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Title: Quantum simulation of scattering in the quantum Ising model

Abstract

We discuss real-time evolution for the quantum Ising model in one spatial dimension with Ns sites. In the limit where the nearest-neighbor interactions J in the spatial directions are small, there is a simple physical picture where qubit states can be interpreted as approximate particle occupations. Using exact diagonalization, for initial states with one or two particles, we show that for small J, discrete Bessel functions provide very accurate expressions for the evolution of the occupancies corresponding to initial states with one and two particles. Boundary conditions play an important role when the evolution time is long enough. We discuss a Trotter procedure to implement the evolution on existing quantum computers and discuss the error associated with the Trotter step size. We discuss the effects of gate and measurement errors on the evolution of one- and two-particle states using four and eight-qubits circuits approximately corresponding to existing or near-term quantum computers.

Authors:
 [1];  [1];  [2]
  1. Univ. of Iowa, Iowa City, IA (United States)
  2. Syracuse Univ., NY (United States)
Publication Date:
Research Org.:
Univ. of Iowa, Iowa City, IA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1515570
Alternate Identifier(s):
OSTI ID: 1613125
Grant/Contract Number:  
SC0019139
Resource Type:
Published Article
Journal Name:
Physical Review. D.
Additional Journal Information:
Journal Volume: 99; Journal Issue: 9; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics; Lattice field theory; Perturbation theory; Quantum simulation; Scattering amplitudes

Citation Formats

Gustafson, Erik, Meurice, Y., and Unmuth-Yockey, Judah. Quantum simulation of scattering in the quantum Ising model. United States: N. p., 2019. Web. doi:10.1103/physrevd.99.094503.
Gustafson, Erik, Meurice, Y., & Unmuth-Yockey, Judah. Quantum simulation of scattering in the quantum Ising model. United States. https://doi.org/10.1103/physrevd.99.094503
Gustafson, Erik, Meurice, Y., and Unmuth-Yockey, Judah. Thu . "Quantum simulation of scattering in the quantum Ising model". United States. https://doi.org/10.1103/physrevd.99.094503.
@article{osti_1515570,
title = {Quantum simulation of scattering in the quantum Ising model},
author = {Gustafson, Erik and Meurice, Y. and Unmuth-Yockey, Judah},
abstractNote = {We discuss real-time evolution for the quantum Ising model in one spatial dimension with Ns sites. In the limit where the nearest-neighbor interactions J in the spatial directions are small, there is a simple physical picture where qubit states can be interpreted as approximate particle occupations. Using exact diagonalization, for initial states with one or two particles, we show that for small J, discrete Bessel functions provide very accurate expressions for the evolution of the occupancies corresponding to initial states with one and two particles. Boundary conditions play an important role when the evolution time is long enough. We discuss a Trotter procedure to implement the evolution on existing quantum computers and discuss the error associated with the Trotter step size. We discuss the effects of gate and measurement errors on the evolution of one- and two-particle states using four and eight-qubits circuits approximately corresponding to existing or near-term quantum computers.},
doi = {10.1103/physrevd.99.094503},
journal = {Physical Review. D.},
number = 9,
volume = 99,
place = {United States},
year = {2019},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/physrevd.99.094503

Citation Metrics:
Cited by: 31 works
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Works referenced in this record:

Order and disorder in gauge systems and magnets
journal, May 1978


Digital quantum computation of fermion-boson interacting systems
text, January 2018


Dynamical properties of the isotropic XY model
journal, February 1970


Quantum-Classical Computation of Schwinger Model Dynamics using Quantum Computers
text, January 2018


Quantum Algorithms for Quantum Field Theories
journal, May 2012


High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits
journal, August 2016


Quantum simulation of frustrated Ising spins with trapped ions
journal, June 2010


High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
text, January 2014


High-Fidelity Preparation, Gates, Memory, and Readout of a Trapped-Ion Quantum Bit
journal, November 2014


Quantum simulation of antiferromagnetic spin chains in an optical lattice
journal, April 2011

  • Simon, Jonathan; Bakr, Waseem S.; Ma, Ruichao
  • Nature, Vol. 472, Issue 7343
  • DOI: 10.1038/nature09994

Lattice gluodynamics at negative g^2
text, January 2004


New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
journal, May 2009


Cloud Quantum Computing of an Atomic Nucleus
text, January 2018


A Note on the Eigenvalue Problem in Crystal Statistics
journal, February 1950


Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory
text, January 2017


Quantum-classical computation of Schwinger model dynamics using quantum computers
journal, September 2018


Efficient Variational Quantum Simulator Incorporating Active Error Minimization
journal, June 2017


Cloud Quantum Computing of an Atomic Nucleus
journal, May 2018


Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis
journal, October 1949


Two soluble models of an antiferromagnetic chain
journal, December 1961


How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation
journal, July 1990


Time-dependent xx-correlation functions in the one-dimensional XY-model
journal, November 1977


Practical Quantum Error Mitigation for Near-Future Applications
journal, July 2018


High-fidelity quantum logic gates using trapped-ion hyperfine qubits
text, January 2015


U(1) Wilson lattice gauge theories in digital quantum simulators
journal, October 2017

  • Muschik, Christine; Heyl, Markus; Martinez, Esteban
  • New Journal of Physics, Vol. 19, Issue 10
  • DOI: 10.1088/1367-2630/aa89ab

Some exact calculations on a chain of spins
journal, January 1967


Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
text, January 2016


Faster quantum algorithm to simulate fermionic quantum field theory
journal, July 2018


Mitigating algorithmic errors in a Hamiltonian simulation
journal, January 2019


Scalar quantum field theories as a benchmark for near-term quantum computers
journal, March 2019

  • Yeter-Aydeniz, Kübra; Dumitrescu, Eugene F.; McCaskey, Alex J.
  • Physical Review A, Vol. 99, Issue 3
  • DOI: 10.1103/PhysRevA.99.032306

Lattice gluodynamics at negative g 2
journal, January 2005


Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
journal, February 1944


An introduction to lattice gauge theory and spin systems
journal, October 1979


Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
journal, June 2016

  • Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp
  • Nature, Vol. 534, Issue 7608
  • DOI: 10.1038/nature18318

Oracles for Gauss's law on digital quantum computers
journal, April 2019


Quantum simulation of the universal features of the Polyakov loop
text, January 2018


Simulation of Nonequilibrium Dynamics on a Quantum Computer
journal, October 2018


Digital quantum computation of fermion-boson interacting systems
journal, October 2018

  • Macridin, Alexandru; Spentzouris, Panagiotis; Amundson, James
  • Physical Review A, Vol. 98, Issue 4
  • DOI: 10.1103/PhysRevA.98.042312

Universal Quantum Simulators
journal, August 1996


Monte Carlo study of Abelian lattice gauge theories
journal, October 1979


Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
text, January 2011


The one-dimensional Ising model with a transverse field
journal, March 1970


Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
journal, September 2017

  • Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan
  • Nature, Vol. 549, Issue 7671
  • DOI: 10.1038/nature23879

Quantum Simulation of the Universal Features of the Polyakov Loop
journal, November 2018


Statistical Mechanics of the Anisotropic Linear Heisenberg Model
journal, September 1962


Quantum computation of scattering in scalar quantum field theories
journal, September 2014

  • Jordan, Stephen P.; Lee, Keith S. M.; Preskill, John
  • Quantum Information and Computation, Vol. 14, Issue 11&12
  • DOI: 10.26421/QIC14.11-12-8

Works referencing / citing this record:

Scattering in the Ising Model Using Quantum Lanczos Algorithm
text, January 2020


Real-time chiral dynamics from a digital quantum simulation
text, January 2020


Real-time dynamics of Chern-Simons fluctuations near a critical point
text, January 2020


General Methods for Digital Quantum Simulation of Gauge Theories
text, January 2019


Quantum computers as universal quantum simulators: state-of-art and perspectives
text, January 2019


Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives
journal, December 2019

  • Tacchino, Francesco; Chiesa, Alessandro; Carretta, Stefano
  • Advanced Quantum Technologies, Vol. 3, Issue 3
  • DOI: 10.1002/qute.201900052