Symmetry-adapted sample-based quantum diagonalization: Application to lattice model

TL;DR

This paper introduces a symmetry-adapted extension of sample-based quantum diagonalization that improves energy convergence and captures symmetry effects in quantum simulations of lattice models.

Contribution

The method rigorously embeds space-group symmetry into quantum diagonalization, enhancing accuracy and efficiency in simulating correlated many-body systems.

Findings

Energy convergence improved in momentum basis

Symmetry embedding enhances simulation accuracy

Superconducting correlations are effectively captured

Abstract

We present a symmetry-adapted extension of sample-based quantum diagonalization (SQD) that rigorously embeds space-group symmetry into the many-body subspace sampled by quantum hardware. The method is benchmarked on the two-leg ladder Hubbard model using both molecular orbital and momentum bases. Energy convergence is shown to be improved in the momentum basis compared to the molecular orbital basis for both the spin-quintet ground state and the spin-singlet excited state. We clarify the relationship between the compactness of the many-body wave function and the sparsity of the representation matrices of symmetry operations. Furthermore, the enhancement of the superconducting correlation function due to the Coulomb interaction is demonstrated. Our method highlights the importance of symmetry structure in random-sampling quantum simulation of correlated systems