Results 1  10
of
15,500
Quantum complexity theory
 in Proc. 25th Annual ACM Symposium on Theory of Computing, ACM
, 1993
"... Abstract. In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s model of a quantum Turing machine (QTM) [Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 97–117]. This constructi ..."
Abstract

Cited by 574 (5 self)
 Add to MetaCart
the modern (complexity theoretic) formulation of the Church–Turing thesis. We show the existence of a problem, relative to an oracle, that can be solved in polynomial time on a quantum Turing machine, but requires superpolynomial time on a boundederror probabilistic Turing machine, and thus not in the class
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
Abstract

Cited by 1277 (4 self)
 Add to MetaCart
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factol: It is not clear whether this is still true when quantum mechanics is taken into consider ..."
Abstract

Cited by 1111 (5 self)
 Add to MetaCart
A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factol: It is not clear whether this is still true when quantum mechanics is taken
Rapid solution of problems by quantum computation
 IN PROC
, 1992
"... A class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method. The quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation. ..."
Abstract

Cited by 441 (4 self)
 Add to MetaCart
A class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method. The quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation.
Quantum mechanics helps in searching for a needle in a haystack
, 1997
"... Quantum mechanics can speed up a range of search applications over unsorted data. For example imagine a phone directory containing N names arranged in completely random order. To find someone's phone number with a probability of 50 % , any classical algorithm (whether deterministic or probabili ..."
Abstract

Cited by 434 (10 self)
 Add to MetaCart
or probabilistic) will need to access the database a minimum of 0.5N times. Quantum mechanical systems can be in a superposition of states and simultaneously examine multiple names. By properly adjusting the phases of various operations, successful computations reinforce each other while others interfere randomly
Realtime Quantum Chemistry
, 2012
"... Significant progress in the development of efficient and fast algorithms for quantum chemical calculations has been made in the past two decades. The main focus has always been the desire to be able to treat ever larger molecules or molecular assemblies— especially linear and sublinear scaling tec ..."
Abstract
 Add to MetaCart
, ideas such as haptic quantum chemistry or interactive quantum chemistry require an immediate provision of quantum chemical information which demands the calculation of data in “real time”. In this perspective, we aim at a definition of realtime quantum chemistry, explore its realm and eventually
Strengths and weaknesses of quantum computing
, 1996
"... Recently a great deal of attention has focused on quantum computation following a sequence of results [4, 16, 15] suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor’s result that factoring and the extraction of discrete logarithms are both solv ..."
Abstract

Cited by 381 (10 self)
 Add to MetaCart
solvable in quantum polynomial time, it is natural to ask whether all of NP can be efficiently solved in quantum polynomial time. In this paper, we address this question by proving that relative to an oracle chosen uniformly at random, with probability 1, the class NP cannot be solved on a quantum Turing
Time, quantum mechanics, and probability
 Synthese
, 1998
"... ABSTRACT. A variety of ideas arisiüg in decoherence theory, and in the ongoing debate over Everett’s relativestate theory, can be linked to issues in relativity theory and the philosophy of time, speci…cally the relational theory of tense and of identity over time. These have been systematically pr ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
probabilities di¤erent from quantum mechanics is easily dealt with. The more fundamental question is how to interpret these probabilities consistent with the relational theory of change, and the relational theory of identity over time. I shall show that the relational theory needs nothing more than the physical
Continuoustime quantum walk on the line
"... Abstract. An explicit expression for the probability distribution of a continuoustime quantum walk on a line is given. As a corollary, a new limit theorem for the walk is also presented. 1 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract. An explicit expression for the probability distribution of a continuoustime quantum walk on a line is given. As a corollary, a new limit theorem for the walk is also presented. 1
DISCRETE TIME QUANTUM MECHANICS
, 1993
"... This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy based on the method of finite elements. We are able to formula ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy based on the method of finite elements. We are able
Results 1  10
of
15,500