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238
On Quantum Sieve Approaches to the Lattice Shortest Vector Problem
, 2014
"... The lattice hortest vector problem, or lattice SVP, has gained a lot of attention in the field of quantum computing. There are a number of reasons for this, including the fact that the hardness of lattice SVP is the foudation of a number of postquantum cryptosystems and that approximateSVP is in N ..."
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The lattice hortest vector problem, or lattice SVP, has gained a lot of attention in the field of quantum computing. There are a number of reasons for this, including the fact that the hardness of lattice SVP is the foudation of a number of postquantum cryptosystems and that approximate
Quantum amplitude amplification and estimation
, 2002
"... Abstract. Consider a Boolean function χ: X → {0, 1} that partitions set X between its good and bad elements, where x is good if χ(x) = 1 and bad otherwise. Consider also a quantum algorithm A such that A0 〉 = � x∈X αxx 〉 is a quantum superposition of the elements of X, and let a denote the proba ..."
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Cited by 174 (14 self)
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show that this quadratic speedup can also be obtained for a large family of search problems for which good classical heuristics exist. Finally, as our main result, we combine ideas from Grover’s and Shor’s quantum algorithms to perform amplitude estimation, a process that allows to estimate the value
Lockfree GaussSieve for linear speedups in parallel high performance SVP calculation
 IN: SBACPAD
, 2014
"... Latticebased cryptography became a hottopic in the past years because it seems to be quantum immune, i.e., resistant to attacks operated with quantum computers. The security of latticebased cryptosystems is determined by the hardness of certain lattice problems, such as the Shortest Vector Pro ..."
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Cited by 6 (1 self)
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Latticebased cryptography became a hottopic in the past years because it seems to be quantum immune, i.e., resistant to attacks operated with quantum computers. The security of latticebased cryptosystems is determined by the hardness of certain lattice problems, such as the Shortest Vector
Quantum counting
 In Proceedings of the 25th International Colloquium on Automata, Languages and Programming
, 1998
"... Abstract. We study some extensions of Grover’s quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching algorithm over classical brute force can still be ..."
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Cited by 118 (3 self)
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Abstract. We study some extensions of Grover’s quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching algorithm over classical brute force can still
Quantum speedup of Monte Carlo methods
, 2015
"... Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work we describe a quantum algorithm whi ..."
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Cited by 1 (1 self)
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which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomised or quantum subroutine with bounded variance, achieving a nearquadratic speedup over the best possible classical algorithm. Combining the algorithm
Speedup via Quantum Sampling
 Physical Review A
, 2008
"... The Markov Chain Monte Carlo method is at the heart of most fullypolynomial randomized approximation schemes for #Pcomplete problems such as estimating the permanent or the value of a polytope. It is therefore very natural and important to determine whether quantum computers can speedup classical ..."
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Cited by 4 (1 self)
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The Markov Chain Monte Carlo method is at the heart of most fullypolynomial randomized approximation schemes for #Pcomplete problems such as estimating the permanent or the value of a polytope. It is therefore very natural and important to determine whether quantum computers can speedup
Sieving for Shortest Vectors in Ideal Lattices
, 2011
"... Lattice based cryptography is gaining more and more importance in the cryptographic community. It is a common approach to use a special class of lattices, socalled ideal lattices, as the basis of lattice based crypto systems. This speeds up computations and saves storage space for cryptographic ke ..."
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Cited by 5 (0 self)
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shortest vector in ideal lattices faster than in regular lattices without special structure. The practical speedup of our algorithm is linear in the degree of the field polynomial. We also propose an ideal lattice variant of the heuristic GaussSieve algorithm that allows for the same speedup.
Speedup techniques for Metropolis algorithms on a lattice
, 1998
"... We investigate new stochastic optimization algorithms on a lattice that speedup the convergence of MonteCarlo algorithms. The first one, the multiresolution algorithm, uses independent multiple local trials of Metropolis algorithms. The second one, the hierarchical algorithm, is associated to the ..."
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We investigate new stochastic optimization algorithms on a lattice that speedup the convergence of MonteCarlo algorithms. The first one, the multiresolution algorithm, uses independent multiple local trials of Metropolis algorithms. The second one, the hierarchical algorithm, is associated
Speedup in Quantum Computation is Associated With Attenuation of Processing Probability
"... Quantum coherence allows the computation of an arbitrary number of distinct computational paths in parallel. Based on quantum parallelism it has been conjectured that exponential or even larger speedups of computations are possible. Here it is shown that, although in principle correct, any speed ..."
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Cited by 4 (1 self)
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Quantum coherence allows the computation of an arbitrary number of distinct computational paths in parallel. Based on quantum parallelism it has been conjectured that exponential or even larger speedups of computations are possible. Here it is shown that, although in principle correct, any
Quantum Speedup for Approximating Partition Functions
, 2008
"... We achieve a quantum speedup of fully polynomial randomized approximation schemes (FPRAS) for estimating partition functions that combine simulated annealing with the MonteCarlo Markov Chain method and use nonadaptive cooling schedules. The improvement in time complexity is twofold: a quadratic r ..."
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Cited by 1 (1 self)
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We achieve a quantum speedup of fully polynomial randomized approximation schemes (FPRAS) for estimating partition functions that combine simulated annealing with the MonteCarlo Markov Chain method and use nonadaptive cooling schedules. The improvement in time complexity is twofold: a quadratic
Results 1  10
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238