



01716nas a2200169   4500008004100000245005800041210005800099260001300157520120700170100002501377700002001402700001801422700002801440700001901468700002201487856003701509       2024                        eng d00aIntegrability of Goldilocks quantum cellular automata0 aIntegrability of Goldilocks quantum cellular automata  c4/3/20243 a<p>Goldilocks quantum cellular automata (QCA) have been simulated on quantum hardware and produce emergent small-world correlation networks. In Goldilocks QCA, a single-qubit unitary is applied to each qubit in a one-dimensional chain subject to a balance constraint: a qubit is updated if its neighbors are in opposite basis states. Here, we prove that a subclass of Goldilocks QCA -- including the one implemented experimentally -- map onto free fermions and therefore can be classically simulated efficiently. We support this claim with two independent proofs, one involving a Jordan--Wigner transformation and one mapping the integrable six-vertex model to QCA. We compute local conserved quantities of these QCA and predict experimentally measurable expectation values. These calculations can be applied to test large digital quantum computers against known solutions. In contrast, typical Goldilocks QCA have equilibration properties and quasienergy-level statistics that suggest nonintegrability. Still, the latter QCA conserve one quantity useful for error mitigation. Our work provides a parametric quantum circuit with tunable integrability properties with which to test quantum hardware.</p>1 aHillberry, Logan, E.1 aPiroli, Lorenzo1 aVernier, Eric1 aHalpern, Nicole, Yunger1 aProsen, Tomaž1 aCarr, Lincoln, D.  uhttps://arxiv.org/abs/2404.02994