Simulation of Classical Thermal States on a Quantum Computer: A Transfer Matrix Approach

Abstract

We 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.

5 pages, 3 figures; (new in version 2: added new figure, title changed, rearranged paragraphs)

References in corpus (3)

• Quantum Simulations of Classical Annealing Processes
• Speed-up via Quantum Sampling
• A Quantum Approach to Classical Statistical Mechanics

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