Quantum Many Body Hamiltonians stored symbolically in polynomial memory

ORAL

Abstract

The quantum many particle Hamiltonian contains many undiscovered new physics, however remains intractable due to its large size. Traditional methods of storing these Hamiltonians in memory will consume exponential amount of memory. If we want to simulate N particles, where each particle can only occupy two states, then the numerical size of the Hamiltonian stored in traditional sparse matrix form will consume O(2N) number of bits. The largest computer we can build is limited by the number of atoms in the observable universe. If every atom in the observable universe is assigned one bit of memory storage, then the maximum number of particles that can be simulated is 270. A typical unit cell simulated in materials science can contain from 100 to 1000 electrons. This illustrates the need for a better method for quantum many particle simulations. We will present a numerical method of storing the quantum many particle Hamiltonian in polynomial memory and still retain useful diagonalization tools for polynomial computation time.

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Presenters

  • Benjamin Commeau

    Univ of Connecticut - Storrs, Physics, Univ of Connecticut

Authors

  • Benjamin Commeau

    Univ of Connecticut - Storrs, Physics, Univ of Connecticut

  • Alexey Feofanov

    University of Innsbruck, University of Waterloo, Korea University, Okinawa Institute of Science and Technology, University of California - Los Angeles, The University of Manchester, University of Puerto Rico at Humacao, Department of Physics & Electronics, University of Puerto Rico at Cayey, Department of Mathematics-Physics, Oak Ridge National Lab, Max Planck Institute for Chemical Physics of Solids, Department of Physics, University of Puerto Rico, Electrical Engineering Department, University of Arkansas, Department of Physics, University of Arkansas, School of Basic Sciences at IIT Mandi, H.P., India, Computational Biology, Flatiron Institute, Physics, Hong Kong Univ of Sci & Tech, University of California, Los Angeles, Max Planck Inst, Institute for Theoretical Physics, University of Cologne, Department of Physics, Simon Fraser University, Deutsches Elektronen Synchrotron (DESY), Institut fur Theoretische Physik, Univerisitat zu Berlin, Institut fur Physik, Univerisitat zu Berlin, Plymouth State University, The Graduate Center, CUNY, Nordita, KTH Royal Institute of Technology and Stockholm University, Univ of Connecticut - Storrs, Univ Stuttgart, University of Chicago, University of Texas at El Paso, University of Tulsa, California Institute of Technology, Georgia Institute of Technology, Universite Paris Diderot, Laboratoire MPQ, Universita di Trento, BEC Center, ICTP Trieste, Universita di Pisa, Inst of Physics Academia Sinica, Batelle, Cal State Univ- San Bernardino, Chemical Engineering, University of Michigan, QCD Labs, Department of Applied Physics, Aalto University, Yale University, MIT, Harvard Univ, Chemical & Environmental Engineering, University of California, Riverside, University of Frankfurt, Germany, University of Hamburg, Germany, Naval Research Laboratory, Cornell Univ, National Institute for Material Science, U.S. Naval Research Laboratory, Washington DC, Materials Engineering, University of Santa Barbara, Institute of Physics, Chinese Academy of Sciences, Univ of Texas, Arlington, MIT Lincoln Laboratory, University of Sydney, Iowa State University, Purdue University, Kansas State University, University of Maryland, John Hopkins University, Universite de Sherbrooke, Physics, Konkuk University, Perimeter Institute, University of Waterloo, D-Wave, San Jose State University, Université de Sherbrooke, Institute of Physics, EPFL - Lausanne​

  • Alexey Feofanov

    University of Innsbruck, University of Waterloo, Korea University, Okinawa Institute of Science and Technology, University of California - Los Angeles, The University of Manchester, University of Puerto Rico at Humacao, Department of Physics & Electronics, University of Puerto Rico at Cayey, Department of Mathematics-Physics, Oak Ridge National Lab, Max Planck Institute for Chemical Physics of Solids, Department of Physics, University of Puerto Rico, Electrical Engineering Department, University of Arkansas, Department of Physics, University of Arkansas, School of Basic Sciences at IIT Mandi, H.P., India, Computational Biology, Flatiron Institute, Physics, Hong Kong Univ of Sci & Tech, University of California, Los Angeles, Max Planck Inst, Institute for Theoretical Physics, University of Cologne, Department of Physics, Simon Fraser University, Deutsches Elektronen Synchrotron (DESY), Institut fur Theoretische Physik, Univerisitat zu Berlin, Institut fur Physik, Univerisitat zu Berlin, Plymouth State University, The Graduate Center, CUNY, Nordita, KTH Royal Institute of Technology and Stockholm University, Univ of Connecticut - Storrs, Univ Stuttgart, University of Chicago, University of Texas at El Paso, University of Tulsa, California Institute of Technology, Georgia Institute of Technology, Universite Paris Diderot, Laboratoire MPQ, Universita di Trento, BEC Center, ICTP Trieste, Universita di Pisa, Inst of Physics Academia Sinica, Batelle, Cal State Univ- San Bernardino, Chemical Engineering, University of Michigan, QCD Labs, Department of Applied Physics, Aalto University, Yale University, MIT, Harvard Univ, Chemical & Environmental Engineering, University of California, Riverside, University of Frankfurt, Germany, University of Hamburg, Germany, Naval Research Laboratory, Cornell Univ, National Institute for Material Science, U.S. Naval Research Laboratory, Washington DC, Materials Engineering, University of Santa Barbara, Institute of Physics, Chinese Academy of Sciences, Univ of Texas, Arlington, MIT Lincoln Laboratory, University of Sydney, Iowa State University, Purdue University, Kansas State University, University of Maryland, John Hopkins University, Universite de Sherbrooke, Physics, Konkuk University, Perimeter Institute, University of Waterloo, D-Wave, San Jose State University, Université de Sherbrooke, Institute of Physics, EPFL - Lausanne​

  • Alexey Feofanov

    University of Innsbruck, University of Waterloo, Korea University, Okinawa Institute of Science and Technology, University of California - Los Angeles, The University of Manchester, University of Puerto Rico at Humacao, Department of Physics & Electronics, University of Puerto Rico at Cayey, Department of Mathematics-Physics, Oak Ridge National Lab, Max Planck Institute for Chemical Physics of Solids, Department of Physics, University of Puerto Rico, Electrical Engineering Department, University of Arkansas, Department of Physics, University of Arkansas, School of Basic Sciences at IIT Mandi, H.P., India, Computational Biology, Flatiron Institute, Physics, Hong Kong Univ of Sci & Tech, University of California, Los Angeles, Max Planck Inst, Institute for Theoretical Physics, University of Cologne, Department of Physics, Simon Fraser University, Deutsches Elektronen Synchrotron (DESY), Institut fur Theoretische Physik, Univerisitat zu Berlin, Institut fur Physik, Univerisitat zu Berlin, Plymouth State University, The Graduate Center, CUNY, Nordita, KTH Royal Institute of Technology and Stockholm University, Univ of Connecticut - Storrs, Univ Stuttgart, University of Chicago, University of Texas at El Paso, University of Tulsa, California Institute of Technology, Georgia Institute of Technology, Universite Paris Diderot, Laboratoire MPQ, Universita di Trento, BEC Center, ICTP Trieste, Universita di Pisa, Inst of Physics Academia Sinica, Batelle, Cal State Univ- San Bernardino, Chemical Engineering, University of Michigan, QCD Labs, Department of Applied Physics, Aalto University, Yale University, MIT, Harvard Univ, Chemical & Environmental Engineering, University of California, Riverside, University of Frankfurt, Germany, University of Hamburg, Germany, Naval Research Laboratory, Cornell Univ, National Institute for Material Science, U.S. Naval Research Laboratory, Washington DC, Materials Engineering, University of Santa Barbara, Institute of Physics, Chinese Academy of Sciences, Univ of Texas, Arlington, MIT Lincoln Laboratory, University of Sydney, Iowa State University, Purdue University, Kansas State University, University of Maryland, John Hopkins University, Universite de Sherbrooke, Physics, Konkuk University, Perimeter Institute, University of Waterloo, D-Wave, San Jose State University, Université de Sherbrooke, Institute of Physics, EPFL - Lausanne​