Molecular Excited States using Quantum Subspace Methods: Accuracy, Resource Reduction, and Error-Mitigated Hardware Implementation of q-sc-EOM

TL;DR

This paper demonstrates a quantum approach for accurately calculating excited-state potential energy surfaces, reducing measurement complexity, and implementing error mitigation on hardware to advance quantum chemistry simulations.

Contribution

It combines quantum algorithms with classical methods to improve accuracy, scalability, and hardware implementation of excited-state calculations in quantum chemistry.

Findings

Reduced measurement scaling from O(N^12) to O(N^5)

Hardware implementation with error mitigation yields reasonably accurate excited-state energies

Gate noise is identified as the main source of error in hardware results

Abstract

Problems in quantum chemical simulations, especially achieving accurate excited-state potential energy surfaces, are among the primary applications to achieve quantum utility. On near-term quantum hardware, variants of the variational quantum eigensolver (VQE) algorithms are the primary choice for chemistry simulation. In this study, a combination of leading ground and excited state quantum algorithms for general excited states, namely, ADAPT-VQE/LUCJ and q-sc-EOM, are utilized to calculate accurate excited state potential energy surfaces in challenging bond-breaking scenarios and compared with the classical scalable EOM-CCSD method. This work investigates avenues toward quantum utility in excited-state quantum chemistry using the q-sc-EOM approach. We assess its accuracy while mitigating major scaling bottlenecks through the Davidson algorithm and basis rotation grouping, reducing the measurement scaling from O(N$^{12}$) to O(N$^{5}$), and implementing the method on quantum hardware with various error mitigation strategies to reduce gate and measurement errors in excited states. The hardware implementation of the q-sc-EOM algorithm, augmented by mitigation of M3 readout error and symmetry projection, produces reasonably accurate excited-state energies with gate noise identified as the predominant source of error. This paves the way for accurate and scalable, generally applicable quantum excited-state methods with potential for quantum utility while identifying critical problems that require advancements.