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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
Optimal synthesis of multiple output Boolean functions using a set of quantum gates by symbolic reachability analysis
 IEEE Trans. on CAD of Integrated Circuits and Systems
, 2006
"... Abstract—This paper proposes an approach to optimally synthesize quantum circuits by symbolic reachability analysis, where the primary inputs and outputs are basis binary and the internal signals can be nonbinary in a multiplevalued domain. The authors present an optimal synthesis method to minimiz ..."
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Cited by 17 (3 self)
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Abstract—This paper proposes an approach to optimally synthesize quantum circuits by symbolic reachability analysis, where the primary inputs and outputs are basis binary and the internal signals can be nonbinary in a multiplevalued domain. The authors present an optimal synthesis method to minimize quantum cost and some speedup methods with nonoptimal quantum cost. The methods here are applicable to small reversible functions. Unlike previous works that use permutative reversible gates, a lower level library that includes nonpermutative quantum gates is used here. The proposed approach obtains the minimum cost quantum circuits for Miller gate, half adder, and full adder, which are better than previous results. This cost is minimum for any circuit using the set of quantum gates in this paper, where the control qubit of 2qubit gates is always basis binary. In addition, the minimum quantum cost in the same manner for Fredkin, Peres, and Toffoli gates is proven. The method can also find the best conversion from an irreversible function to a reversible circuit as a byproduct of the generality of its formulation, thus synthesizing in principle arbitrary multioutput Boolean functions with quantum gate library. This paper constitutes the first successful experience of applying formal methods and satisfiability to quantum logic synthesis. Index Terms—Formal verification, logic synthesis, model checking, quantum computing, reversible logic, satisfiability. I.
Principles and demonstrations of quantum information processing by NMR spectroscopy
 Applicable Algebra in Engineering, Communications and Computing
, 1998
"... Abstract. This paper surveys our recent research on quantum information processing by nuclear magnetic resonance (NMR) spectroscopy. We begin with a brief introduction to the product operator formalism, on which the theory of NMR spectroscopy is based, and use it throughout the rest of the paper to ..."
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Cited by 3 (2 self)
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Abstract. This paper surveys our recent research on quantum information processing by nuclear magnetic resonance (NMR) spectroscopy. We begin with a brief introduction to the product operator formalism, on which the theory of NMR spectroscopy is based, and use it throughout the rest of the paper to show how it provides an concise framework within which to analyze quantum computations and decoherence. The implementation of quantum algorithms by NMR depends upon the availability of special kinds of mixed states, called pseudopure states, and we consider a number of different methods for preparing pseudopure states, along with what is known about how they scale with the number of spins. The quantummechanical nature of processes involving such macroscopic pseudopure states also is a matter of debate, and we attempt to make this debate more concrete by presenting the results of NMR experiments which validate Hardy’s paradox, subject to certain assumptions that we explicitly state. Finally, a detailed product operator description is given of recent NMR experiments which demonstrate the principles behind a threebit quantum error correcting code. Portions of this survey were presented at the AeroSense Workshop on Photonic
Geometric quantum computation with NMR
 Nature
"... An exciting recent development has been the discovery that the computational power of quantum computers exceeds that of Turing machines [1]. The experimental realisation of the basic constituents of quantum information processing devices, namely faulttolerant quantum logic gates, is a central issue ..."
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An exciting recent development has been the discovery that the computational power of quantum computers exceeds that of Turing machines [1]. The experimental realisation of the basic constituents of quantum information processing devices, namely faulttolerant quantum logic gates, is a central issue. This requires conditional quantum dynamics, in which one subsystem undergoes a coherent evolution that depends on the quantum state of another subsystem [2]. In particular, the subsystem may acquire a conditional phase shift. Here we consider a novel scenario in which this phase is of geometric rather than dynamical origin [3,4]. As the conditional geometric (Berry) phase depends only on the geometry of the path executed it is resilient to certain types of errors, and offers the potential of an intrinsically faulttolerant way of performing quantum gates. Nuclear Magnetic Resonance (NMR) has already been used to demonstrate both simple quantum information processing [5–9] and Berry’s phase [10–12]. Here we report an NMR experiment which implements a conditional Berry phase, and thus a controlled phase shift gate. This constitutes the first elementary
Robust quantum information processing with techniques from liquid state NMR. arXive eprint quantph/0301019
, 2003
"... NMR ..."
Complete Quantum Teleportation By Nuclear Magnetic Resonance
, 1998
"... vide a complete reconstruction of the original object? No: all physical systems are ultimately quantum mechanical, and quantum mechanics tells us that it is impossible to completely determine the state of an unknown quantum system, making it impossible to use the classical measurement procedure to m ..."
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Cited by 2 (0 self)
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vide a complete reconstruction of the original object? No: all physical systems are ultimately quantum mechanical, and quantum mechanics tells us that it is impossible to completely determine the state of an unknown quantum system, making it impossible to use the classical measurement procedure to move a quantum system from one location to another. Bennett et al have suggested a remarkable procedure for teleporting quantum states. Quantum teleportation may be described abstractly in terms of two parties, Alice and Bob. Alice has in her possession an unknown state j\Psii = ffj0i + fij1i of a single quantum bit (qubit)  a two level quantum system. The goal of teleportation is to transport the state of that qubit to Bob. In addition, Alice and Bob each possess one qubit of a two qubit entangled state, j\Psii A (j0i A j0i B + j1i A j1i B ) ; (1) 2 where subscripts A are used to denote Alice's systems, and subscripts B to denote Bob's system. Here and throughout we omit overall norm
Nuclear Magnetic Resonance: a quantum technology for computation and spectroscopy
, 2000
"... In this article we consider nuclear magnetic resonance (NMR) as an example of a quantum technology; we consider in particular detail the implementation of quantum computers using NMR. We begin by outlining the physical principles underlying NMR, and give an introduction to the quantum mechanics invo ..."
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In this article we consider nuclear magnetic resonance (NMR) as an example of a quantum technology; we consider in particular detail the implementation of quantum computers using NMR. We begin by outlining the physical principles underlying NMR, and give an introduction to the quantum mechanics involved. We next discuss the general characteristics of quantum technologies and the ways and extent to which these characteristics are expressed in NMR. We then give an introduction to the subject of quantum computation and its implementation using NMR. Finally, we describe some spectroscopy techniques which also exploit the quantum nature of NMR. ∗ To whom correspondence may be addressed. 1 1
Quantum Computing is a TwoTrick Pony
, 1999
"... Two milestones in the brief history of quantum computation (QC) are Shor's algorithm for prime factorization and Grover's algorithm for database search, which yield exponential and square root complexity improvements respectively over their classical counterparts. This paper reviews these two alg ..."
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Two milestones in the brief history of quantum computation (QC) are Shor's algorithm for prime factorization and Grover's algorithm for database search, which yield exponential and square root complexity improvements respectively over their classical counterparts. This paper reviews these two algorithms, and discusses them in terms of generalized contexts which have come to light since their original presentation. The two algorithms are instances of two techniques the Fourier transform and amplitude amplication which are the basis of the eciency gains of many of today's QC algorithms. In at least one algorithm, the two techniques are used together.
FROM INTERFEROMETERS TO COMPUTERS
, 1998
"... Feynman [1] in his talk during the First Conference on the Physics of Computation held at MIT in Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradi ..."
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Feynman [1] in his talk during the First Conference on the Physics of Computation held at MIT in Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multiparticle) interferometers. We show how most known quantum algorithms, including quantum algorithms for factorizing and counting, may be cast in this manner, Quantum searching is described as inducing a desired relative phase between two eigenvectors to yield constructive interference on the sought elements and destructive interference on the remaining terms. 1981 observed that it appears to be impossible to simulate a general quantum evolution on a classical probabilistic computer in an efficient way. He pointed out that any classical simulation of quantum evolution appears to involve an exponential slowdown in time as compared to the natural evolution since the amount of information required to describe the evolving quantum state in classical terms generally grows exponentially in time. However, instead of viewing this as an obstacle, Feynman regarded it as an opportunity. If it requires so much computation to work out what will happen in a complicated multiparticle interference experiment, then, he argued, the very act of setting up such an experiment and measuring the outcome is tantamount to performing a complex computation. Indeed, all quantum multiparticle interferometers are quantum computers and some interesting computational problems can be based on estimating internal phase shifts in these interferometers. This approach leads to a unified picture of quantum algorithms and has been recently discussed in detail by Cleve. [2] Let us start with the textbook example of quantum interference, namely the doubleslit experiment, which, in a more rnodern version, can be rephrased in terms of MachZehnder interferometry
The fconditioned Phase Transform
, 2000
"... We present a quantum algorithm for the fconditioned phase transform which does not require any initialization of ancillary register. We also develop a quantum algorithm that can solve the generalized DeutschJozsa problem by a single evaluation of a function. 1 ..."
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We present a quantum algorithm for the fconditioned phase transform which does not require any initialization of ancillary register. We also develop a quantum algorithm that can solve the generalized DeutschJozsa problem by a single evaluation of a function. 1