Clifford symmetries in quantum many-body systems

TL;DR

This paper introduces an algorithm leveraging the Clifford group to efficiently find symmetries in quantum many-body Hamiltonians, aiding understanding and solving of complex models.

Contribution

The authors develop a novel graph-based algorithm that automates symmetry detection in large quantum systems using Clifford group properties.

Findings

Successfully applied to Hamiltonians with up to 1000 qubits

Revealed deeper insights into model structures

Complemented human intuition with computational method

Abstract

Obtaining the symmetries of a model is a critical step towards developing an understanding and ultimately analytically or numerically solving the model. However, finding symmetries is generally extremely complicated, often being the result of insightful thinking. In this work, we complement human ingenuity with an algorithm. We leverage the classically efficient Clifford group to find symmetries for arbitrary many-body Hamiltonians via a graph representation. We demonstrate our method on random and physical Hamiltonians, with instances of up to one thousand qubits and demonstrate how our approach can provide deeper understanding of the model.