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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 ..."
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Cited by 17 (2 self)
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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 ..."
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Cited by 14 (1 self)
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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
 Proc. of STACS 2004, Lecture Notes in Comput. Sci
, 2004
"... The oracle identification problem (OIP) is, given a set S of M Boolean oracles out of 2 N ones, to determine which oracle in S is the current blackbox oracle. We can exploit the information that candidates of the current oracle is restricted to S. The OIP contains several concrete problems such as ..."
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Cited by 9 (3 self)
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The oracle identification problem (OIP) is, given a set S of M Boolean oracles out of 2 N ones, to determine which oracle in S is the current blackbox oracle. We can exploit the information that candidates of the current oracle is restricted to S. The OIP contains several concrete problems such as the original Grover search and the BernsteinVazirani problem. Our interest is in the quantum query complexity, for which we present several upper and lower bounds. They are quite general and mostly optimal: (i) The query complexity of OIP is O ( √ N log M log N log log M) for any S such that M = S > N, which is better than the obvious bound N if M < 2 N / log3 N. (ii) It is O ( √ N) for any S if S  = N, which includes the upper bound for the Grover search as a special case. (iii) For a wide range of oracles (S  = N) such as random oracles and balanced oracles, the query complexity is Θ ( � N/K), where K is a simple parameter determined by S. 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 ..."
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Cited by 1 (1 self)
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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 ..."
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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.
On Quantum Coding for Ensembles of Mixed States
, 2000
"... 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 o ..."
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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. 1 Introduction The emergence of potentially useful theoretical protocols for using quantum states in cryptography and quantum computation has increased the theoretical (and perhaps ultimately practical) importance of questions about how quantum states can be compressed, transmitted across noisy or lowdimensional channels, and recovered, and otherwise manipulated in a fashion analogous to classical information. Most of the work done on these matters, beginning with [1], has focused on the manipulation of pure states, with mixed states appearing only in intermediate stages, as the result of noise. An exception is [2], which considered the copying or broadcasting of mixed stat...
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 ..."
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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
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 ..."
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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
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 ..."
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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
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 ..."
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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.