Quantum algorithms for the variational optimization of correlated electronic states with stochastic reconfiguration and the linear method

TL;DR

This paper introduces quantum algorithms for variationally optimizing correlated electronic wavefunctions using stochastic reconfiguration and the linear method, achieving polynomial cost and accurate results on challenging molecules.

Contribution

It presents a quantum approach for variational electronic structure calculations with polynomial scaling, outperforming classical optimizers in accuracy and efficiency.

Findings

Classical simulations show the linear method finds lower energies than L-BFGS-B.

LUCJ ansatz predicts ground-state energies within 1 kcal/mol of exact results.

Quantum algorithms achieve polynomial cost, enabling scalable strongly correlated state optimization.

Abstract

Solving the electronic Schrodinger equation for strongly correlated ground states is a long-standing challenge. We present quantum algorithms for the variational optimization of wavefunctions correlated by products of unitary operators, such as Local Unitary Cluster Jastrow (LUCJ) ansatzes, using stochastic reconfiguration and the linear method. While an implementation on classical computing hardware would require exponentially growing compute cost, the cost (number of circuits and shots) of our quantum algorithms is polynomial in system size. We find that classical simulations of optimization with the linear method consistently find lower energy solutions than with the L-BFGS-B optimizer across the dissociation curves of the notoriously difficult N$_2$ and C$_2$ dimers; LUCJ predictions of the ground-state energies deviate from exact diagonalization by 1 kcal/mol or less at all points on the potential energy curve. While we do characterize the effect of shot noise on the LM optimization, these noiseless results highlight the critical but often overlooked role that optimization techniques must play in attacking the electronic structure problem (on both classical and quantum hardware), for which even mean-field optimization is formally NP hard. We also discuss the challenge of obtaining smooth curves in these strongly correlated regimes, and propose a number of quantum-friendly solutions ranging from symmetry-projected ansatz forms to a symmetry-constrained optimization algorithm.