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002824395 005__ 20230131115915.0
002824395 0248_ $$aoai:cds.cern.ch:2824395$$pcerncds:FULLTEXT$$pcerncds:CERN:FULLTEXT$$pcerncds:CERN
002824395 037__ $$9arXiv$$aarXiv:2208.03333$$cquant-ph
002824395 037__ $$9arXiv:reportnumber$$aCERN-TH-2022-133
002824395 035__ $$9arXiv$$aoai:arXiv.org:2208.03333
002824395 035__ $$9Inspire$$aoai:inspirehep.net:2133192$$d2023-01-30T12:40:56Z$$h2023-01-31T03:03:46Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002824395 035__ $$9Inspire$$a2133192
002824395 041__ $$aeng
002824395 100__ $$aGrabowska, Dorota M.$$mdorota.grabowska@cern.ch$$uCERN$$vTheoretical Physics Department, CERN, 1211 Geneva 23, Switzerland
002824395 245__ $$9arXiv$$aOvercoming exponential scaling with system size in Trotter-Suzuki implementations of constrained Hamiltonians: 2+1 U(1) lattice gauge theories
002824395 269__ $$c2022-08-05
002824395 300__ $$a9 p
002824395 500__ $$9arXiv$$a9 pages, 1 Figure. V2 clarifies how to calculate the Degree of
Coupling and how weaved matrices are constructed to reduce the Degree of
Coupling
002824395 520__ $$9arXiv$$aFor many quantum systems of interest, the classical computational cost of simulating their time evolution scales exponentially in the system size. At the same time, quantum computers have been shown to allow for simulations of some of these systems using resources that scale polynomially with the system size. Given the potential for using quantum computers for simulations that are not feasible using classical devices, it is paramount that one studies the scaling of quantum algorithms carefully. This work identifies a term in the Hamiltonian of a class of constrained systems that naively requires quantum resources that scale exponentially in the system size. An important example is a compact U(1) gauge theory on lattices with periodic boundary conditions. Imposing the magnetic Gauss' law a priori introduces a constraint into that Hamiltonian that naively results in an exponentially deep circuit. A method is then developed that reduces this scaling to polynomial in the system size, using a redefinition of the operator basis. An explicit construction of the matrices defining the change of operator basis, as well as the scaling of the associated computational cost, is given.
002824395 540__ $$3preprint$$aCC BY 4.0$$uhttp://creativecommons.org/licenses/by/4.0/
002824395 595__ $$aCERN-TH
002824395 65017 $$2arXiv$$ahep-ph
002824395 65017 $$2SzGeCERN$$aParticle Physics - Phenomenology
002824395 65017 $$2arXiv$$ahep-lat
002824395 65017 $$2SzGeCERN$$aParticle Physics - Lattice
002824395 65017 $$2arXiv$$aquant-ph
002824395 65017 $$2SzGeCERN$$aGeneral Theoretical Physics
002824395 690C_ $$aCERN
002824395 690C_ $$aPREPRINT
002824395 700__ $$aKane, Christopher$$mcfkane@arizona.edu$$uArizona U.$$vDepartment of Physics, University of Arizona, Tucson, AZ 85719, USA
002824395 700__ $$aNachman, Benjamin$$mbpnachman@lbl.gov$$uLBL, Berkeley$$vPhysics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
002824395 700__ $$aBauer, Christian W.$$mcwbauer@lbl.gov$$uLBL, Berkeley$$vPhysics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
002824395 8564_ $$82383013$$s1809048$$uhttp://cds.cern.ch/record/2824395/files/2208.03333.pdf$$yFulltext
002824395 8564_ $$82383014$$s697748$$uhttp://cds.cern.ch/record/2824395/files/OriginalBasis.png$$y00000 : Degree of coupling in the original basis. The system has maximum DoC, resulting in circuit depths that are exponential in the volume.
002824395 8564_ $$82383015$$s143618$$uhttp://cds.cern.ch/record/2824395/files/WeavedBasis.png$$y00001 : Degree of connectivity in the weaved basis. This reduction in connectivity results in a circuit depth that scales polynomially in the volume. : Diagrammatic depiction of the Degree of Connectivity for a system with 16 total operators. Fig.~\ref{fig:OriginalBasis} shows the result for a Hamiltonian with the original constraint giving rise to maximal ${\rm DoC} = 16$. Fig.~\ref{fig:WeavedBasis} illustrates the DoC after the operator basis has been transformed to reduce the degree of connectivity, using the weaved operation. The degree of connectivity is now $\rm DoC = 4$, coming from the terms involving $\CO_1$, $\CO_5$, $\CO_9$ and $\CO_{13}$. Note that both Hamiltonians have the same spectrum, up to digitization effects. The operator $\CO_i$ could be $\CP_i$ or $\CQ_i$.
002824395 960__ $$a11
002824395 980__ $$aPREPRINT