A New Angle on Quantum Subspace Diagonalization for Quantum Chemistry

TL;DR

This paper introduces a novel thresholding method with eigenvector-preserving rotations to improve the noise robustness of quantum subspace diagonalization, significantly reducing sample requirements in quantum chemistry simulations.

Contribution

The authors develop a new rotation-based thresholding technique for noisy generalized eigenvalue problems, enhancing quantum subspace diagonalization's efficiency and noise tolerance.

Findings

Sample reduction up to 100 times for certain systems.

Potential for up to 10,000 times fewer samples with optimal transformations.

Applicable to noisy, ill-conditioned eigenvalue problems beyond quantum chemistry.

Abstract

Quantum subspace diagonalization and quantum Krylov algorithms offer a feasible, pre- or early-fault tolerant alternative to quantum phase estimation for using quantum computers to estimate the low-lying spectra of quantum systems. However, despite promising proof-of-principle results, such methods suffer from high sensitivity to noise (including intrinsic sources such as sampling noise), making their utility for realistic industry-relevant problems an open question. To improve the potential applicability of such methods, we introduce a new variant of thresholding for noisy generalized eigenvalue problems that arise in quantum subspace diagonalization that has the potential to better control sensitivity to noise. Our approach leverages eigenvector-preserving transformations (rotations) of the generalized eigenvalue problem prior to thresholding. We study this effect in practical settings by applying this rotation thresholding scheme to an iterative quantum Krylov algorithm for several chemical systems, including the industry-relevant Fe(III)-NTA chelate complex. We develop a particular heuristic to select the rotation angle from noisy data and find for certain systems and noise regimes that the samples required to reach a target error for ground state estimation can be reduced by a factor of up to 100. Furthermore, with oracle access to the optimal transformation, more dramatic improvements are possible and we observe reductions in sample requirements by up to $10^4$, motivating the continued development of methods that can realize these improvements in practice. While we develop our approach in the context of quantum subspace diagonalization, the improved thresholding scheme we develop could be advantageous in any context where one must solve noisy, ill-conditioned generalized eigenvalue problems.