Many-Body Thermodynamics on Quantum Computers via Partition Function Zeros

Akhil Francis; Peter Schauss; Peter Schauss; Peter Schauss; Peter Schauss; Peter Schauss; Peter Schauss; Peter Schauss; Peter Schauss

Many-Body Thermodynamics on Quantum Computers via Partition Function Zeros

ORAL

Abstract

Partition functions are ubiquitous in physics: they are important in determining the thermodynamic properties of many-body systems, and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the complex plane allows us to obtains its zeros and thus the entire function. Moreover, the scaling and nature of these zeros can elucidate phase transitions. Here we show how to find partition function zeros on noisy intermediate-scale trapped ion quantum computers in a scalable manner, using the XXZ model as a prototype. We illustrate the transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the determination of critical phenomena for systems that cannot be solved otherwise.

Nov. 5, 2020, 11:48 AM – Nov. 5, 2020, 12:00 PM

Authors

Akhil Francis

North Carolina State University
Peter Schauss

University of Notre Dame, Los Alamos National Laboratory, North Carolina State University, University of Notre dame, Columbia University, Mississippi State Univ, University of Pennsylvania, Carnegie Mellon University, University of Puerto Rico at Humacao, JLAB, MIT, University of Alabama at Birmingham, Florida State University, NHMFL, University College Dublin, Department of Physics, Florida State University; National High Magnetic Field Laboratory, CNR-Instituto Nanoscienze, Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology, Department of Chemistry, Florida State University, University of Alabama at Birmingham, Department of Physics, Birmingham, AL 35294-1170,USA, Department of Chemistry, Virginia Polytechnic Institute and State University, Francis Marion University, University of Richmond, Valdosta State University, University of Pittsburgh, Fermi National Lab, university of minnesota, Univ of Virginia, Joint Quantum Institute, University of Maryland, Georgetown University, IonQ Inc.
Peter Schauss

University of Notre Dame, Los Alamos National Laboratory, North Carolina State University, University of Notre dame, Columbia University, Mississippi State Univ, University of Pennsylvania, Carnegie Mellon University, University of Puerto Rico at Humacao, JLAB, MIT, University of Alabama at Birmingham, Florida State University, NHMFL, University College Dublin, Department of Physics, Florida State University; National High Magnetic Field Laboratory, CNR-Instituto Nanoscienze, Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology, Department of Chemistry, Florida State University, University of Alabama at Birmingham, Department of Physics, Birmingham, AL 35294-1170,USA, Department of Chemistry, Virginia Polytechnic Institute and State University, Francis Marion University, University of Richmond, Valdosta State University, University of Pittsburgh, Fermi National Lab, university of minnesota, Univ of Virginia, Joint Quantum Institute, University of Maryland, Georgetown University, IonQ Inc.
Peter Schauss

University of Notre Dame, Los Alamos National Laboratory, North Carolina State University, University of Notre dame, Columbia University, Mississippi State Univ, University of Pennsylvania, Carnegie Mellon University, University of Puerto Rico at Humacao, JLAB, MIT, University of Alabama at Birmingham, Florida State University, NHMFL, University College Dublin, Department of Physics, Florida State University; National High Magnetic Field Laboratory, CNR-Instituto Nanoscienze, Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology, Department of Chemistry, Florida State University, University of Alabama at Birmingham, Department of Physics, Birmingham, AL 35294-1170,USA, Department of Chemistry, Virginia Polytechnic Institute and State University, Francis Marion University, University of Richmond, Valdosta State University, University of Pittsburgh, Fermi National Lab, university of minnesota, Univ of Virginia, Joint Quantum Institute, University of Maryland, Georgetown University, IonQ Inc.
Peter Schauss

University of Notre Dame, Los Alamos National Laboratory, North Carolina State University, University of Notre dame, Columbia University, Mississippi State Univ, University of Pennsylvania, Carnegie Mellon University, University of Puerto Rico at Humacao, JLAB, MIT, University of Alabama at Birmingham, Florida State University, NHMFL, University College Dublin, Department of Physics, Florida State University; National High Magnetic Field Laboratory, CNR-Instituto Nanoscienze, Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology, Department of Chemistry, Florida State University, University of Alabama at Birmingham, Department of Physics, Birmingham, AL 35294-1170,USA, Department of Chemistry, Virginia Polytechnic Institute and State University, Francis Marion University, University of Richmond, Valdosta State University, University of Pittsburgh, Fermi National Lab, university of minnesota, Univ of Virginia, Joint Quantum Institute, University of Maryland, Georgetown University, IonQ Inc.
Peter Schauss

University of Notre Dame, Los Alamos National Laboratory, North Carolina State University, University of Notre dame, Columbia University, Mississippi State Univ, University of Pennsylvania, Carnegie Mellon University, University of Puerto Rico at Humacao, JLAB, MIT, University of Alabama at Birmingham, Florida State University, NHMFL, University College Dublin, Department of Physics, Florida State University; National High Magnetic Field Laboratory, CNR-Instituto Nanoscienze, Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology, Department of Chemistry, Florida State University, University of Alabama at Birmingham, Department of Physics, Birmingham, AL 35294-1170,USA, Department of Chemistry, Virginia Polytechnic Institute and State University, Francis Marion University, University of Richmond, Valdosta State University, University of Pittsburgh, Fermi National Lab, university of minnesota, Univ of Virginia, Joint Quantum Institute, University of Maryland, Georgetown University, IonQ Inc.
Peter Schauss

University of Notre Dame, Los Alamos National Laboratory, North Carolina State University, University of Notre dame, Columbia University, Mississippi State Univ, University of Pennsylvania, Carnegie Mellon University, University of Puerto Rico at Humacao, JLAB, MIT, University of Alabama at Birmingham, Florida State University, NHMFL, University College Dublin, Department of Physics, Florida State University; National High Magnetic Field Laboratory, CNR-Instituto Nanoscienze, Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology, Department of Chemistry, Florida State University, University of Alabama at Birmingham, Department of Physics, Birmingham, AL 35294-1170,USA, Department of Chemistry, Virginia Polytechnic Institute and State University, Francis Marion University, University of Richmond, Valdosta State University, University of Pittsburgh, Fermi National Lab, university of minnesota, Univ of Virginia, Joint Quantum Institute, University of Maryland, Georgetown University, IonQ Inc.
Peter Schauss

University of Notre Dame, Los Alamos National Laboratory, North Carolina State University, University of Notre dame, Columbia University, Mississippi State Univ, University of Pennsylvania, Carnegie Mellon University, University of Puerto Rico at Humacao, JLAB, MIT, University of Alabama at Birmingham, Florida State University, NHMFL, University College Dublin, Department of Physics, Florida State University; National High Magnetic Field Laboratory, CNR-Instituto Nanoscienze, Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology, Department of Chemistry, Florida State University, University of Alabama at Birmingham, Department of Physics, Birmingham, AL 35294-1170,USA, Department of Chemistry, Virginia Polytechnic Institute and State University, Francis Marion University, University of Richmond, Valdosta State University, University of Pittsburgh, Fermi National Lab, university of minnesota, Univ of Virginia, Joint Quantum Institute, University of Maryland, Georgetown University, IonQ Inc.
Peter Schauss

University of Notre Dame, Los Alamos National Laboratory, North Carolina State University, University of Notre dame, Columbia University, Mississippi State Univ, University of Pennsylvania, Carnegie Mellon University, University of Puerto Rico at Humacao, JLAB, MIT, University of Alabama at Birmingham, Florida State University, NHMFL, University College Dublin, Department of Physics, Florida State University; National High Magnetic Field Laboratory, CNR-Instituto Nanoscienze, Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology, Department of Chemistry, Florida State University, University of Alabama at Birmingham, Department of Physics, Birmingham, AL 35294-1170,USA, Department of Chemistry, Virginia Polytechnic Institute and State University, Francis Marion University, University of Richmond, Valdosta State University, University of Pittsburgh, Fermi National Lab, university of minnesota, Univ of Virginia, Joint Quantum Institute, University of Maryland, Georgetown University, IonQ Inc.