The quantum super-Krylov method

TL;DR

This paper introduces a quantum super-Krylov method that estimates ground-state energies using only real-time evolutions and recovery probabilities, making it suitable for current quantum hardware and robust to noise.

Contribution

It proposes a novel Krylov quantum diagonalization approach that avoids challenging subroutines, employing numerical differentiation and a new derivative estimation algorithm.

Findings

Converges exponentially quickly under certain spectral assumptions.

Compatible with near-term quantum hardware due to reliance on real-time evolutions.

Demonstrated effectiveness through tensor network simulations.

Abstract

The problem of estimating the ground-state energy of a quantum system is ubiquitous in chemistry and condensed matter physics. Krylov quantum diagonalization (KQD) has emerged as a promising approach for this task. However, many KQD methods rely on subroutines, particularly the Hadamard test, that are challenging to implement on near-term quantum computers. We present a novel KQD method that uses only real-time evolutions and recovery probabilities, making it well adapted for existing quantum hardware. The method entails numerical differentiation in post-processing, and so we present a novel derivative estimation algorithm that is robust to noisy data. Under assumptions on the spectrum of the Hamiltonian, we prove that our algorithm converges exponentially quickly to the ground-state energy and present a numerical demonstration using tensor network simulations.