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42
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
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...
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.
Grover's Algorithm for Multiobject Search in Quantum Computing
"... Abstract L. K. Grover's search algorithm in quantum computing gives an optimal, squareroot speedupin the search for a single object in a large unsorted database. In this paper, we expound Grover's algorithm in a Hilbertspace framework that isolates its geometrical essence, and we generalizeit to t ..."
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Cited by 8 (1 self)
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Abstract L. K. Grover's search algorithm in quantum computing gives an optimal, squareroot speedupin the search for a single object in a large unsorted database. In this paper, we expound Grover's algorithm in a Hilbertspace framework that isolates its geometrical essence, and we generalizeit to the case where more than one object satisfies the search criterion.
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
Molecular information technology
 CR. REV. SOL. STATE
, 2005
"... Molecular materials are endowed with unique properties of unrivaled potential for high density integration of computing systems. Present applications of molecules range from organic semiconductor materials for lowcost circuits to genetically modified proteins for commercial imaging equipment. To f ..."
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Cited by 5 (3 self)
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Molecular materials are endowed with unique properties of unrivaled potential for high density integration of computing systems. Present applications of molecules range from organic semiconductor materials for lowcost circuits to genetically modified proteins for commercial imaging equipment. To fully realize the potential of molecules in computation, information processing concepts that relinquish narrow prescriptive control over elementary structures and functions are needed, and selforganizing architectures have to be developed. Investigations into qualitatively new concepts of information processing are underway in the areas of reactiondiffusion computing, selfassembly computing, and conformationbased computing. Molecular computing is best considered not as competitor for conventional computing, but as an opportunity for new applications. Microrobotics and bioimmersive computing are among the domains likely to benefit from advances in molecular computing. Progress will depend on both novel computing concepts and
Singlestep quantum search using problem structure.” eprint quantph/9812049
"... The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random kSAT allows determining the asymptotic average behavior of these al ..."
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Cited by 4 (2 self)
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The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random kSAT allows determining the asymptotic average behavior of these algorithms, showing they improve on quantum algorithms, such as amplitude amplification, that ignore detailed problem structure but remain exponential for hard problem instances. Compared to good classical methods, the algorithm performs better, on average, for weakly and highly constrained problems but worse for hard cases. The analytic techniques introduced here also apply to other quantum algorithms, supplementing the limited evaluation possible with classical simulations and showing how quantum computing can use ensemble properties of NP search problems.
Quantum computation and quantum information
 International Journal of Parallel, Emergent and Distributed Systems
, 2006
"... The paper is intended to be a survey of all the important aspects and results that have shaped the eld of quantum computation and quantum information. The reader is rst familiarized with those features and principles of quantum mechanics providing a more e cient and secure information processing. Th ..."
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Cited by 3 (3 self)
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The paper is intended to be a survey of all the important aspects and results that have shaped the eld of quantum computation and quantum information. The reader is rst familiarized with those features and principles of quantum mechanics providing a more e cient and secure information processing. Their applications to the general theory of information, cryptography, algorithms, computational complexity and errorcorrection are then discussed. Prospects for building a practical quantum computer are also analyzed. 1 Introduction and
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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Cited by 3 (0 self)
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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