LOCALITY, SYMMETRY, AND DIGITAL SIMULATION OF QUANTUM SYSTEMS

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dc.contributor.advisorGorshkov, Alexey V.en_US
dc.contributor.advisorTaylor, Jacob M.en_US
dc.contributor.authorTran, Cong Minhen_US
dc.contributor.departmentPhysicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2021-09-17T05:37:00Z
dc.date.available2021-09-17T05:37:00Z
dc.date.issued2021en_US
dc.description.abstractBesides potentially delivering a huge leap in computational power, quantum computers also offer an essential platform for simulating properties of quantum systems. Consequently, various algorithms have been developed for approximating the dynamics of a target system on quantum computers. But generic quantum simulation algorithms—developed to simulate all Hamiltonians—are unlikely to result in optimal simulations of most physically relevant systems; optimal quantum algorithms need to exploit unique properties of target systems. The aim of this dissertation is to study two prominent properties of physical systems, namely locality and symmetry, and subsequently leverage these properties to design efficient quantum simulation algorithms. In the first part of the dissertation, we explore the locality of quantum systems and the fundamental limits on the propagation of information in power-law interacting systems. In particular, we prove upper limits on the speed at which information can propagate in power-law systems. We also demonstrate how such speed limits can be achieved by protocols for transferring quantum information and generating quantum entanglement. We then use these speed limits to constrain the propagation of error and improve the performance of digital quantum simulation. Additionally, we consider the implications of the speed limits on entanglement generation, the dynamics of correlation, the heating time, and the scrambling time in power-law interacting systems. In the second part of the dissertation, we propose a scheme to leverage the symmetry of target systems to suppress error in digital quantum simulation. We first study a phenomenon called destructive error interference, where the errors from different steps of a simulation cancel out each other. We then show that one can induce the destructive error interference by interweaving the simulation with unitary transformations generated by the symmetry of the target system, effectively providing a faster quantum simulation by symmetry protection. We also derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection.en_US
dc.identifierhttps://doi.org/10.13016/rzpy-tlxg
dc.identifier.urihttp://hdl.handle.net/1903/27827
dc.language.isoenen_US
dc.subject.pqcontrolledQuantum physicsen_US
dc.subject.pqcontrolledCondensed matter physicsen_US
dc.subject.pqcontrolledComputer scienceen_US
dc.subject.pquncontrolledEntanglement generationen_US
dc.subject.pquncontrolledError mitigationen_US
dc.subject.pquncontrolledLieb-Robinson bounden_US
dc.subject.pquncontrolledQuantum algorithmen_US
dc.subject.pquncontrolledQuantum simulationen_US
dc.subject.pquncontrolledState transferen_US
dc.titleLOCALITY, SYMMETRY, AND DIGITAL SIMULATION OF QUANTUM SYSTEMSen_US
dc.typeDissertationen_US

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