Accelerated Convergence of Contracted Quantum Eigensolvers through a Quasi-Second-Order, Locally Parameterized Optimization

TL;DR

This paper introduces a quasi-second-order optimization approach to accelerate the convergence of contracted quantum eigensolvers, improving efficiency and accuracy for quantum chemistry simulations on near-term and future quantum computers.

Contribution

It applies classical quasi-second-order optimization techniques to quantum eigensolvers, achieving superlinear convergence and reducing noise accumulation in quantum computations.

Findings

Superlinear convergence of the wavefunction to the ACSE solution.

Enhanced efficiency in quantum chemistry simulations on NISQ and fault-tolerant devices.

Comparison showing advantages over traditional variational quantum eigensolvers.

Abstract

A contracted quantum eigensolver (CQE) finds a solution to the many-electron Schr\"odinger equation by solving its integration (or contraction) to the 2-electron space -- a contracted Schr\"odinger equation (CSE) -- on a quantum computer. When applied to the anti-Hermitian part of the CSE (ACSE), the CQE iterations optimize the wave function with respect to a general product ansatz of two-body exponential unitary transformations that can exactly solve the Schr\"odinger equation. In this work, we accelerate the convergence of the CQE and its wavefunction ansatz via tools from classical optimization theory. By treating the CQE algorithm as an optimization in a local parameter space, we can apply quasi-second-order optimization techniques, such as quasi-Newton approaches or non-linear conjugate gradient approaches. Practically these algorithms result in superlinear convergence of the wavefunction to a solution of the ACSE. Convergence acceleration is important because it can both minimize the accumulation of noise on near-term intermediate-scale quantum (NISQ) computers and achieve highly accurate solutions on future fault-tolerant quantum devices. We demonstrate the algorithm, as well as some heuristic implementations relevant for cost-reduction considerations, comparisons with other common methods such as variational quantum eigensolvers, and a fermionic-encoding-free form of the CQE.