Sample-Based Krylov Quantum Diagonalization for the Schwinger Model on Trapped-Ion and Superconducting Quantum Processors

TL;DR

This paper introduces Sample-based Krylov Quantum Diagonalization (SKQD), a hybrid quantum-classical method for approximating ground states of lattice gauge theories, demonstrated on the Schwinger model using trapped-ion and superconducting quantum processors.

Contribution

The paper presents SKQD, a novel hybrid quantum-classical algorithm that efficiently approximates ground states of lattice gauge theories, reducing Hilbert space complexity and applicable on current quantum hardware.

Findings

Accurately captures the phase structure of the Schwinger model.

Demonstrates consistent performance on different quantum hardware platforms.

Shows that SKQD reduces the effective Hilbert space size.

Abstract

We apply the recently proposed Sample-based Krylov Quantum Diagonalization (SKQD) method to lattice gauge theories, using the Schwinger model with a $\theta$-term as a benchmark. SKQD approximates the ground state of a Hamiltonian, employing a hybrid quantum-classical approach: (i) constructing a Krylov space from bitstrings sampled from time-evolved quantum states, and (ii) classically diagonalizing the Hamiltonian within this subspace. We study the dependence of the ground-state energy and particle number on the value of the $\theta$-term, accurately capturing the model's phase structure. The algorithm is implemented on trapped-ion and superconducting quantum processors, demonstrating consistent performance across platforms. We show that SKQD substantially reduces the effective Hilbert space, and although the Krylov space dimension still scales exponentially, the slower growth underscores its promise for simulating lattice gauge theories in larger volumes.