Quantum circuit matrix product state ansatz for large-scale simulations of molecules

TL;DR

This paper introduces a quantum circuit matrix product state (QCMPS) approach that efficiently approximates molecular ground states using fewer qubits, matching the accuracy of traditional methods like DMRG with significantly reduced quantum resources.

Contribution

The study presents a novel QCMPS ansatz optimized for quantum computers, achieving high accuracy in molecular simulations with fewer qubits and circuit depth.

Findings

QCMPS reaches chemical accuracy with only 6 qubits for 50 orbitals

QCMPS achieves similar accuracy to DMRG with exponentially larger bond dimension

QCMPS is promising for variational quantum eigensolver applications in chemistry

Abstract

As in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is determined by the size of the matrices or in other words the bond dimension, which unfortunately should be very large in many cases. In this study, we propose to calculate the ground state energies of molecular systems by variationally optimizing quantum circuit MPS (QCMPS) with a relatively small number of qubits. It is demonstrated that with carefully chosen circuit structure and orbital localization scheme, QCMPS can reach a similar accuracy as that achieved in DMRG with an exponentially large bond dimension. QCMPS simulation of a linear molecule with 50 orbitals can reach the chemical accuracy using only 6 qubits at a moderate circuit depth. These results suggest that QCMPS is a promising wave function ansatz in the variational quantum eigensolver algorithm for molecular systems.