Quantum-Centric Algorithm for Sample-Based Krylov Diagonalization

TL;DR

This paper introduces a quantum diagonalization algorithm combining classical and quantum Krylov subspace methods, enabling efficient ground state approximation for many-body systems on near-term quantum hardware.

Contribution

It presents a novel quantum diagonalization algorithm that leverages quantum Krylov states and classical diagonalization, with proven polynomial convergence under certain conditions.

Findings

Successfully simulated impurity models with up to 41 bath sites.

Achieved results in excellent agreement with established DMRG calculations.

Demonstrated scalability on quantum processors and supercomputers.

Abstract

Approximating the ground state of many-body systems is a key computational bottleneck underlying important applications in physics and chemistry. The most widely known quantum algorithm for ground state approximation, quantum phase estimation, is out of reach of current quantum processors due to its high circuit-depths. Subspace-based quantum diagonalization methods offer a viable alternative for pre- and early-fault-tolerant quantum computers. Here, we introduce a quantum diagonalization algorithm which combines two key ideas on quantum subspaces: a classical diagonalization based on quantum samples, and subspaces constructed with quantum Krylov states. We prove that our algorithm converges in polynomial time under the working assumptions of Krylov quantum diagonalization and sparseness of the ground state. We then demonstrate the scalability of our approach by performing the largest ground-state quantum simulation of impurity models using a Heron quantum processors and the Frontier supercomputer. We consider both the single-impurity Anderson model with 41 bath sites, and a system with 4 impurities and 7 bath sites per impurity. Our results are in excellent agreement with Density Matrix Renormalization Group calculations.