A Theory of Quantum Subspace Diagonalization

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