Evaluating Sample-Based Krylov Quantum Diagonalization for Heisenberg Models with Applications to Materials Science

TL;DR

This paper evaluates the Sample-based Krylov Quantum Diagonalization algorithm on Heisenberg models, demonstrating its accuracy in ground state energy calculations and magnetization, with successful hardware implementation and applicability to 2D systems.

Contribution

The paper introduces and benchmarks SKQD for Heisenberg models, showing its effectiveness in strongly correlated regimes and on quantum hardware, extending applicability beyond 1D.

Findings

Accurately reproduces ground-state energies and magnetization.

Consistent agreement with DMRG and exact diagonalization.

Successful implementation on quantum hardware with 18- and 30-qubit chains.

Abstract

We evaluate the Sample-based Krylov Quantum Diagonalization (SKQD) algorithm on one- and two-dimensional Heisenberg models, including strongly correlated regimes in which the ground state is dense. Using problem-informed initial states and magnetization-sector sweeps, SKQD accurately reproduces ground-state energies and field-dependent magnetization across a range of anisotropies. Benchmarks against DMRG and exact diagonalization show consistent qualitative agreement, with accuracy improving systematically in more anisotropic regimes. We further demonstrate SKQD on quantum hardware by implementing 18- and 30-qubit Heisenberg chains, obtaining magnetization curves that match theoretical expectations. Simulations on small 2D square-lattice systems further demonstrate that the method applies effectively beyond 1D geometries.