Classical Simulation of High Temperature Quantum Ising Models

March 5, 2020 - Leanne Yanabu

Diagram of classical simulation

Elizabeth Crosson and Sam Slezak have published a preprint demonstrating the efficiency of a classical algorithm for simulating high temperature thermal states of the generalized transverse Ising model.

This result follows a body of work on efficient simulations for specific types of transverse Ising models, in which it has been previously established that efficient classical algorithms exist for ferromagnetic transverse Ising models on any graph at any temperature as well as for certain 1-D models at any temperature.

This work extends the class of simulable models to those defined on an arbitrary graph with arbitrary couplings, given that the temperature is above a system dependent threshold. This threshold depends only on the degree of the interaction graph and the coupling strengths.

This work defines theoretical limitations for quantum annealing devices, ruling out the possibility of quantum advantage above certain operating temperatures.

In particular we calculate that for a device with a maximum interaction degree of 6 and a maximum coupling strength of 1GHZ the threshold of classical simulability is around 800mK.