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dc.contributor.authorBukov, Marinen_US
dc.contributor.authorSels, Driesen_US
dc.contributor.authorPolkovnikov, Anatolien_US
dc.date.accessioned2019-06-12T18:21:19Z
dc.date.available2019-06-12T18:21:19Z
dc.date.issued2019-02-20
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000459213500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationMarin Bukov, Dries Sels, Anatoli Polkovnikov. 2019. "Geometric Speed Limit of Accessible Many-Body State Preparation." PHYSICAL REVIEW X, Volume 9, Issue 1, pp. ? - ? (21). https://doi.org/10.1103/PhysRevX.9.011034
dc.identifier.issn2160-3308
dc.identifier.urihttps://hdl.handle.net/2144/35976
dc.description.abstractWe analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is bounded from below by the geodesic length set by the quantum geometric tensor. The conjecture implies a geometric lower bound for the quantum speed limit (QSL). We prove the conjecture for arbitrary, sufficiently slow protocols using adiabatic perturbation theory and show that the bound is saturated by geodesic protocols, which keep the energy variance constant along the trajectory. Our conjecture implies that any optimal unit-fidelity protocol, even those that drive the system far from equilibrium, are fundamentally constrained by the quantum geometry of adiabatic evolution. When the control space includes all possible couplings, spanning the full Hilbert space, we recover the well-known Mandelstam-Tamm bound. However, using only accessible local controls to anneal in complex models such as glasses or to target individual excited states in quantum chaotic systems, the geometric bound for the quantum speed limit can be exponentially large in the system size due to a diverging geodesic length. We validate our conjecture both analytically by constructing counter-diabatic and fast-forward protocols for a three-level system, and numerically in nonintegrable spin chains and a nonlocal SYK model.en_US
dc.description.sponsorshipThe authors wish to thank Anatoly Dymarsky for interesting and useful discussions. M. B. acknowledges support from the Emergent Phenomena in Quantum Systems initiative of the Gordon and Betty Moore Foundation, the ERC synergy grant UQUAM, and the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Quantum Algorithm Teams Program. D. S. acknowledges support from the FWO as part of the Research Foundation-Flanders and CMTV. A. P. was supported by NSF DMR-1506340, NSF DMR-1813499, and AFOSR FA9550-16-1-0334. This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958. We used QuSpin for simulating the dynamics of the spin systems [89,90]. The authors are pleased to acknowledge that the computational work reported on in this paper was performed on the Shared Computing Cluster, which is administered by Boston University's Research Computing Services. The authors also acknowledge the Research Computing Services group for providing consulting support, which has contributed to the results reported within this paper. (Emergent Phenomena in Quantum Systems initiative of the Gordon and Betty Moore Foundation; ERC synergy grant UQUAM; U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Quantum Algorithm Teams Program; FWO as part of the Research Foundation-Flanders; CMTV; DMR-1506340 - NSF; DMR-1813499 - NSF; FA9550-16-1-0334 - AFOSR; NSF PHY-1748958 - National Science Foundation)en_US
dc.format.extentp. 21en_US
dc.languageEnglish
dc.language.isoen_US
dc.publisherAMER PHYSICAL SOCen_US
dc.relation.ispartofPHYSICAL REVIEW X
dc.rightsAttribution 4.0 Internationalen_US
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectScience & technologyen_US
dc.subjectPhysical sciencesen_US
dc.subjectPhysics, multidisciplinaryen_US
dc.subjectPhysicsen_US
dc.subjectCondensed matter physicsen_US
dc.subjectQuantum physicsen_US
dc.subjectQuantumen_US
dc.subjectEvolutionen_US
dc.subjectSystemsen_US
dc.titleGeometric speed limit of accessible many-body state preparationen_US
dc.typeArticleen_US
dc.description.versionPublished versionen_US
dc.identifier.doi10.1103/PhysRevX.9.011034
pubs.elements-sourceweb-of-scienceen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Physicsen_US
pubs.publication-statusPublisheden_US
dc.identifier.orcid0000-0002-5549-7400 (Polkovnikov, Anatoli)
dc.identifier.mycv364150


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