Quantum Algorithms for Testing Hamiltonian Symmetry

TL;DR

This paper introduces quantum algorithms designed to efficiently test Hamiltonian symmetries, linking symmetry detection to acceptance probabilities, and demonstrates their implementation on current quantum hardware.

Contribution

The paper presents novel quantum algorithms for symmetry testing in Hamiltonians, connecting physical symmetry properties with quantum computational acceptance probabilities.

Findings

Algorithms successfully tested on existing quantum computers.

Acceptance probabilities correlate with Hamiltonian symmetry.

Demonstrated effectiveness on simple symmetric and asymmetric cases.

Abstract

Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian exhibits symmetry with respect to a group. We demonstrate that familiar expressions of Hamiltonian symmetry in quantum mechanics correspond directly with the acceptance probabilities of our algorithms. We execute one of our symmetry-testing algorithms on existing quantum computers for simple examples of both symmetric and asymmetric cases.