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Results 1 - 10
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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 post-quantum cryptosystems and that approximate-SVP 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 post-quantum 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 A|0 〉 = � x∈X αx|x 〉 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
Lock-free GaussSieve for linear speedups in parallel high performance SVP calculation
- IN: SBAC-PAD
, 2014
"... Lattice-based cryptography became a hot-topic in the past years be-cause it seems to be quantum immune, i.e., resistant to attacks op-erated with quantum computers. The security of lattice-based cryp-tosystems 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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Lattice-based cryptography became a hot-topic in the past years be-cause it seems to be quantum immune, i.e., resistant to attacks op-erated with quantum computers. The security of lattice-based cryp-tosystems 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 subrou-tine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm
Speed-up via Quantum Sampling
- Physical Review A
, 2008
"... The Markov Chain Monte Carlo method is at the heart of most fully-polynomial randomized approximation schemes for #P-complete 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 speed-up 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 fully-polynomial randomized approximation schemes for #P-complete 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 speed-up
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, so-called 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.
Speed-up techniques for Metropolis algorithms on a lattice
, 1998
"... We investigate new stochastic optimization algorithms on a lattice that speed-up the convergence of Monte-Carlo algorithms. The first one, the multi-resolution 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 speed-up the convergence of Monte-Carlo algorithms. The first one, the multi-resolution 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 Speed-up for Approximating Partition Functions
, 2008
"... We achieve a quantum speed-up of fully polynomial randomized approximation schemes (FPRAS) for estimating partition functions that combine simulated annealing with the Monte-Carlo Markov Chain method and use non-adaptive 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 speed-up of fully polynomial randomized approximation schemes (FPRAS) for estimating partition functions that combine simulated annealing with the Monte-Carlo Markov Chain method and use non-adaptive cooling schedules. The improvement in time complexity is twofold: a quadratic
Results 1 - 10
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238
