This is in direct contrast to the “sea of gates ” architectures presently assumed by most quantum computing studies. 1
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
The Effect of Communication Costs in SolidState Quantum Computing Architectures
, 2003
"... Quantum computation has become an intriguing technology with which to attack difficult problems and to enhance system security. Quantum algorithms, however, have been analyzed under idealized assumptions without important physical constraints in mind. In this paper, we analyze two key constraints: t ..."
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Cited by 13 (3 self)
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Quantum computation has become an intriguing technology with which to attack difficult problems and to enhance system security. Quantum algorithms, however, have been analyzed under idealized assumptions without important physical constraints in mind. In this paper, we analyze two key constraints: the short spatial distance of quantum interactions and the short temporal life of quantum data. In particular, quantum computations must make use of extremely robust error correction techniques to extend the life of quantum data. We present optimized spatial layouts of quantum error correction circuits for quantum bits embedded in silicon. We analyze the complexity of error correction under the constraint that interaction between these bits is near neighbor and data must be propagated via swap operations from one part of the circuit to another. We discover two interesting results from our quantum layouts. First, the recursive nature of quantum error correction circuits requires a additional communication technique more powerful than nearneighbor swaps – too much error accumulates if we attempt to swap over long distances. We show that quantum teleportation can be used to implement recursive structures. We also show that the reliability of the quantum swap operation is the limiting factor in solidstate quantum computation.
Quantum computing: Pro and con
 Proc. Royal Soc. London A
, 1997
"... I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; ..."
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Cited by 10 (0 self)
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I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed faulttolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in highprecision experimental physics. A broad interdisciplinary effort will be needed if quantum computers are to fulfil their destiny as the world's fastest computing devices. This paper is an expanded version of remarks that were prepared for a panel discussion
Toward a scalable, siliconbased quantum computing architecture
 JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS
, 2003
"... Advances in quantum devices have brought scalable quantum computation closer to reality. We focus on the systemlevel issues of how quantum devices can be brought together to form a scalable architecture. In particular, we examine promising siliconbased proposals. We discover that communication of ..."
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Cited by 8 (1 self)
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Advances in quantum devices have brought scalable quantum computation closer to reality. We focus on the systemlevel issues of how quantum devices can be brought together to form a scalable architecture. In particular, we examine promising siliconbased proposals. We discover that communication of quantum data is a critical resource in such proposals. We find that traditional techniques using quantum SWAP gates are exponentially expensive as distances increase and propose quantum teleportation as a means to communicate data over longer distances on a chip. Furthermore, we find that realistic quantum errorcorrection circuits use a recursive structure that benefits from using teleportation for longdistance communication. We identify a set of important architectural building blocks necessary for constructing scalable communication and computation. Finally, we explore an actual layout scheme for recursive error correction, and demonstrate the exponential growth in communication costs with levels of recursion, and that teleportation limits those costs.