A Hybrid Classical/Quantum Approach for Large-Scale Studies of Quantum Systems with Density Matrix Embedding Theory

TL;DR

This paper introduces a hybrid classical/quantum method using density matrix embedding theory (DMET) combined with variational quantum eigensolver techniques to efficiently study large quantum systems, validated through simulation.

Contribution

It presents a new embedding scheme compatible with hybrid quantum-classical algorithms, expanding the toolkit for analyzing large quantum systems without large-scale fault-tolerant quantum computers.

Findings

Successfully reproduces ground state energies of the Hubbard model

Demonstrates convergence to the infinite limit using quantum simulations

Validates the approach with a quantum abstract machine simulator

Abstract

Determining ground state energies of quantum systems by hybrid classical/quantum methods has emerged as a promising candidate application for near-term quantum computational resources. Short of large-scale fault-tolerant quantum computers, small-scale devices can be leveraged with current computational techniques to identify important subspaces of relatively large Hamiltonians. Inspired by the work that described the merging of dynamical mean-field theory (DMFT) with a small-scale quantum computational resource as an impurity solver [Bauer et al., arXiv:1510.03859v2], we describe an alternative embedding scheme, density matrix embedding theory (DMET), that naturally fits with the output from the variational quantum eigensolver and other hybrid approaches. This approach is validated using a quantum abstract machine simulator [Smith et al., arXiv:1608.03355] that reproduces the ground state energy of the Hubbard model converged to the infinite limit.