RT Journal Article
SR Electronic
T1 A quantumâ€“quantum Metropolis algorithm
JF Proceedings of the National Academy of Sciences
JO Proc Natl Acad Sci USA
FD National Academy of Sciences
SP 754
OP 759
DO 10.1073/pnas.1111758109
VO 109
IS 3
A1 Yung, Man-Hong
A1 Aspuru-Guzik, AlĂˇn
YR 2012
UL http://www.pnas.org/content/109/3/754.abstract
AB The classical Metropolis sampling method is a cornerstone of many statistical modeling applications that range from physics, chemistry, and biology to economics. This method is particularly suitable for sampling the thermal distributions of classical systems. The challenge of extending this method to the simulation of arbitrary quantum systems is that, in general, eigenstates of quantum Hamiltonians cannot be obtained efficiently with a classical computer. However, this challenge can be overcome by quantum computers. Here, we present a quantum algorithm which fully generalizes the classical Metropolis algorithm to the quantum domain. The meaning of quantum generalization is twofold: The proposed algorithm is not only applicable to both classical and quantum systems, but also offers a quantum speedup relative to the classical counterpart. Furthermore, unlike the classical method of quantum Monte Carlo, this quantum algorithm does not suffer from the negative-sign problem associated with fermionic systems. Applications of this algorithm include the study of low-temperature properties of quantum systems, such as the Hubbard model, and preparing the thermal states of sizable molecules to simulate, for example, chemical reactions at an arbitrary temperature.