Canadian Summer School on Quantum Information (CSSQI) (10th : 2010)

Quantum algorithm for preparing thermal Gibbs states Wocjan, Pawel


We present a quantum algorithm for preparing thermal Gibbs states of interacting quantum systems. This algorithm is based on Grover’s technique for quantum state engineering, and its running time is dominated by the factor sqrt{D/Z}, where D and Z_beta denote the dimension of the quantum system and its partition function at inverse temperature beta, respectively. We discuss the differences between this algorithm and quantum Metropolis sampling (see the presentation by David Poulin) and outline the analysis of the errors that arise due to imperfect simulation of Hamiltonian time evolutions and limited performance of phase estimation (finite accuracy and nonzero probability of failure).

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