Yung, Man-HongNagaj, DanielWhitfield, James D.Aspuru-Guzik, Alan2011-01-132010Yung, Man-Hong, Daniel Nagaj, James D. Whitfield, and Alán Aspuru-Guzik. 2010. Simulation of classical thermal states on a quantum computer: A transfer matrix approach. Physical Review Series A 82(6): 060302(R).1050-2947http://nrs.harvard.edu/urn-3:HUL.InstRepos:4657435We present a hybrid quantum-classical algorithm to simulate thermal states of a classical Hamiltonians on a quantum computer. Our scheme employs a sequence of locally controlled rotations, building up the desired state by adding qubits one at a time. We identify a class of classical models for which our method is efficient and avoids potential exponential overheads encountered by Grover-like or quantum Metropolis schemes. Our algorithm also gives an exponential advantage for 2D Ising models with magnetic field on a square lattice, compared with the previously known Zalka's algorithm.en-USquantum physicsJournal Article2011-01-1310.1103/PhysRevA.82.060302