Simulating methylamine using symmetry adapted qubit-excitation-based variational quantum eigensolver

TL;DR

This paper introduces optimized strategies for simulating methylamine with variational quantum eigensolvers, significantly reducing computational resources while maintaining accuracy, advancing practical quantum chemistry applications.

Contribution

It combines symmetry adaptation, compact excitation circuits, and qubit tapering to enhance VQE efficiency, demonstrated on small molecules and applied to methylamine.

Findings

Reduced two-qubit operations from 600,000 to 12,000 for methylamine

Validated strategies on small molecules like LiH and BeH2

Provided resource estimates for larger molecules

Abstract

In this work, we propose and analyze optimization strategies for the VQE algorithm that combine various methods, including molecular point group symmetries (symmetry adaptation), compact excitation circuits (qubit-excitation-based), different types of excitation sets, and qubit tapering. These strategies allow for a significant reduction in computational requirements while ensuring convergence to the correct energies. First, we apply these combinations to small molecules, such as LiH and BeH2, to evaluate their compatibility, accuracy, and potential applicability to larger problems. We then simulate the methylamine molecule within its restricted active space using the best-performing optimization strategies. Finally, we complete our analysis by estimating the resources required for full active-space simulations of the methylamine and formic acid molecules. Our best-performing optimization strategy reduces the number of two-qubit operations for simulating the methylamine molecule from 600,000 (in the STO-3G basis with a naive Unitary Coupled Cluster ansatz) to approximately 12,000, using 26 qubits. Thus, the proposed combination of optimization methods can reduce the number of two-qubit operations by nearly two orders of magnitude. Although, we present alternative approaches that are of interest in the context of the further optimization in the number of two-qubit operation, we note that these approaches do not perform well enough in terms of the convergence to required energies. While these challenges persist, our resource analysis represents a valuable step towards the practical use of quantum computers and the development of better methods for optimizing computing resources.