Results 1  10
of
113
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]. ..."
Abstract

Cited by 219 (65 self)
 Add to MetaCart
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].
Towards a quantum programming language
 Mathematical Structures in Computer Science
, 2004
"... The field of quantum computation suffers from a lack of syntax. In the absence of a convenient programming language, algorithms are frequently expressed in terms of hardware circuits or Turing machines. Neither approach particularly encourages structured programming or abstractions such as data type ..."
Abstract

Cited by 111 (13 self)
 Add to MetaCart
The field of quantum computation suffers from a lack of syntax. In the absence of a convenient programming language, algorithms are frequently expressed in terms of hardware circuits or Turing machines. Neither approach particularly encourages structured programming or abstractions such as data types. In this paper, we describe the syntax and semantics of a simple quantum programming language. This language provides highlevel features such as loops, recursive procedures, and structured data types. It is statically typed, and it has an interesting denotational semantics in terms of complete partial orders of superoperators. 1
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 ..."
Abstract

Cited by 46 (12 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 39 (10 self)
 Add to MetaCart
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
Quantum summation with an application to integration
, 2001
"... We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences which satisfy a psummability ( condition and for d integration of functions from Lebesgue spaces Lp [0, 1] ) and analyze their convergence rates. We ..."
Abstract

Cited by 39 (11 self)
 Add to MetaCart
We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences which satisfy a psummability ( condition and for d integration of functions from Lebesgue spaces Lp [0, 1] ) and analyze their convergence rates. We also prove lower bounds which show that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of Brassard, Høyer, Mosca, and Tapp (2000) on computing the mean for bounded sequences and complements results of Novak (2001) on integration of functions from Hölder classes.
Quantum multiprover interactive proof systems with limited prior entanglement
 Journal of Computer and System Sciences
"... This paper gives the first formal treatment of a quantum analogue of multiprover interactive proof systems. In quantum multiprover interactive proof systems there can be two natural situations: one is with prior entanglement among provers, and the other does not allow prior entanglement among prov ..."
Abstract

Cited by 32 (5 self)
 Add to MetaCart
This paper gives the first formal treatment of a quantum analogue of multiprover interactive proof systems. In quantum multiprover interactive proof systems there can be two natural situations: one is with prior entanglement among provers, and the other does not allow prior entanglement among provers. This paper focuses on the latter situation and proves that, if provers do not share any prior entanglement each other, the class of languages that have quantum multiprover interactive proof systems is equal to NEXP. It implies that the quantum multiprover interactive proof systems without prior entanglement have no gain to the classical ones. This result can be extended to the following statement of the cases with prior entanglement: if a language L has a quantum multiprover interactive proof system allowing at most polynomially many prior entangled qubits among provers, L is necessarily in NEXP. Another interesting result shown in this paper is that, in the case the prover does not have his private qubits, the class of languages that have singleprover quantum interactive proof systems is also equal to NEXP. Our results are also of importance in the sense of giving exact correspondances between quantum and classical complexity classes, because there have been known only a few results giving such correspondances.
Quantum Merlin Arthur proof systems, manuscript
, 2001
"... Quantum MerlinArthur proof systems are a weak form of quantum interactive proof systems, where mighty Merlin as a prover presents a proof in a pure quantum state and Arthur as a verifier performs polynomialtime quantum computation to verify its correctness with high success probability. For a more ..."
Abstract

Cited by 26 (7 self)
 Add to MetaCart
Quantum MerlinArthur proof systems are a weak form of quantum interactive proof systems, where mighty Merlin as a prover presents a proof in a pure quantum state and Arthur as a verifier performs polynomialtime quantum computation to verify its correctness with high success probability. For a more general treatment, this paper considers quantum “multipleMerlin”Arthur proof systems in which Arthur uses multiple quantum proofs unentangled each other for his verification. Although classical multiproof systems are easily shown to be essentially equivalent to classical singleproof systems, it is unclear whether quantum multiproof systems collapse to quantum singleproof systems. This paper investigates the possibility that quantum multiproof systems collapse to quantum singleproof systems, and shows that (i) a necessary and sufficient condition under which the number of quantum proofs is reducible to two and (ii) using multiple quantum proofs does not increase the power of quantum MerlinArthur proof systems in the case of perfect soundness. Our proof for the latter result also gives a new characterization of the class NQP, which bridges two existing concepts of “quantum nondeterminism”. It is also shown that (iii) there is a relativized world in which coNP (actually coUP) does not have quantum MerlinArthur proof systems even with multiple quantum proofs. 1 1
On quantum statistical inference
 J. Roy. Statist. Soc. B
, 2001
"... [Read before The Royal Statistical Society at a meeting organized by the Research Section ..."
Abstract

Cited by 24 (5 self)
 Add to MetaCart
[Read before The Royal Statistical Society at a meeting organized by the Research Section
A Rosetta stone for quantum mechanics with an introduction to quantum computation
, 2002
"... Abstract. The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading ..."
Abstract

Cited by 21 (11 self)
 Add to MetaCart
Abstract. The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading