Simulations of frustrated Ising Hamiltonians using quantum approximate optimization
Abstract
Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground-state properties are essential in understanding these materials, however, computational complexity limits conventional methods for studying these states. Here we investigate an alternative approach to preparing materials ground states using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers. We study classical Ising spin models on unit cells of square, Shastry-Sutherland and triangular lattices, with varying field amplitudes and couplings in the material Hamiltonian. We find relationships between the theoretical QAOA success probability and the structure of the ground state, indicating that only a modest number of measurements (≲100) are needed to find the ground state of our nine-spin Hamiltonians, even for parameters leading to frustrated magnetism. We further demonstrate the approach in calculations on a trapped-ion quantum computer and succeed in recovering each ground state of the Shastry-Sutherland unit cell with probabilities close to ideal theoretical values. The results demonstrate the viability of QAOA for materials ground state preparation in the frustrated Ising limit, giving important first steps towards larger sizes and more complex Hamiltonians where quantum computational advantage may prove essential in developing a systematic understanding of novel materials.
- Authors:
-
[1];
[1];
[1];
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Purdue Univ., West Lafayette, IN (United States)
- Purdue Univ., West Lafayette, IN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1905415
- Grant/Contract Number:
- AC05-00OR22725
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences
- Additional Journal Information:
- Journal Volume: 381; Journal Issue: 2241; Journal ID: ISSN 1364-503X
- Publisher:
- The Royal Society Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; quantum approximate optimization; Ising; quantum computing; frustrated magnetism; quantum simulation
Citation Formats
Lotshaw, Phillip C., Xu, Hanjing, Khalid, Bilal, Buchs, Gilles, Humble, Travis S., and Banerjee, Arnab. Simulations of frustrated Ising Hamiltonians using quantum approximate optimization. United States: N. p., 2022.
Web. doi:10.1098/rsta.2021.0414.
Lotshaw, Phillip C., Xu, Hanjing, Khalid, Bilal, Buchs, Gilles, Humble, Travis S., & Banerjee, Arnab. Simulations of frustrated Ising Hamiltonians using quantum approximate optimization. United States. https://doi.org/10.1098/rsta.2021.0414
Lotshaw, Phillip C., Xu, Hanjing, Khalid, Bilal, Buchs, Gilles, Humble, Travis S., and Banerjee, Arnab. Mon .
"Simulations of frustrated Ising Hamiltonians using quantum approximate optimization". United States. https://doi.org/10.1098/rsta.2021.0414. https://www.osti.gov/servlets/purl/1905415.
@article{osti_1905415,
title = {Simulations of frustrated Ising Hamiltonians using quantum approximate optimization},
author = {Lotshaw, Phillip C. and Xu, Hanjing and Khalid, Bilal and Buchs, Gilles and Humble, Travis S. and Banerjee, Arnab},
abstractNote = {Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground-state properties are essential in understanding these materials, however, computational complexity limits conventional methods for studying these states. Here we investigate an alternative approach to preparing materials ground states using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers. We study classical Ising spin models on unit cells of square, Shastry-Sutherland and triangular lattices, with varying field amplitudes and couplings in the material Hamiltonian. We find relationships between the theoretical QAOA success probability and the structure of the ground state, indicating that only a modest number of measurements (≲100) are needed to find the ground state of our nine-spin Hamiltonians, even for parameters leading to frustrated magnetism. We further demonstrate the approach in calculations on a trapped-ion quantum computer and succeed in recovering each ground state of the Shastry-Sutherland unit cell with probabilities close to ideal theoretical values. The results demonstrate the viability of QAOA for materials ground state preparation in the frustrated Ising limit, giving important first steps towards larger sizes and more complex Hamiltonians where quantum computational advantage may prove essential in developing a systematic understanding of novel materials.},
doi = {10.1098/rsta.2021.0414},
journal = {Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences},
number = 2241,
volume = 381,
place = {United States},
year = {Mon Dec 05 00:00:00 EST 2022},
month = {Mon Dec 05 00:00:00 EST 2022}
}
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Works referenced in this record:
Fractional Magnetization Plateaus and Magnetic Order in the Shastry-Sutherland Magnet
journal, October 2008
- Siemensmeyer, K.; Wulf, E.; Mikeska, H. -J.
- Physical Review Letters, Vol. 101, Issue 17
Parameter Transfer for Quantum Approximate Optimization of Weighted MaxCut
journal, April 2023
- Shaydulin, Ruslan; Lotshaw, Phillip C.; Larson, Jeffrey
- ACM Transactions on Quantum Computing, Vol. 4, Issue 3
Dynamical preparation of quantum spin liquids in Rydberg atom arrays
text, January 2022
- Giudici, Giuliano; Lukin, Mikhail D.; Pichler, Hannes
- arXiv
Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales
journal, June 2016
- Winter, Stephen M.; Li, Ying; Jeschke, Harald O.
- Physical Review B, Vol. 93, Issue 21
Quantum optimization with a novel Gibbs objective function and ansatz architecture search
journal, April 2020
- Li, Li; Fan, Minjie; Coram, Marc
- Physical Review Research, Vol. 2, Issue 2
Studying Two-Dimensional Systems with the Density Matrix Renormalization Group
journal, March 2012
- Stoudenmire, E. M.; White, Steven R.
- Annual Review of Condensed Matter Physics, Vol. 3, Issue 1
Scaling quantum approximate optimization on near-term hardware
journal, July 2022
- Lotshaw, Phillip C.; Nguyen, Thien; Santana, Anthony
- Scientific Reports, Vol. 12, Issue 1
Probing topological spin liquids on a programmable quantum simulator
journal, December 2021
- Semeghini, G.; Levine, H.; Keesling, A.
- Science, Vol. 374, Issue 6572
Applying the Quantum Approximate Optimization Algorithm to the Tail-Assignment Problem
journal, September 2020
- Vikstål, Pontus; Grönkvist, Mattias; Svensson, Marika
- Physical Review Applied, Vol. 14, Issue 3
Error Propagation in NISQ Devices for Solving Classical Optimization Problems
journal, December 2022
- González-García, Guillermo; Trivedi, Rahul; Cirac, J. Ignacio
- PRX Quantum, Vol. 3, Issue 4
Noise-induced barren plateaus in variational quantum algorithms
journal, November 2021
- Wang, Samson; Fontana, Enrico; Cerezo, M.
- Nature Communications, Vol. 12, Issue 1
Ground states of the Triangular Ising model with two-and three-spin interactions
journal, December 1986
- Brandt, U.; Stolze, J.
- Zeitschrift f�r Physik B Condensed Matter, Vol. 64, Issue 4
Simulating the Shastry-Sutherland Ising Model Using Quantum Annealing
journal, December 2020
- Kairys, Paul; King, Andrew D.; Ozfidan, Isil
- PRX Quantum, Vol. 1, Issue 2
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
journal, February 2019
- Hadfield, Stuart; Wang, Zhihui; O'Gorman, Bryan
- Algorithms, Vol. 12, Issue 2
Realizing topologically ordered states on a quantum processor
text, January 2021
- Satzinger, K. J.; Liu, Y.; Smith, A.
- arXiv
Circuit depth scaling for quantum approximate optimization
journal, October 2022
- Akshay, V.; Philathong, H.; Campos, E.
- Physical Review A, Vol. 106, Issue 4
A quantum processor based on coherent transport of entangled atom arrays
journal, April 2022
- Bluvstein, Dolev; Levine, Harry; Semeghini, Giulia
- Nature, Vol. 604, Issue 7906
Quantum simulation
journal, March 2014
- Georgescu, I. M.; Ashhab, S.; Nori, Franco
- Reviews of Modern Physics, Vol. 86, Issue 1
Parameter Transfer for Quantum Approximate Optimization of Weighted MaxCut
journal, April 2023
- Shaydulin, Ruslan; Lotshaw, Phillip C.; Larson, Jeffrey
- ACM Transactions on Quantum Computing, Vol. 4, Issue 3
Degeneracy of the Plateau and Antiferromagnetic Phases in the Shastry-Sutherland Magnet
journal, October 2018
- Trinh, Jennifer; Mitra, Sreemanta; Panagopoulos, Christos
- Physical Review Letters, Vol. 121, Issue 16
Empirical performance bounds for quantum approximate optimization
journal, November 2021
- Lotshaw, Phillip C.; Humble, Travis S.; Herrman, Rebekah
- Quantum Information Processing, Vol. 20, Issue 12
Electronic transport on the Shastry-Sutherland lattice in Ising-type rare-earth tetraborides
journal, May 2017
- Ye, Linda; Suzuki, Takehito; Checkelsky, Joseph G.
- Physical Review B, Vol. 95, Issue 17
Evidence of the Berezinskii-Kosterlitz-Thouless phase in a frustrated magnet
journal, November 2020
- Hu, Ze; Ma, Zhen; Liao, Yuan-Da
- Nature Communications, Vol. 11, Issue 1
Numerical study of magnetization processes in rare-earth tetraborides
journal, August 2010
- Farkašovský, Pavol; Čenčariková, Hana; Mat’aš, Slavomír
- Physical Review B, Vol. 82, Issue 5
Signatures of a Quantum Griffiths Phase Close to an Electronic Nematic Quantum Phase Transition
journal, December 2021
- Reiss, Pascal; Graf, David; Haghighirad, Amir A.
- Physical Review Letters, Vol. 127, Issue 24
Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator
journal, October 2020
- Pagano, Guido; Bapat, Aniruddha; Becker, Patrick
- Proceedings of the National Academy of Sciences, Vol. 117, Issue 41
Efficient variational simulation of non-trivial quantum states
journal, January 2019
- Ho, Wen Wei; Hsieh, Timothy H.
- SciPost Physics, Vol. 6, Issue 3
Finite-Size Scaling on a Digital Quantum Simulator Using Quantum Restricted Boltzmann Machine
journal, May 2022
- Khalid, Bilal; Sureshbabu, Shree Hari; Banerjee, Arnab
- Frontiers in Physics, Vol. 10
On the computational complexity of Ising spin glass models
journal, October 1982
- Barahona, F.
- Journal of Physics A: Mathematical and General, Vol. 15, Issue 10
Using a Mixed Integer Quadratic Programming Solver for the Unconstrained Quadratic 0-1 Problem
journal, June 2006
- Billionnet, Alain; Elloumi, Sourour
- Mathematical Programming, Vol. 109, Issue 1
Empirical performance bounds for quantum approximate optimization
journal, November 2021
- Lotshaw, Phillip C.; Humble, Travis S.; Herrman, Rebekah
- Quantum Information Processing, Vol. 20, Issue 12
Comprehensive study of the dynamics of a classical Kitaev spin liquid
journal, October 2017
- Samarakoon, A. M.; Banerjee, A.; Zhang, S. -S.
- Physical Review B, Vol. 96, Issue 13
Extraction of interaction parameters for
α − RuCl 3
journal, June 2022
- Samarakoon, Anjana M.; Laurell, Pontus; Balz, Christian
- Physical Review Research, Vol. 4, Issue 2
Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond
journal, September 2020
- Bando, Yuki; Susa, Yuki; Oshiyama, Hiroki
- Physical Review Research, Vol. 2, Issue 3
Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice
journal, November 2020
- Wessler, Christian; Roessli, Bertrand; Krämer, Karl W.
- npj Quantum Materials, Vol. 5, Issue 1
Improving Variational Quantum Optimization using CVaR
journal, April 2020
- Barkoutsos, Panagiotis Kl.; Nannicini, Giacomo; Robert, Anton
- Quantum, Vol. 4
Ground States of the Ising Model on the Shastry-Sutherland Lattice and the Origin of the Fractional Magnetization Plateaus in Rare-Earth-Metal Tetraborides
journal, October 2012
- Dublenych, Yu. I.
- Physical Review Letters, Vol. 109, Issue 16
Observation of topological phenomena in a programmable lattice of 1,800 qubits
journal, August 2018
- King, Andrew D.; Carrasquilla, Juan; Raymond, Jack
- Nature, Vol. 560, Issue 7719
Magnetic three states of matter: A quantum Monte Carlo study of spin liquids
journal, September 2015
- Kamiya, Yoshitomo; Kato, Yasuyuki; Nasu, Joji
- Physical Review B, Vol. 92, Issue 10
Phase transitions in a programmable quantum spin glass simulator
journal, July 2018
- Harris, R.; Sato, Y.; Berkley, A. J.
- Science, Vol. 361, Issue 6398
Quantum spin liquids
journal, January 2020
- Broholm, C.; Cava, R. J.; Kivelson, S. A.
- Science, Vol. 367, Issue 6475
Quantifying the efficiency of state preparation via quantum variational eigensolvers
audiovisual, January 2020
- 2020, International conference for the quantum science and technology community; Johri, Sonika; Matos, Gabriel
- Underline Science Inc.
Magnetic anisotropy and magnon gap state of SmB4 single crystal
journal, May 2010
- Kim, J. Y.; Sung, N. H.; Kang, B. Y.
- Journal of Applied Physics, Vol. 107, Issue 9
Disorder-Induced Mimicry of a Spin Liquid in
journal, October 2017
- Zhu, Zhenyue; Maksimov, P. A.; White, Steven R.
- Physical Review Letters, Vol. 119, Issue 15
Limitations of optimization algorithms on noisy quantum devices
journal, October 2021
- Stilck França, Daniel; García-Patrón, Raul
- Nature Physics, Vol. 17, Issue 11
Specific features of the magnetic properties of RB4(R = Ce, Sm and Yb) tetraborides. Effects of pressure
journal, March 2015
- Panfilov, A. S.; Grechnev, G. E.; Zhuravleva, I. P.
- Low Temperature Physics, Vol. 41, Issue 3
Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
journal, December 2022
- Weidenfeller, Johannes; Valor, Lucia C.; Gacon, Julien
- Quantum, Vol. 6
Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations
journal, May 2005
- Troyer, Matthias; Wiese, Uwe-Jens
- Physical Review Letters, Vol. 94, Issue 17
Sonographic and histological development of high-intensity focused ultrasound in rabbit muscle
journal, October 2012
- Jiang, Lixin; Hu, Bing; Guo, Qian
- Experimental and Therapeutic Medicine, Vol. 5, Issue 1
Digital Annealing Route to Complex Magnetic Phase Discovery
conference, November 2021
- Jha, Akshat A.; Stoyanoff, Eliana L.; Khundzakishvili, Guga
- 2021 International Conference on Rebooting Computing (ICRC)
Ising formulations of many NP problems
journal, January 2014
- Lucas, Andrew
- Frontiers in Physics, Vol. 2
Realizing topologically ordered states on a quantum processor
journal, December 2021
- Satzinger, K. J.; Liu, Y. -J; Smith, A.
- Science, Vol. 374, Issue 6572
Probing Topological Spin Liquids on a Programmable Quantum Simulator
text, January 2021
- Semeghini, Giulia; Levine, Harry; Keesling, Alexander
- arXiv
Multi-angle quantum approximate optimization algorithm
journal, April 2022
- Herrman, Rebekah; Lotshaw, Phillip C.; Ostrowski, James
- Scientific Reports, Vol. 12, Issue 1
Ground states of the Ising model on an anisotropic triangular lattice: stripes and zigzags
journal, September 2013
- Dublenych, Yu I.
- Journal of Physics: Condensed Matter, Vol. 25, Issue 40
Order-by-disorder in the antiferromagnetic Ising model on an elastic triangular lattice
text, January 2010
- Shokef, Yair; Souslov, Anton; Lubensky, Tom C.
- arXiv
Quantifying the efficiency of state preparation via quantum variational eigensolvers
text, January 2020
- Matos, Gabriel; Johri, Sonika; Papić, Zlatko
- arXiv
Formulating and Solving Routing Problems on Quantum Computers
journal, January 2021
- Harwood, Stuart; Gambella, Claudio; Trenev, Dimitar
- IEEE Transactions on Quantum Engineering, Vol. 2
Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder
journal, January 2017
- Wessel, Stefan; Normand, Bruce; Mila, Frédéric
- SciPost Physics, Vol. 3, Issue 1
Order by disorder in the antiferromagnetic Ising model on an elastic triangular lattice
journal, July 2011
- Shokef, Y.; Souslov, A.; Lubensky, T. C.
- Proceedings of the National Academy of Sciences, Vol. 108, Issue 29
Exact ground state of a quantum mechanical antiferromagnet
journal, August 1981
- Sriram Shastry, B.; Sutherland, Bill
- Physica B+C, Vol. 108, Issue 1-3
Ordering, metastability and phase transitions in two-dimensional systems
journal, April 1973
- Kosterlitz, J M; Thouless, D J
- Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203
Multi-step magnetization of the Ising model on a Shastry–Sutherland lattice: a Monte Carlo simulation
journal, August 2012
- Huang, W. C.; Huo, L.; Tian, G.
- Journal of Physics: Condensed Matter, Vol. 24, Issue 38
Neutron Diffraction Study on the Multiple Magnetization Plateaus in under Pulsed High Magnetic Field
journal, August 2009
- Yoshii, S.; Ohoyama, K.; Kurosawa, K.
- Physical Review Letters, Vol. 103, Issue 7
QCOR: A Language Extension Specification for the Heterogeneous Quantum-Classical Model of Computation
journal, April 2020
- Mintz, Tiffany M.; McCaskey, Alexander J.; Dumitrescu, Eugene F.
- ACM Journal on Emerging Technologies in Computing Systems, Vol. 16, Issue 2
Signature of magnetic monopole and Dirac string dynamics in spin ice
journal, March 2009
- Jaubert, L. D. C.; Holdsworth, P. C. W.
- Nature Physics, Vol. 5, Issue 4
Colloquium : Ice rule and emergent frustration in particle ice and beyond
journal, December 2019
- Ortiz-Ambriz, Antonio; Nisoli, Cristiano; Reichhardt, Charles
- Reviews of Modern Physics, Vol. 91, Issue 4
The Quantum Alternating Operator Ansatz on Maximum k-Vertex Cover
conference, October 2020
- Cook, Jeremy; Eidenbenz, Stephan; Bartschi, Andreas
- 2020 IEEE International Conference on Quantum Computing and Engineering (QCE)
Optimization by Simulated Annealing
journal, May 1983
- Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P.
- Science, Vol. 220, Issue 4598
On the computational complexity of Ising spin glass models
journal, October 1982
- Barahona, F.
- Journal of Physics A: Mathematical and General, Vol. 15, Issue 10
Frustration and quantum criticality
journal, May 2018
- Vojta, Matthias
- Reports on Progress in Physics, Vol. 81, Issue 6
Quantum Simulators: Architectures and Opportunities
journal, February 2021
- Altman, Ehud; Brown, Kenneth R.; Carleo, Giuseppe
- PRX Quantum, Vol. 2, Issue 1
Qubit spin ice
journal, July 2021
- King, Andrew D.; Nisoli, Cristiano; Dahl, Edward D.
- Science, Vol. 373, Issue 6554
Multi-angle quantum approximate optimization algorithm
journal, April 2022
- Herrman, Rebekah; Lotshaw, Phillip C.; Ostrowski, James
- Scientific Reports, Vol. 12, Issue 1
Improving soft magnetic properties in FINEMET-like alloys with Ga addition
journal, October 2019
- Zhu, Qianke; Chen, Zhe; Zhang, Shuling
- Journal of Magnetism and Magnetic Materials, Vol. 487
Ground states of the Ising model on an anisotropic triangular lattice: stripes and zigzags
journal, September 2013
- Dublenych, Yu I.
- Journal of Physics: Condensed Matter, Vol. 25, Issue 40