Molecular Symmetry in VQE: A Dual Approach for Trapped-Ion Simulations of Benzene

TL;DR

This paper presents symmetry-based circuit optimization and error mitigation techniques for VQE algorithms on trapped-ion quantum devices, enabling more complex chemical simulations like benzene with reduced circuit depth and improved accuracy.

Contribution

It introduces a dual approach combining symmetry-inspired classical post-selection and circuit optimization tailored for trapped-ion hardware to enhance VQE performance.

Findings

Achieved near milli-Hartree accuracy in benzene simulation.

Constructed an 8-qubit VQE circuit with 69 entangling gates.

Demonstrated feasibility of complex chemical simulations on current quantum hardware.

Abstract

Understanding complex chemical systems -- such as biomolecules, catalysts, and novel materials -- is a central goal of quantum simulations. Near-term strategies hinge on the use of variational quantum eigensolver (VQE) algorithms combined with a suitable ansatz. However, straightforward application of many chemically-inspired ansatze yields prohibitively deep circuits. In this work, we employ several circuit optimization methods tailored for trapped-ion quantum devices to enhance the feasibility of intricate chemical simulations. The techniques aim to lessen the depth of the unitary coupled cluster with singles and doubles (uCCSD) ansatz's circuit compilation, a considerable challenge on current noisy quantum devices. Furthermore, we use symmetry-inspired classical post-selection methods to further refine the outcomes and minimize errors in energy measurements, without adding quantum overhead. Our strategies encompass optimal mapping from orbital to qubit, term reordering to minimize entangling gates, and the exploitation of molecular spin and point group symmetry to eliminate redundant parameters. The inclusion of error mitigation via post-selection based on known molecular symmetries improves the results to near milli-Hartree accuracy. These methods, when applied to a benzene molecule simulation, enabled the construction of an 8-qubit circuit with 69 two-qubit entangling operations, pushing the limits for variational quantum eigensolver (VQE) circuits executed on quantum hardware to date.