Use of Quantum Sampling to Calculate Mean Values of Observables and Partition Function of a Quantum System

Details Use of Quantum Sampling to Calculate Mean Values of Observables and Partition Function of a Quantum System Use of Quantum Sampling to Calculate Mean Values of Observables and Partition Function of a Quantum System

2009-12-22

arxiv.org/abs/0912.4402v3

Physics

Quantum Physics

V1-12 pages(5 files: 1.tex, 3 .sty, 1 .eps);V2-minor changes;V3-minor changes and extension of scenario(c)

Scientific paper

We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with polynomial efficiency, certain diagonal matrix elements of an observable. This sub-algorithm is performed on a quantum computer, using quantum phase estimation and tomography. The second sub-algorithm is for sampling a probability distribution. This sub-algorithm is not polynomially efficient. It can be performed either on a classical or a quantum computer, but a quantum computer can perform it quadratically faster.

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