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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 46 (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
On universal and faulttolerant quantum computing: a novel basis and a new constructive proof of universality for Shor’s basis
 In Proceedings of the 40th Annual Symposium on Foundations of Computer Science
, 1999
"... A novel universal and faulttolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two singlequbit gates 1 (Hadamard and σz 4), and one doublequbit gate (ControlledNOT). ..."
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Cited by 26 (1 self)
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A novel universal and faulttolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two singlequbit gates 1 (Hadamard and σz 4), and one doublequbit gate (ControlledNOT). Since the set consisting of ControlledNOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of π) singlequbit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and faulttolerant basis proposed in [25, 17]. 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 23 (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 21 (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
An evaluation framework and instruction set architecture for iontrap based quantum microarchitectures
 In Proc. 32nd Annual International Symposium on Computer Architecture
, 2005
"... The theoretical study of quantum computation has yielded efficient algorithms for some traditionally hard problems. Correspondingly, experimental work on the underlying physical implementation technology has progressed steadily. However, almost no work has yet been done which explores the architectu ..."
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Cited by 21 (1 self)
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The theoretical study of quantum computation has yielded efficient algorithms for some traditionally hard problems. Correspondingly, experimental work on the underlying physical implementation technology has progressed steadily. However, almost no work has yet been done which explores the architecture design space of large scale quantum computing systems. In this paper, we present a set of tools that enable the quantitative evaluation of architectures for quantum computers. The infrastructure we created comprises a complete compilation and simulation system for computers containing thousands of quantum bits. We begin by compiling complete algorithms into a quantum instruction set. This ISA enables the simple manipulation of quantum state. Another tool we developed automatically transforms quantum software into an equivalent, faulttolerant version required to operate on real quantum devices. Next, our infrastructure transforms the ISA into a set of lowlevel micro architecture specific control operations. In the future, these operations can be used to directly control a quantum computer. For now, our simulation framework quickly uses them to determine the reliability of the application for the target micro architecture. Finally, we propose a simple, regular architecture for iontrap based quantum computers. Using our software infrastructure, we evaluate the design trade offs of this micro architecture. 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 12 (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.
New trends in quantum computing
 Proceedings of 13th 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
Implementation of Grover’s quantum search algorithm in a scalable system
 Phys. Rev. A
, 2005
"... For my mom and dad ii ACKNOWLEDGEMENTS My graduate school experience here at Michigan has been amazing and that is due, in large part, to the people that I have met and the friends that I have made along the way. First and foremost I need to thank Chris for letting me work in his lab, Chris, thank y ..."
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Cited by 7 (1 self)
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For my mom and dad ii ACKNOWLEDGEMENTS My graduate school experience here at Michigan has been amazing and that is due, in large part, to the people that I have met and the friends that I have made along the way. First and foremost I need to thank Chris for letting me work in his lab, Chris, thank you so much. In my six years here I have learned more than I could have possibly imagined. When I look back to when I first joined the lab, compared to where I am now the difference, in my mind at least, is unreal. In your lab I had the opportunity to learn about so many different aspects of experimental physics, from microwave sources, to optics and lasers, to atomic physics. Thank you for all of the opportunities you have given me and for supporting me along the way. I feel well prepared for whatever my physics future holds and I am truly grateful. Next I need to thank all my collegues especially Louis, Patty, and Paul with whom I worked and from whom I learned the most. Louis and Patty, thank you for showing
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
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 7 (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.