How tractable is the simulation of open quantum system dynamics of Ising models?

ORAL

Abstract

A near-term goal for Noisy Intermediate Scale Quantum (NISQ) devices is quantum simulation of nonequilibrium dynamics in many-body systems [Preskill Quantum 2, 79 (2018)]. While the exact unitary dynamics of a closed many-body quantum systems is generally intractable, recent work has shown that approximate simulations of NISQ devices are tractable [Zhou, et al, arXiv:2002.07730; Noh, et al, arXiv:2003.13163]. We expect that classical simulation of certain quantum observables becomes tractable above a certain level of decoherence. We assume open quantum system dynamics given by a Lindblad master equation, which we solve using quantum trajectories and a matrix product state representation. We study this in the context of Ising spin chains in 1D, inspired by experiments using arrays of Rydberg atoms and trapped ions. We explore how decoherence allows for a larger truncation of the bond dimension of tensors in the matrix product state representation while still maintaining a good approximation to the exact dynamics. We find that for a fixed error budget, the complexity of the matrix product representation, is reduced for open quantum systems. This suggests that quantum simulation of many-body dynamics on NISQ devices may be classically tractable for some decoherence strengths.

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Authors

  • Anupam Mitra

    University of New Mexico, Center for Quantum Information and Control, University of New Mexico

  • Barry Ritchie

    University of New Mexico, Ion Linac Systems, Tech-X Corporation, Los Alamos National Laboratory, Ronald Reagan UCLA Medical Center, Brigham Young University, Brigham Young University - Provo, United States Air Force Academy, university of Michigan, SISSA, Trieste, Stanford University, Worcester Polytechnic Institute, Grinnell College, Department of Physics, Arizona State University, Brookhaven National Laboratory, University of Southern California, Argonne National Laboratory, Department of Electrical and Computer Engineering, University of New Mexico, Department of Electrical and Computer Engineering and Department of Mechanical Engineering, University of New Mexico, Lock Haven University, Illinois State University, Department of Physics, Utah State University, Logan, Utah, 84322, Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, USA, Department of Materials, Devices, and Energy Technologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA, Kyoto University, University of Guadalajara, University of Florida, Embry-Riddle Aeronautical University, Air Force Research Laboratory, Space Vehicles Directorate, Assurance Technology Corporation, Carlisle, MA, Georgia Tech Research Institute, Atlanta, GA, Utah State University, Georgia Institute of Technology, University of Tennessee, Knoxville, Arizona State University, Department of Physics, United States Air Force Academy, 80840 USAFA, CO, USA, Shaffer Consulting Inc, Max Planck Institute for Astrophysics, Harvard University, Max Planck Institute for Gravitational Physics, Albert Einstein Institute, ASU

  • Barry Ritchie

    University of New Mexico, Ion Linac Systems, Tech-X Corporation, Los Alamos National Laboratory, Ronald Reagan UCLA Medical Center, Brigham Young University, Brigham Young University - Provo, United States Air Force Academy, university of Michigan, SISSA, Trieste, Stanford University, Worcester Polytechnic Institute, Grinnell College, Department of Physics, Arizona State University, Brookhaven National Laboratory, University of Southern California, Argonne National Laboratory, Department of Electrical and Computer Engineering, University of New Mexico, Department of Electrical and Computer Engineering and Department of Mechanical Engineering, University of New Mexico, Lock Haven University, Illinois State University, Department of Physics, Utah State University, Logan, Utah, 84322, Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, USA, Department of Materials, Devices, and Energy Technologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA, Kyoto University, University of Guadalajara, University of Florida, Embry-Riddle Aeronautical University, Air Force Research Laboratory, Space Vehicles Directorate, Assurance Technology Corporation, Carlisle, MA, Georgia Tech Research Institute, Atlanta, GA, Utah State University, Georgia Institute of Technology, University of Tennessee, Knoxville, Arizona State University, Department of Physics, United States Air Force Academy, 80840 USAFA, CO, USA, Shaffer Consulting Inc, Max Planck Institute for Astrophysics, Harvard University, Max Planck Institute for Gravitational Physics, Albert Einstein Institute, ASU

  • Barry Ritchie

    University of New Mexico, Ion Linac Systems, Tech-X Corporation, Los Alamos National Laboratory, Ronald Reagan UCLA Medical Center, Brigham Young University, Brigham Young University - Provo, United States Air Force Academy, university of Michigan, SISSA, Trieste, Stanford University, Worcester Polytechnic Institute, Grinnell College, Department of Physics, Arizona State University, Brookhaven National Laboratory, University of Southern California, Argonne National Laboratory, Department of Electrical and Computer Engineering, University of New Mexico, Department of Electrical and Computer Engineering and Department of Mechanical Engineering, University of New Mexico, Lock Haven University, Illinois State University, Department of Physics, Utah State University, Logan, Utah, 84322, Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, USA, Department of Materials, Devices, and Energy Technologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA, Kyoto University, University of Guadalajara, University of Florida, Embry-Riddle Aeronautical University, Air Force Research Laboratory, Space Vehicles Directorate, Assurance Technology Corporation, Carlisle, MA, Georgia Tech Research Institute, Atlanta, GA, Utah State University, Georgia Institute of Technology, University of Tennessee, Knoxville, Arizona State University, Department of Physics, United States Air Force Academy, 80840 USAFA, CO, USA, Shaffer Consulting Inc, Max Planck Institute for Astrophysics, Harvard University, Max Planck Institute for Gravitational Physics, Albert Einstein Institute, ASU