Monte Carlo Methods in Statistical Physics

1979 ◽  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Statistical Physics

scholarly journals Quantum speedup of Monte Carlo methods

2015 ◽  
Vol 471 (2181) ◽  
pp. 20150301 ◽  
Author(s):  
Ashley Montanaro
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Statistical Physics ◽  
Probability Distributions ◽  
General Setting ◽  
Quantum Algorithm ◽  
Quantum Walks ◽  
Partition Functions ◽  
Performance Bounds ◽  
Quantum Speedup

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 which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.

Monte Carlo Methods in Statistical Physics

2001 ◽  
Vol 96 (454) ◽  
pp. 778-778 ◽  
Author(s):  
Robert L Strawderman
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Statistical Physics
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