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34
An Introduction to Quantum Computing for NonPhysicists
 Los Alamos Physics Preprint Archive http://xxx.lanl.gov/abs/quantph/9809016
, 2000
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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 70 (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 48 (5 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.
Quantum computing with trapped ions
, 2008
"... Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various implementations of qubits, quantum gates and some key experiments ..."
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Cited by 16 (2 self)
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Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various implementations of qubits, quantum gates and some key experiments are discussed. Furthermore, we review some implementations of quantum algorithms such as a deterministic teleportation of quantum information and an error correction scheme.
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 8 (1 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
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 5 (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
Coherent Interactions in RareEarthIonDoped Crystals for applications
 in Quantum Information Science, Doctoral Thesis, LRAP333
"... Additions and errors recognized between the printing of this thesis (Dec. 2004) and the publishing of this electronic version (Feb. 2005): ADDENDUM Since the printing of this thesis, the following papers have been published in their final form: Paper II Phys. Rev. B 70, 214116 (2004) Paper VII Phys. ..."
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Cited by 3 (0 self)
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Additions and errors recognized between the printing of this thesis (Dec. 2004) and the publishing of this electronic version (Feb. 2005): ADDENDUM Since the printing of this thesis, the following papers have been published in their final form: Paper II Phys. Rev. B 70, 214116 (2004) Paper VII Phys. Rev. B 70, 214115 (2004)
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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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
Robust quantum information processing with techniques from liquid state NMR
, 2003
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Quantum Computer Emulator
 COMPUTER PHYSICS COMMUNICATIONS 132 (2000) 1–20
, 2000
"... We describe a Quantum Computer Emulator for a generic, general purpose Quantum Computer. This emulator consists of a simulator of the physical realization of the quantum computer and a graphical user interface to program and control the simulator. We illustrate the use of the quantum computer emulat ..."
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We describe a Quantum Computer Emulator for a generic, general purpose Quantum Computer. This emulator consists of a simulator of the physical realization of the quantum computer and a graphical user interface to program and control the simulator. We illustrate the use of the quantum computer emulator through various implementations of the Deutsch–Jozsa and