Title

Quantum algorithm for approximating partition functions

Authors

Authors

P. Wocjan; C. F. Chiang; D. Nagaj;A. Abeyesinghe

Abbreviated Journal Title

Phys. Rev. A

Keywords

Optics; Physics, Atomic, Molecular & Chemical

Abstract

We present a quantum algorithm based on classical fully polynomial randomized approximation schemes (FPRASs) for estimating partition functions that combine simulated annealing with the Monte Carlo Markov chain method and use nonadaptive cooling schedules. We achieve a twofold polynomial improvement in time complexity: a quadratic reduction with respect to the spectral gap of the underlying Markov chains and a quadratic reduction with respect to the parameter characterizing the desired accuracy of the estimate output by the FPRAS. Both reductions are intimately related and cannot be achieved separately. First, we use Grover's fixed-point search, quantum walks, and phase estimation to efficiently prepare approximate coherent encodings of stationary distributions of the Markov chains. The speed up we obtain in this way is due to the quadratic relation between the spectral and phase gaps of classical and quantum walks. The second speed up with respect to accuracy comes from generalized quantum counting used instead of classical sampling to estimate expected values of quantum observables.

Journal Title

Physical Review A

Volume

80

Issue/Number

2

Publication Date

1-1-2009

Document Type

Article

Language

English

First Page

8

WOS Identifier

WOS:000269638200071

ISSN

1050-2947

Share

COinS