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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 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
QUANTUM STRATEGIES
, 1998
"... We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely related to the traditional MATCHING PENNIES game. While not eve ..."
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Cited by 38 (0 self)
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We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely related to the traditional MATCHING PENNIES game. While not every twoperson zerosum finite game has an equilibrium in the set of pure strategies, von Neumann showed that there is always an equilibrium at which each player follows a mixed strategy. A mixed strategy deviating from the equilibrium strategy cannot increase a player’s expected payoff. We show, however, that in our example a player who implements a quantum strategy can increase his expected payoff, and explain the relation to efficient quantum algorithms. We prove that in general a quantum strategy is always at least as good as a classical one, and furthermore that when both players use quantum strategies there need not be any equilibrium, but if both are allowed mixed quantum strategies there must be.
Molecular Scale Heat Engines and Scalable Quantum Computation
 IN 31ST STOC
, 1999
"... We describe a quantum mechanical heat engine. Like its classical counterpart introduced by Carnot, this engine carries out a reversible process in which an input of energy to the system results in a separation of cold and hot regions. The method begins with a reinterpretation in thermodynamic terms ..."
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Cited by 19 (2 self)
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We describe a quantum mechanical heat engine. Like its classical counterpart introduced by Carnot, this engine carries out a reversible process in which an input of energy to the system results in a separation of cold and hot regions. The method begins with a reinterpretation in thermodynamic terms of a simple step introduced by von Neumann to extract fair coin flips from sequences of biased coin flips. Some of the experimental setups proposed for implementation of quantum computers, begin with the quantum bits of the computer initially in a mixed state. Each qubit is ffl polarized  in the state j0i with probability 1+ffl 2 , and in the state j1i with probability 1\Gammaffl 2 , independently (or nearly so) of all other bits. The heat engine may be used to transform this initial collection of n qubits into a state in which a nearoptimal m = n[ 1+ffl 2 lg(1 + ffl) + 1\Gammaffl 2 lg(1 \Gamma ffl) \Gamma o(1)] qubits are in the joint state j0 m i. These qubits can then be use...
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
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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Cited by 1 (0 self)
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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
Contents
, 2002
"... Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spect ..."
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Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only presentday technology about to reach this number of qubits, further increases in complexity will require new methods. We sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step of which is a solid state NMRbased QIP