Results 1  10
of
14
On Quantum Coding for Ensembles of Mixed States
"... We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of ..."
Abstract

Cited by 21 (3 self)
 Add to MetaCart
(Show Context)
We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of the problem.
Efficient quantum algorithms for estimating Gauss sums
, 2002
"... We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction from the discrete logarithm problem to Gauss sum estimation we ..."
Abstract

Cited by 19 (2 self)
 Add to MetaCart
(Show Context)
We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction from the discrete logarithm problem to Gauss sum estimation we also give evidence that this problem is hard for classical algorithms. The workings of the quantum algorithm rely on the interaction between the additive characters of the Fourier transform and the multiplicative characters of the Gauss sum.
Quantum identification of boolean oracles
 In Proc. of 21st STACS, volume 2996 of LNCS
, 2004
"... ..."
(Show Context)
Use of a Quantum Computer to do Importance and MetropolisHastings Sampling of a Classical Bayesian Network
, 2008
"... Importance sampling and MetropolisHastings sampling (of which Gibbs sampling is a special case) are two methods commonly used to sample multivariate probability distributions (that is, Bayesian networks). Heretofore, the sampling of Bayesian networks has been done on a conventional “classical comp ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
(Show Context)
Importance sampling and MetropolisHastings sampling (of which Gibbs sampling is a special case) are two methods commonly used to sample multivariate probability distributions (that is, Bayesian networks). Heretofore, the sampling of Bayesian networks has been done on a conventional “classical computer”. In this paper, we propose methods for doing importance sampling and MetropolisHastings sampling of a classical Bayesian network on a quantum computer. 1
Data Structures in Natural Computing: Databases as Weak or Strong Anticipatory Systems
"... Abstract. Information systems anticipate the real world. Classical databases store, organise and search collections of data of that real world but only as weak anticipatory information systems. This is because of the reductionism and normalisation needed to map the structuralism of natural data on t ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
Abstract. Information systems anticipate the real world. Classical databases store, organise and search collections of data of that real world but only as weak anticipatory information systems. This is because of the reductionism and normalisation needed to map the structuralism of natural data on to idealised machines with von Neumann architectures consisting of fixed instructions. Category theory developed as a formalism to explore the theoretical concept of naturality shows that methods like sketches arising from graph theory as only nonnatural models of naturality cannot capture realworld structures for strong anticipatory information systems. Databases need a schema of the natural world. Natural computing databases need the schema itself to be also natural. Natural computing methods including neural computers, evolutionary automata, molecular and nanocomputing and quantum computation have the potential to be strong. At present they are mainly at the stage of weak anticipatory systems.
Locality, Weak or Strong Anticipation and Quantum Computing. I. Nonlocality in Quantum Theory
"... Abstract The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the ChurchTuring hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Categ ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the ChurchTuring hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Category theory provides the necessary coordinatefree mathematical language which is both constructive and nonlocal to subsume the various interpretations of quantum theory in one pullback/pushout Dolittle diagram. This diagram can be used to test and classify physical devices and proposed algorithms for weak or strong anticipation. Quantum Information Science is more than a merger of ChurchTuring and quantum theories. It has constructively to bridge the nonlocal chasm between the weak anticipation of mathematics and the strong anticipation of physics.
The
, 2008
"... We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction from the discrete logarithm problem to Gauss sum estimation we ..."
Abstract
 Add to MetaCart
(Show Context)
We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction from the discrete logarithm problem to Gauss sum estimation we also give evidence that this problem is hard for classical algorithms. The workings of the quantum algorithm rely on the interaction between the additive characters of the Fourier transform and the multiplicative characters of the Gauss sum.
Quantum Computers and Unstructured Search: Finding and Counting Items with an Arbitrarily Entangled Initial State
, 2001
"... Grover’s quantum algorithm for an unstructured search problem and the Count algorithm by Brassard et al. are generalized to the case when the initial state is arbitrarily and maximally entangled. This ansatz might be relevant with quantum subroutines, when the computational qubits and the environmen ..."
Abstract
 Add to MetaCart
(Show Context)
Grover’s quantum algorithm for an unstructured search problem and the Count algorithm by Brassard et al. are generalized to the case when the initial state is arbitrarily and maximally entangled. This ansatz might be relevant with quantum subroutines, when the computational qubits and the environment are coupled, and in general when the control over the quantum system is partial. 1
Quantum Computation and Information Project, ERATO,
, 2005
"... The oracle identification problem (OIP) was introduced by Ambainis et. al. [4], which is given as a set S of M oracles and a hidden oracle f. Our task is to figure out which oracle in S is equal to the hidden f by doing queries to f. OIP includes several problems such as Grover Search as special cas ..."
Abstract
 Add to MetaCart
(Show Context)
The oracle identification problem (OIP) was introduced by Ambainis et. al. [4], which is given as a set S of M oracles and a hidden oracle f. Our task is to figure out which oracle in S is equal to the hidden f by doing queries to f. OIP includes several problems such as Grover Search as special cases. In this paper, we design robust algorithms, i.e., those which are tolerant against noisy oracles, for OIP. Our results include: (i) For any oracle set S such that S  is polynomial in N, O ( √ N) queries are enough to identify the hidden oracle, which is obviously optimal since this OIP includes Grover Search as a special case. (ii) For the case that S  ≤ 2Nd (d < 1), we design an algorithm whose query complexity is O ( √ N log M / logN) and matches the lower bound proved in [4]. (iii) We can furthermore design a robust algorithm whose complexity changes smoothly between the complexity of (ii) and the complexity of recovering all information about the hidden oracle whose complexity is O(N) as showed by Buhrman et. al. in [11]. Thus our new algorithms are not only robust but also their query complexities are even better than the previous noiseless case [4]. 1