Emergent Mind

A theory of quantum subspace diagonalization

(2110.07492)
Published Oct 14, 2021 in quant-ph , cs.NA , and math.NA

Abstract

Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large\rev{-}scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized eigenvalue problem, with a matrix pair corrupted by a non-negligible amount of noise that is far above the machine precision. Despite pessimistic predictions from classical \rev{worst-case} perturbation theories, these methods can perform reliably well if the generalized eigenvalue problem is solved using a standard truncation strategy. By leveraging and advancing classical results in matrix perturbation theory, we provide a theoretical analysis of this surprising phenomenon, proving that under certain natural conditions, a quantum subspace diagonalization algorithm can accurately compute the smallest eigenvalue of a large Hermitian matrix. We give numerical experiments demonstrating the effectiveness of the theory and providing practical guidance for the choice of truncation level. Our new results can also be of independent interest to solving eigenvalue problems outside the context of quantum computation.

We're not able to analyze this paper right now due to high demand.

Please check back later (sorry!).

Generate a summary of this paper on our Pro plan:

We ran into a problem analyzing this paper.

Newsletter

Get summaries of trending comp sci papers delivered straight to your inbox:

Unsubscribe anytime.