arXiv:2605.18966

Clifford symmetries in quantum many-body systems

Charlie Nation, Rick P. A. Simon, Shreya Banerjee, Francesco Martini, Alessandro Ricottone, Federico Cerisola, Luca Dellantonio

quant-phSubmitted May 18, 2026• Announced May 20, 2026• 0 citations

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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.

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