Variational Power of Quantum Circuit Tensor Networks

Haghshenas, Reza; Gray, Johnnie; Potter, Andrew C.; Chan, Garnet Kin-Lic

doi:10.1103/PhysRevX.12.011047

Title: Variational Power of Quantum Circuit Tensor Networks

Abstract

We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multiscale entanglement renormalization Ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than 10⁴ parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for the 1D and 2D Heisenberg and 1D Fermi-Hubbard models. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of advantage in quantum expressiveness in the representation of physical ground states.

Authors:

;

; Potter, Andrew C.; Chan, Garnet Kin-Lic

Publication Date:: Fri Mar 11 00:00:00 EST 2022

Research Org.:: Emory Univ., Atlanta, GA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC); Simons Foundation; National Science Foundation (NSF); Amazon Web Services, Inc.

OSTI Identifier:: 1854378

Alternate Identifier(s):: OSTI ID: 1980361

Grant/Contract Number:: SC0019374; 2040549

Resource Type:: Published Article

Journal Name:: Physical Review. X

Additional Journal Information:: Journal Name: Physical Review. X Journal Volume: 12 Journal Issue: 1; Journal ID: ISSN 2160-3308

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; quantum computation; quantum simulation; tensor network methods

Citation Formats


                    Haghshenas, Reza, Gray, Johnnie, Potter, Andrew C., and Chan, Garnet Kin-Lic. Variational Power of Quantum Circuit Tensor Networks.  United States: N. p., 2022. 
Web.  doi:10.1103/PhysRevX.12.011047.

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                    Haghshenas, Reza, Gray, Johnnie, Potter, Andrew C., & Chan, Garnet Kin-Lic. Variational Power of Quantum Circuit Tensor Networks.  United States.  https://doi.org/10.1103/PhysRevX.12.011047

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                    Haghshenas, Reza, Gray, Johnnie, Potter, Andrew C., and Chan, Garnet Kin-Lic. Fri .  
"Variational Power of Quantum Circuit Tensor Networks".  United States.  https://doi.org/10.1103/PhysRevX.12.011047.

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@article{osti_1854378,

  title        = {Variational Power of Quantum Circuit Tensor Networks},

  author       = {Haghshenas, Reza and Gray, Johnnie and Potter, Andrew C. and Chan, Garnet Kin-Lic},

  abstractNote = {We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multiscale entanglement renormalization Ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than 104 parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for the 1D and 2D Heisenberg and 1D Fermi-Hubbard models. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of advantage in quantum expressiveness in the representation of physical ground states.},

  doi          = {10.1103/PhysRevX.12.011047},

  journal      = {Physical Review. X},

  number       = 1,

  volume       = 12,

  place        = {United States},

  year         = {Fri Mar 11 00:00:00 EST 2022},

  month        = {Fri Mar 11 00:00:00 EST 2022}

}

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Title: Variational Power of Quantum Circuit Tensor Networks

Abstract

Citation Formats

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Isometric Tensor Network States in Two Dimensions
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Cost function dependent barren plateaus in shallow parametrized quantum circuits
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Rigorous results on valence-bond ground states in antiferromagnets
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Quantum Algorithms for Quantum Chemistry and Quantum Materials Science
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Matrix product state representations
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Unifying neural-network quantum states and correlator product states via tensor networks
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Accelerated Variational Quantum Eigensolver
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Sequential generation of matrix-product states in cavity QED
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