Simulation of classical thermal states on a quantum computer: A transfermatrix approach
Abstract
We present a hybrid quantumclassical algorithm to simulate thermal states of 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 identified a class of classical models for which our method is efficient and avoids potential exponential overheads encountered by Groverlike or quantum Metropolis schemes. Our algorithm also gives an exponential advantage for twodimensional Ising models with magnetic field on a square lattice, compared with the previously known Zalka’s algorithm.
 Publication:

Physical Review A
 Pub Date:
 December 2010
 DOI:
 10.1103/PhysRevA.82.060302
 arXiv:
 arXiv:1005.0020
 Bibcode:
 2010PhRvA..82f0302Y
 Keywords:

 03.67.Ac;
 05.10.Cc;
 05.50.+q;
 Quantum algorithms protocols and simulations;
 Renormalization group methods;
 Lattice theory and statistics;
 Quantum Physics
 EPrint:
 5 pages, 3 figures