Variational quantum simulation of critical Ising model with symmetry averaging

TL;DR

This paper demonstrates that symmetry averaging significantly improves the accuracy of variational quantum simulations of the critical Ising model using DMERA circuits, reducing systematic errors without extra resource costs.

Contribution

It introduces symmetry averaging as a method to mitigate systematic errors in variational quantum simulations of critical systems, enhancing accuracy without additional qubits or circuit depth.

Findings

DMERA outperforms standard QAOA ansatz for the critical Ising model.

Symmetry averaging reduces systematic errors by up to four orders of magnitude.

Classical algorithms enable simulation of hundreds of qubits for this approach.

Abstract

Here, we investigate the use of deep multi-scale entanglement renormalization (DMERA) circuits as a variational ansatz for ground states of gapless systems. We use the exactly-solvable one-dimensional critical transverse-field Ising model as a testbed. Numerically exact simulation of the ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, DMERA strongly outperforms a standard QAOA-style ansatz, and that a major source of systematic error in correlation functions approximated using DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. We propose that this technique for mitigating systematic error could be applied to NISQ simulations of physical systems with other symmetries.