Faster Digital Quantum Simulation by Symmetry Protection

Simulating the dynamics of quantum systems is an important application computers and has seen a variety implementations on current hardware. We show that by introducing gates implementing unitary transformations generated symmetries system, one can induce destructive interference between errors from different steps simulation, effectively giving faster simulation symmetry protection. derive rigorous bounds error symmetry-protected algorithm identify conditions for optimal In particular, when are chosen as powers unitary, approximately projected to so-called Zeno subspaces. prove bound this approximation error, exponentially improving recent result Burgarth, Facchi, Gramegna, Pascazio. apply symmetry-protection technique simulations XXZ Heisenberg interactions with local disorder Schwinger model in field theory. For both systems, reduce several orders magnitude over unprotected simulation. Finally, we provide numerical evidence suggesting also protect against other types coherent, temporally correlated errors, such 1/f noise commonly found solid-state experiments.2 MoreReceived 6 July 2020Accepted 12 January 2021DOI:https://doi.org/10.1103/PRXQuantum.2.010323Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasGauge theoriesMany-body localizationQuantum algorithmsQuantum controlQuantum simulationQuantum InformationCondensed Matter, Materials & Applied PhysicsNuclear Physics