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60
Foundations of Genetic Programming
, 2002
"... The goal of getting computers to automatically solve problems is central to artificial intelligence, machine learning, and the broad area encompassed by what Turing called “machine intelligence ” [161, 162]. ..."
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Cited by 219 (65 self)
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The goal of getting computers to automatically solve problems is central to artificial intelligence, machine learning, and the broad area encompassed by what Turing called “machine intelligence ” [161, 162].
Communicating quantum processes
 In POPL 2005
, 2005
"... We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the picalculus with primitives for measurement and transformation of quantum state; in particular, quantum ..."
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Cited by 39 (10 self)
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We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the picalculus with primitives for measurement and transformation of quantum state; in particular, quantum bits (qubits) can be transmitted from process to process along communication channels. CQP has a static type system which classifies channels, distinguishes between quantum and classical data, and controls the use of quantum state. We formally define the syntax, operational semantics and type system of CQP, prove that the semantics preserves typing, and prove that typing guarantees that each qubit is owned by a unique process within a system. We illustrate CQP by defining models of several quantum communication systems, and outline our plans for using CQP as the foundation for formal analysis and verification of combined quantum and classical systems. 1
Hidden translation and orbit coset in quantum computing
 IN PROC. 35TH ACM STOC
, 2003
"... We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of nonabelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently ..."
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Cited by 39 (7 self)
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We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of nonabelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently Hidden Translation in Z n p, whenever p is a fixed prime. For the induction step, we introduce the problem Orbit Coset generalizing both Hidden Translation and Hidden Subgroup, and prove a powerful selfreducibility result: Orbit Coset in a finite group G is reducible to Orbit Coset in G/N and subgroups of N, for any solvable normal subgroup N of G. Our selfreducibility framework combined with Kuperberg’s subexponential quantum algorithm for solving Hidden Translation in any abelian group, leads to subexponential quantum algorithms for Hidden Translation and Hidden Subgroup in any solvable group.
Information and Computation: Classical and Quantum Aspects
 REVIEWS OF MODERN PHYSICS
, 2001
"... Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely ..."
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Cited by 23 (2 self)
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Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some outstanding aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as a few samples of the impact of quanta in the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement in information processing by a quantum computer. We provide finally some examples of current experimental
More on Optical Holonomic Quantum Computer
"... We in this paper consider a further generalization of the (optical) holonomic quantum computation proposed by Zanardi and Rasetti (quant–ph 9904011), and reinforced by Fujii (quant–ph 9910069) and Pachos and Chountasis (quant–ph 9912093). We construct a quantum computational bundle on some parameter ..."
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Cited by 14 (14 self)
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We in this paper consider a further generalization of the (optical) holonomic quantum computation proposed by Zanardi and Rasetti (quant–ph 9904011), and reinforced by Fujii (quant–ph 9910069) and Pachos and Chountasis (quant–ph 9912093). We construct a quantum computational bundle on some parameter space, and calculate nonabelian Berry connections and curvatures explicitly in the special cases. Our main tool is unitary coherent operators based on Lie algebras su(n+1) and su(n,1), where the case of n = 1 is the previous one.
Probabilistic model–checking of quantum protocols
 DCM 2006: PROCEEDINGS OF THE 2ND INTERNATIONAL WORKSHOP ON DEVELOPMENTS IN COMPUTATIONAL MODELS
, 2005
"... We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantummechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communicati ..."
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Cited by 11 (6 self)
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We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantummechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communication systems can and have been implemented using presentday technology; therefore, the ability to model and analyse such systems rigorously is of primary importance. While current analyses of quantum protocols use a traditional mathematical approach and require considerable understanding of the underlying physics, we argue that automated verification techniques provide an elegant alternative. We demonstrate these techniques through the use of prism, a probabilistic modelchecking tool. Our approach is conceptually simpler than existing proofs, and allows us to disambiguate protocol definitions and assess their properties. It also facilitates detailed analyses of actual implemented systems. We illustrate our techniques by modelling a selection of quantum protocols (namely superdense coding, quantum teleportation, and quantum error correction) and verifying their basic correctness properties. Our results provide a foundation for further work on modelling and analysing larger systems such as those used for quantum cryptography, in which basic protocols are used as components.
On SelfDual Quantum Codes, Graphs, and Boolean Functions
, 2005
"... A short introduction to quantum error correction is given, and it is shown that zerodimensional quantum codes can be represented as selfdual additive codes over GF(4) and also as graphs. We show that graphs representing several such codes with high minimum distance can be described as nested regul ..."
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Cited by 10 (2 self)
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A short introduction to quantum error correction is given, and it is shown that zerodimensional quantum codes can be represented as selfdual additive codes over GF(4) and also as graphs. We show that graphs representing several such codes with high minimum distance can be described as nested regular graphs having minimum regular vertex degree and containing long cycles. Two graphs correspond to equivalent quantum codes if they are related by a sequence of local complementations. We use this operation to generate orbits of graphs, and thus classify all inequivalent selfdual additive codes over GF(4) of length up to 12, where previously only all codes of length up to 9 were known. We show that these codes can be interpreted as quadratic Boolean functions, and we define nonquadratic quantum codes, corresponding to Boolean functions of higher degree. We look at various cryptographic properties of Boolean functions, in particular the propagation criteria. The new aperiodic propagation criterion (APC) and the APC distance are then defined. We show that the
Quantum neural networks
 In Journal of Computer and System Sciences
, 2001
"... This paper initiates the study of quantum computing within the constraints of using a polylogarithmic (O(log k n),k ≥ 1) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has focussed on using a polynomial number of qubits. A new mathematical ..."
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Cited by 10 (0 self)
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This paper initiates the study of quantum computing within the constraints of using a polylogarithmic (O(log k n),k ≥ 1) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has focussed on using a polynomial number of qubits. A new mathematical model of computation called Quantum Neural Networks (QNNs) is defined, building on Deutsch’s model of quantum computational network. The model introduces a nonlinear and irreversible gate, similar to the speculative operator defined by Abrams and Lloyd. The precise dynamics of this operator are defined and while giving examples in which nonlinear Schrödinger’s equations are applied, we speculate on its possible implementation. The many practical problems associated with the current model of quantum computing are alleviated in the new model. It is shown that QNNs of logarithmic size and constant depth have the same computational power as threshold circuits, which are used for modeling neural networks. QNNs of polylogarithmic size and polylogarithmic depth can solve the problems in NC, the class of problems with theoretically fast parallel solutions. Thus, the new model may indeed provide an approach for building scalable parallel computers.