skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Simulating the Shastry-Sutherland Ising Model Using Quantum Annealing

Abstract

A core concept in condensed matter physics is geometric frustration that leads to emergent spin phases in magnetic materials. These distinct phases, which depart from the conventional ferromagnet or the antiferromagnet, require unique computational techniques to decipher. In this study, we use the canonical Ising Shastry-Sutherland lattice to demonstrate new techniques for solving frustrated Hamiltonians using a quantum annealer of programmable superconducting qubits. This Hamiltonian can be tuned to produce a variety of intriguing ground states ranging from short- and long-range orders and fractional order parameters. We show that a large-scale finite-field quantum annealing experiment is possible on 468 logical spins of this model embedded into the quantum hardware. We determine microscopic spin configurations using an iterative quantum annealing protocol and develop mean-field boundary conditions to attenuate finite-size effects and defects. We not only recover all phases of the Shastry-Sutherland Ising model—including the well-known fractional magnetization plateau in a longitudinal field—but also predict the spin behavior at the critical points with significant ground-state degeneracy and in the presence of defects. The results lead us to establish the connection to the diffuse neutron scattering experiments by calculation of the static structure factors.

Authors:
ORCiD logo; ORCiD logo; ; ORCiD logo; ; ; ORCiD logo
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1735690
Alternate Identifier(s):
OSTI ID: 1737497
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Published Article
Journal Name:
PRX Quantum
Additional Journal Information:
Journal Name: PRX Quantum Journal Volume: 1 Journal Issue: 2; Journal ID: ISSN 2691-3399
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; frustrated magnetism; quantum computation; quantum simulation; Ising model

Citation Formats

Kairys, Paul, King, Andrew D., Ozfidan, Isil, Boothby, Kelly, Raymond, Jack, Banerjee, Arnab, and Humble, Travis S.. Simulating the Shastry-Sutherland Ising Model Using Quantum Annealing. United States: N. p., 2020. Web. https://doi.org/10.1103/prxquantum.1.020320.
Kairys, Paul, King, Andrew D., Ozfidan, Isil, Boothby, Kelly, Raymond, Jack, Banerjee, Arnab, & Humble, Travis S.. Simulating the Shastry-Sutherland Ising Model Using Quantum Annealing. United States. https://doi.org/10.1103/prxquantum.1.020320
Kairys, Paul, King, Andrew D., Ozfidan, Isil, Boothby, Kelly, Raymond, Jack, Banerjee, Arnab, and Humble, Travis S.. Mon . "Simulating the Shastry-Sutherland Ising Model Using Quantum Annealing". United States. https://doi.org/10.1103/prxquantum.1.020320.
@article{osti_1735690,
title = {Simulating the Shastry-Sutherland Ising Model Using Quantum Annealing},
author = {Kairys, Paul and King, Andrew D. and Ozfidan, Isil and Boothby, Kelly and Raymond, Jack and Banerjee, Arnab and Humble, Travis S.},
abstractNote = {A core concept in condensed matter physics is geometric frustration that leads to emergent spin phases in magnetic materials. These distinct phases, which depart from the conventional ferromagnet or the antiferromagnet, require unique computational techniques to decipher. In this study, we use the canonical Ising Shastry-Sutherland lattice to demonstrate new techniques for solving frustrated Hamiltonians using a quantum annealer of programmable superconducting qubits. This Hamiltonian can be tuned to produce a variety of intriguing ground states ranging from short- and long-range orders and fractional order parameters. We show that a large-scale finite-field quantum annealing experiment is possible on 468 logical spins of this model embedded into the quantum hardware. We determine microscopic spin configurations using an iterative quantum annealing protocol and develop mean-field boundary conditions to attenuate finite-size effects and defects. We not only recover all phases of the Shastry-Sutherland Ising model—including the well-known fractional magnetization plateau in a longitudinal field—but also predict the spin behavior at the critical points with significant ground-state degeneracy and in the presence of defects. The results lead us to establish the connection to the diffuse neutron scattering experiments by calculation of the static structure factors.},
doi = {10.1103/prxquantum.1.020320},
journal = {PRX Quantum},
number = 2,
volume = 1,
place = {United States},
year = {2020},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/prxquantum.1.020320

Save / Share:

Works referenced in this record:

Fractional Magnetization Plateaus and Magnetic Order in the Shastry-Sutherland Magnet TmB 4
journal, October 2008


Observation of topological phenomena in a programmable lattice of 1,800 qubits
journal, August 2018


Exact ground state of a quantum mechanical antiferromagnet
journal, August 1981


Phase transitions in a programmable quantum spin glass simulator
journal, July 2018


Quantum spin liquids
journal, January 2020


Realization of the kagome spin ice state in a frustrated intermetallic compound
journal, March 2020


Architectural Considerations in the Design of a Superconducting Quantum Annealing Processor
journal, August 2014

  • Bunyk, P. I.; Hoskinson, Emile M.; Johnson, Mark W.
  • IEEE Transactions on Applied Superconductivity, Vol. 24, Issue 4
  • DOI: 10.1109/TASC.2014.2318294

Multi-step magnetization of the Ising model on a Shastry–Sutherland lattice: a Monte Carlo simulation
journal, August 2012


A „self consistent” monte carlo method for the heisenberg ferromagnet
journal, June 1972

  • Müller-Krumbhaar, H.; Binder, K.
  • Zeitschrift für Physik A Hadrons and nuclei, Vol. 254, Issue 3
  • DOI: 10.1007/BF01379785

Quantum annealing with manufactured spins
journal, May 2011

  • Johnson, M. W.; Amin, M. H. S.; Gildert, S.
  • Nature, Vol. 473, Issue 7346
  • DOI: 10.1038/nature10012

Spin Ice State in Frustrated Magnetic Pyrochlore Materials
journal, November 2001


Field-induced magnetic states in holmium tetraboride
journal, January 2017


Optimization by Simulated Annealing
journal, May 1983


Order parameter fluctuations at a buried quantum critical point
journal, April 2012

  • Feng, Y.; Wang, J.; Jaramillo, R.
  • Proceedings of the National Academy of Sciences, Vol. 109, Issue 19
  • DOI: 10.1073/pnas.1202434109

Searching for quantum speedup in quasistatic quantum annealers
journal, November 2015


Fast clique minor generation in Chimera qubit connectivity graphs
journal, October 2015

  • Boothby, Tomas; King, Andrew D.; Roy, Aidan
  • Quantum Information Processing, Vol. 15, Issue 1
  • DOI: 10.1007/s11128-015-1150-6

Magnetism of rare earth tetraborides
journal, January 2010


Quantum Annealing of a Disordered Magnet
journal, April 1999


Strong interplay between stripe spin fluctuations, nematicity and superconductivity in FeSe
journal, December 2015

  • Wang, Qisi; Shen, Yao; Pan, Bingying
  • Nature Materials, Vol. 15, Issue 2
  • DOI: 10.1038/nmat4492

Degeneracy of the 1 / 8 Plateau and Antiferromagnetic Phases in the Shastry-Sutherland Magnet TmB 4
journal, October 2018


Minor-embedding in adiabatic quantum computation: I. The parameter setting problem
journal, September 2008