Chemistry beyond the Hartree-Fock limit via quantum computed moments

TL;DR

This paper demonstrates that quantum computed moments (QCM) on superconducting quantum processors can accurately estimate molecular ground-state energies beyond Hartree-Fock, showing promise for chemical accuracy despite quantum errors.

Contribution

The work introduces and experimentally validates the QCM approach for hydrogen chains, improving energy estimates and error mitigation on near-term quantum hardware.

Findings

Achieved 99.9% accuracy of ground-state energy for H6

Demonstrated precision of about 10mH for H6 and 0.1mH for H2

Showed QCM's potential for error suppression and chemical accuracy

Abstract

Quantum computers hold promise to circumvent the limitations of conventional computing for difficult molecular problems. However, the accumulation of quantum logic errors on real devices represents a major challenge, particularly in the pursuit of chemical accuracy requiring the inclusion of dynamical effects. In this work we implement the quantum computed moments (QCM) approach for hydrogen chain molecular systems up to H$_6$. On a superconducting quantum processor, Hamiltonian moments, $\langle \mathcal{H}^p\rangle$ are computed with respect to the Hartree-Fock state, which are then employed in Lanczos expansion theory to determine an estimate for the ground-state energy which incorporates electronic correlations and manifestly improves on the variational result. Post-processing purification of the raw QCM data takes the estimate through the Hartree-Fock variational limit to within 99.9% of the exact electronic ground-state energy for the largest system studied, H$_6$. Calculated dissociation curves indicate precision at about 10mH for this system and as low as 0.1mH for molecular hydrogen, H$_2$, over a range of bond lengths. In the context of stringent precision requirements for chemical problems, these results provide strong evidence for the error suppression capability of the QCM method, particularly when coupled with post-processing error mitigation. Greater emphasis on more efficient representations of the Hamiltonian and classical preprocessing steps may enable the solution of larger systems on near-term quantum processors.