Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States

TL;DR

This paper introduces modified algorithms based on Lieb-Robinson bounds for simulating non-equilibrium and thermal quantum states, enabling larger system sizes and efficient analysis of disordered spin systems.

Contribution

It presents a novel modification to quantum circuit mapping that reduces resource requirements by leveraging light-cone observations, and applies quantum belief propagation to disordered spin chains.

Findings

Doubling of system size achievable in simulations

Effective approximation of time evolution with light-cone matching

Successful application to disordered and frustrated spin systems

Abstract

We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer resources required. This modification is based on a principle of "observing" the system outside the light-cone. We apply this method to study spin relaxation in systems started out of equilibrium with initial conditions that give rise to very rapid entanglement growth. We also show that it is possible to approximate time evolution under a local Hamiltonian by a quantum circuit whose light-cone naturally matches the Lieb-Robinson velocity. Asymptotically, these modified methods allow a doubling of the system size that one can obtain compared to direct simulation. We then consider a different problem of thermal properties of disordered spin chains and use quantum belief propagation to average over different configurations. We test this algorithm on one dimensional systems with mixed ferromagnetic and anti-ferromagnetic bonds, where we can compare to quantum Monte Carlo, and then we apply it to the study of disordered, frustrated spin systems.