Simulations of frustrated Ising Hamiltonians using quantum approximate optimization

Lotshaw, Phillip C.; Xu, Hanjing; Khalid, Bilal; Buchs, Gilles; Humble, Travis S.; Banerjee, Arnab

doi:10.1098/rsta.2021.0414

Title: Simulations of frustrated Ising Hamiltonians using quantum approximate optimization

Journal Article · Mon Dec 05 00:00:00 EST 2022 · Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences

DOI:https://doi.org/10.1098/rsta.2021.0414· OSTI ID:1905415

^[1]; Xu, Hanjing ^[2]; Khalid, Bilal ^[3];

^[1];

^[1]; Banerjee, Arnab ^[3]

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)

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1905415

Journal Information:: Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences, Vol. 381, Issue 2241; ISSN 1364-503X

Publisher:: The Royal Society PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (74)

Fractional Magnetization Plateaus and Magnetic Order in the Shastry-Sutherland Magnet ${TmB}_{4}$ Siemensmeyer, K.; Wulf, E.; Mikeska, H. -J. Physical Review Letters, Vol. 101, Issue 17 https://doi.org/10.1103/physrevlett.101.177201	journal	October 2008
Parameter Transfer for Quantum Approximate Optimization of Weighted MaxCut Shaydulin, Ruslan; Lotshaw, Phillip C.; Larson, Jeffrey ACM Transactions on Quantum Computing, Vol. 4, Issue 3 https://doi.org/10.1145/3584706	journal	April 2023
Dynamical preparation of quantum spin liquids in Rydberg atom arrays Giudici, Giuliano; Lukin, Mikhail D.; Pichler, Hannes arXiv https://doi.org/10.48550/arxiv.2201.04034	text	January 2022
Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales Winter, Stephen M.; Li, Ying; Jeschke, Harald O. Physical Review B, Vol. 93, Issue 21 https://doi.org/10.1103/PhysRevB.93.214431	journal	June 2016
Quantum optimization with a novel Gibbs objective function and ansatz architecture search Li, Li; Fan, Minjie; Coram, Marc Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023074	journal	April 2020
Studying Two-Dimensional Systems with the Density Matrix Renormalization Group Stoudenmire, E. M.; White, Steven R. Annual Review of Condensed Matter Physics, Vol. 3, Issue 1 https://doi.org/10.1146/annurev-conmatphys-020911-125018	journal	March 2012
Scaling quantum approximate optimization on near-term hardware Lotshaw, Phillip C.; Nguyen, Thien; Santana, Anthony Scientific Reports, Vol. 12, Issue 1 https://doi.org/10.1038/s41598-022-14767-w	journal	July 2022
Probing topological spin liquids on a programmable quantum simulator Semeghini, G.; Levine, H.; Keesling, A. Science, Vol. 374, Issue 6572 https://doi.org/10.1126/science.abi8794	journal	December 2021
Applying the Quantum Approximate Optimization Algorithm to the Tail-Assignment Problem Vikstål, Pontus; Grönkvist, Mattias; Svensson, Marika Physical Review Applied, Vol. 14, Issue 3 https://doi.org/10.1103/PhysRevApplied.14.034009	journal	September 2020
Error Propagation in NISQ Devices for Solving Classical Optimization Problems González-García, Guillermo; Trivedi, Rahul; Cirac, J. Ignacio PRX Quantum, Vol. 3, Issue 4 https://doi.org/10.1103/PRXQuantum.3.040326	journal	December 2022
Noise-induced barren plateaus in variational quantum algorithms Wang, Samson; Fontana, Enrico; Cerezo, M. Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-27045-6	journal	November 2021
Ground states of the Triangular Ising model with two-and three-spin interactions Brandt, U.; Stolze, J. Zeitschrift f�r Physik B Condensed Matter, Vol. 64, Issue 4 https://doi.org/10.1007/BF01312843	journal	December 1986
Simulating the Shastry-Sutherland Ising Model Using Quantum Annealing Kairys, Paul; King, Andrew D.; Ozfidan, Isil PRX Quantum, Vol. 1, Issue 2 https://doi.org/10.1103/PRXQuantum.1.020320	journal	December 2020
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz Hadfield, Stuart; Wang, Zhihui; O'Gorman, Bryan Algorithms, Vol. 12, Issue 2 https://doi.org/10.3390/a12020034	journal	February 2019
Realizing topologically ordered states on a quantum processor Satzinger, K. J.; Liu, Y.; Smith, A. arXiv https://doi.org/10.48550/arxiv.2104.01180	text	January 2021
Circuit depth scaling for quantum approximate optimization Akshay, V.; Philathong, H.; Campos, E. Physical Review A, Vol. 106, Issue 4 https://doi.org/10.1103/PhysRevA.106.042438	journal	October 2022
A quantum processor based on coherent transport of entangled atom arrays Bluvstein, Dolev; Levine, Harry; Semeghini, Giulia Nature, Vol. 604, Issue 7906 https://doi.org/10.1038/s41586-022-04592-6	journal	April 2022
Quantum simulation Georgescu, I. M.; Ashhab, S.; Nori, Franco Reviews of Modern Physics, Vol. 86, Issue 1 https://doi.org/10.1103/RevModPhys.86.153	journal	March 2014
Degeneracy of the $1 / 8$ Plateau and Antiferromagnetic Phases in the Shastry-Sutherland Magnet ${TmB}_{4}$ Trinh, Jennifer; Mitra, Sreemanta; Panagopoulos, Christos Physical Review Letters, Vol. 121, Issue 16 https://doi.org/10.1103/PhysRevLett.121.167203	journal	October 2018
Empirical performance bounds for quantum approximate optimization Lotshaw, Phillip C.; Humble, Travis S.; Herrman, Rebekah Quantum Information Processing, Vol. 20, Issue 12 https://doi.org/10.1007/s11128-021-03342-3	journal	November 2021
Electronic transport on the Shastry-Sutherland lattice in Ising-type rare-earth tetraborides Ye, Linda; Suzuki, Takehito; Checkelsky, Joseph G. Physical Review B, Vol. 95, Issue 17 https://doi.org/10.1103/PhysRevB.95.174405	journal	May 2017
Evidence of the Berezinskii-Kosterlitz-Thouless phase in a frustrated magnet Hu, Ze; Ma, Zhen; Liao, Yuan-Da Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-19380-x	journal	November 2020
Numerical study of magnetization processes in rare-earth tetraborides Farkašovský, Pavol; Čenčariková, Hana; Mat’aš, Slavomír Physical Review B, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRevB.82.054409	journal	August 2010
Signatures of a Quantum Griffiths Phase Close to an Electronic Nematic Quantum Phase Transition Reiss, Pascal; Graf, David; Haghighirad, Amir A. Physical Review Letters, Vol. 127, Issue 24 https://doi.org/10.1103/PhysRevLett.127.246402	journal	December 2021
Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator Pagano, Guido; Bapat, Aniruddha; Becker, Patrick Proceedings of the National Academy of Sciences, Vol. 117, Issue 41 https://doi.org/10.1073/pnas.2006373117	journal	October 2020
Quantum Computing in the NISQ era and beyond Preskill, John Quantum, Vol. 2 https://doi.org/10.22331/q-2018-08-06-79	journal	August 2018
Efficient variational simulation of non-trivial quantum states Ho, Wen Wei; Hsieh, Timothy H. SciPost Physics, Vol. 6, Issue 3 https://doi.org/10.21468/SciPostPhys.6.3.029	journal	January 2019
Finite-Size Scaling on a Digital Quantum Simulator Using Quantum Restricted Boltzmann Machine Khalid, Bilal; Sureshbabu, Shree Hari; Banerjee, Arnab Frontiers in Physics, Vol. 10 https://doi.org/10.3389/fphy.2022.915863	journal	May 2022
On the computational complexity of Ising spin glass models Barahona, F. Journal of Physics A: Mathematical and General, Vol. 15, Issue 10 https://doi.org/10.1088/0305-4470/15/10/028	journal	October 1982
Using a Mixed Integer Quadratic Programming Solver for the Unconstrained Quadratic 0-1 Problem Billionnet, Alain; Elloumi, Sourour Mathematical Programming, Vol. 109, Issue 1 https://doi.org/10.1007/s10107-005-0637-9	journal	June 2006
Comprehensive study of the dynamics of a classical Kitaev spin liquid Samarakoon, A. M.; Banerjee, A.; Zhang, S. -S. Physical Review B, Vol. 96, Issue 13 https://doi.org/10.1103/PhysRevB.96.134408	journal	October 2017
Extraction of interaction parameters for α−RuCl3 from neutron data using machine learning Samarakoon, Anjana M.; Laurell, Pontus; Balz, Christian Physical Review Research, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevResearch.4.L022061	journal	June 2022
Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond Bando, Yuki; Susa, Yuki; Oshiyama, Hiroki Physical Review Research, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevResearch.2.033369	journal	September 2020
Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice Wessler, Christian; Roessli, Bertrand; Krämer, Karl W. npj Quantum Materials, Vol. 5, Issue 1 https://doi.org/10.1038/s41535-020-00287-1	journal	November 2020
Improving Variational Quantum Optimization using CVaR Barkoutsos, Panagiotis Kl.; Nannicini, Giacomo; Robert, Anton Quantum, Vol. 4 https://doi.org/10.22331/q-2020-04-20-256	journal	April 2020
Quantum Spin Liquids Broholm, C.; Cava, R. J.; Kivelson, S. A. arXiv https://doi.org/10.48550/arxiv.1905.07040	text	January 2019
Ground States of the Ising Model on the Shastry-Sutherland Lattice and the Origin of the Fractional Magnetization Plateaus in Rare-Earth-Metal Tetraborides Dublenych, Yu. I. Physical Review Letters, Vol. 109, Issue 16 https://doi.org/10.1103/physrevlett.109.167202	journal	October 2012
Qubit Spin Ice King, Andrew D.; Nisoli, Cristiano; Dahl, Edward D. Zenodo https://doi.org/10.5281/zenodo.4776361	dataset	January 2021
Observation of topological phenomena in a programmable lattice of 1,800 qubits King, Andrew D.; Carrasquilla, Juan; Raymond, Jack Nature, Vol. 560, Issue 7719 https://doi.org/10.1038/s41586-018-0410-x	journal	August 2018
Magnetic three states of matter: A quantum Monte Carlo study of spin liquids Kamiya, Yoshitomo; Kato, Yasuyuki; Nasu, Joji Physical Review B, Vol. 92, Issue 10 https://doi.org/10.1103/PhysRevB.92.100403	journal	September 2015
Phase transitions in a programmable quantum spin glass simulator Harris, R.; Sato, Y.; Berkley, A. J. Science, Vol. 361, Issue 6398 https://doi.org/10.1126/science.aat2025	journal	July 2018
Quantum spin liquids Broholm, C.; Cava, R. J.; Kivelson, S. A. Science, Vol. 367, Issue 6475 https://doi.org/10.1126/science.aay0668	journal	January 2020
Quantifying the efficiency of state preparation via quantum variational eigensolvers 2020, International conference for the quantum science and technology community; Johri, Sonika; Matos, Gabriel Underline Science Inc. https://doi.org/10.48448/vp18-vk47	audiovisual	January 2020
Magnetic anisotropy and magnon gap state of SmB4 single crystal Kim, J. Y.; Sung, N. H.; Kang, B. Y. Journal of Applied Physics, Vol. 107, Issue 9 https://doi.org/10.1063/1.3365061	journal	May 2010
Disorder-Induced Mimicry of a Spin Liquid in ${YbMgGaO}_{4}$ Zhu, Zhenyue; Maksimov, P. A.; White, Steven R. Physical Review Letters, Vol. 119, Issue 15 https://doi.org/10.1103/PhysRevLett.119.157201	journal	October 2017
Limitations of optimization algorithms on noisy quantum devices Stilck França, Daniel; García-Patrón, Raul Nature Physics, Vol. 17, Issue 11 https://doi.org/10.1038/s41567-021-01356-3	journal	October 2021
Specific features of the magnetic properties of RB₄(R = Ce, Sm and Yb) tetraborides. Effects of pressure Panfilov, A. S.; Grechnev, G. E.; Zhuravleva, I. P. Low Temperature Physics, Vol. 41, Issue 3 https://doi.org/10.1063/1.4916067	journal	March 2015
Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware Weidenfeller, Johannes; Valor, Lucia C.; Gacon, Julien Quantum, Vol. 6 https://doi.org/10.22331/q-2022-12-07-870	journal	December 2022
Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations Troyer, Matthias; Wiese, Uwe-Jens Physical Review Letters, Vol. 94, Issue 17 https://doi.org/10.1103/PhysRevLett.94.170201	journal	May 2005
Sonographic and histological development of high-intensity focused ultrasound in rabbit muscle Jiang, Lixin; Hu, Bing; Guo, Qian Experimental and Therapeutic Medicine, Vol. 5, Issue 1 https://doi.org/10.3892/etm.2012.742	journal	October 2012
Digital Annealing Route to Complex Magnetic Phase Discovery Jha, Akshat A.; Stoyanoff, Eliana L.; Khundzakishvili, Guga 2021 International Conference on Rebooting Computing (ICRC) https://doi.org/10.1109/ICRC53822.2021.00027	conference	November 2021
Ising formulations of many NP problems Lucas, Andrew Frontiers in Physics, Vol. 2 https://doi.org/10.3389/fphy.2014.00005	journal	January 2014
Realizing topologically ordered states on a quantum processor Satzinger, K. J.; Liu, Y. -J; Smith, A. Science, Vol. 374, Issue 6572 https://doi.org/10.1126/science.abi8378	journal	December 2021
Probing Topological Spin Liquids on a Programmable Quantum Simulator Semeghini, Giulia; Levine, Harry; Keesling, Alexander arXiv https://doi.org/10.48550/arxiv.2104.04119	text	January 2021
Multi-angle quantum approximate optimization algorithm Herrman, Rebekah; Lotshaw, Phillip C.; Ostrowski, James Scientific Reports, Vol. 12, Issue 1 https://doi.org/10.1038/s41598-022-10555-8	journal	April 2022
Ground states of the Ising model on an anisotropic triangular lattice: stripes and zigzags Dublenych, Yu I. Journal of Physics: Condensed Matter, Vol. 25, Issue 40 https://doi.org/10.1088/0953-8984/25/40/406003	journal	September 2013
Order-by-disorder in the antiferromagnetic Ising model on an elastic triangular lattice Shokef, Yair; Souslov, Anton; Lubensky, Tom C. arXiv https://doi.org/10.48550/arxiv.1008.2499	text	January 2010
Quantifying the efficiency of state preparation via quantum variational eigensolvers Matos, Gabriel; Johri, Sonika; Papić, Zlatko arXiv https://doi.org/10.48550/arxiv.2007.14338	text	January 2020
Formulating and Solving Routing Problems on Quantum Computers Harwood, Stuart; Gambella, Claudio; Trenev, Dimitar IEEE Transactions on Quantum Engineering, Vol. 2 https://doi.org/10.1109/TQE.2021.3049230	journal	January 2021
Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder Wessel, Stefan; Normand, Bruce; Mila, Frédéric SciPost Physics, Vol. 3, Issue 1 https://doi.org/10.21468/SciPostPhys.3.1.005	journal	January 2017
Order by disorder in the antiferromagnetic Ising model on an elastic triangular lattice Shokef, Y.; Souslov, A.; Lubensky, T. C. Proceedings of the National Academy of Sciences, Vol. 108, Issue 29 https://doi.org/10.1073/pnas.1014915108	journal	July 2011
Exact ground state of a quantum mechanical antiferromagnet Sriram Shastry, B.; Sutherland, Bill Physica B+C, Vol. 108, Issue 1-3 https://doi.org/10.1016/0378-4363(81)90838-X	journal	August 1981
Ordering, metastability and phase transitions in two-dimensional systems Kosterlitz, J M; Thouless, D J Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203 https://doi.org/10.1088/0022-3719/6/7/010	journal	April 1973
Multi-step magnetization of the Ising model on a Shastry–Sutherland lattice: a Monte Carlo simulation Huang, W. C.; Huo, L.; Tian, G. Journal of Physics: Condensed Matter, Vol. 24, Issue 38 https://doi.org/10.1088/0953-8984/24/38/386003	journal	August 2012
Neutron Diffraction Study on the Multiple Magnetization Plateaus in ${TbB}_{4}$ under Pulsed High Magnetic Field Yoshii, S.; Ohoyama, K.; Kurosawa, K. Physical Review Letters, Vol. 103, Issue 7 https://doi.org/10.1103/PhysRevLett.103.077203	journal	August 2009
QCOR: A Language Extension Specification for the Heterogeneous Quantum-Classical Model of Computation Mintz, Tiffany M.; McCaskey, Alexander J.; Dumitrescu, Eugene F. ACM Journal on Emerging Technologies in Computing Systems, Vol. 16, Issue 2 https://doi.org/10.1145/3380964	journal	April 2020
Signature of magnetic monopole and Dirac string dynamics in spin ice Jaubert, L. D. C.; Holdsworth, P. C. W. Nature Physics, Vol. 5, Issue 4 https://doi.org/10.1038/nphys1227	journal	March 2009
Colloquium : Ice rule and emergent frustration in particle ice and beyond Ortiz-Ambriz, Antonio; Nisoli, Cristiano; Reichhardt, Charles Reviews of Modern Physics, Vol. 91, Issue 4 https://doi.org/10.1103/revmodphys.91.041003	journal	December 2019
The Quantum Alternating Operator Ansatz on Maximum k-Vertex Cover Cook, Jeremy; Eidenbenz, Stephan; Bartschi, Andreas 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) https://doi.org/10.1109/QCE49297.2020.00021	conference	October 2020
Optimization by Simulated Annealing Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P. Science, Vol. 220, Issue 4598 https://doi.org/10.1126/science.220.4598.671	journal	May 1983
Frustration and quantum criticality Vojta, Matthias Reports on Progress in Physics, Vol. 81, Issue 6 https://doi.org/10.1088/1361-6633/aab6be	journal	May 2018
Quantum Simulators: Architectures and Opportunities Altman, Ehud; Brown, Kenneth R.; Carleo, Giuseppe PRX Quantum, Vol. 2, Issue 1 https://doi.org/10.1103/PRXQuantum.2.017003	journal	February 2021
Qubit spin ice King, Andrew D.; Nisoli, Cristiano; Dahl, Edward D. Science, Vol. 373, Issue 6554 https://doi.org/10.1126/science.abe2824	journal	July 2021
Improving soft magnetic properties in FINEMET-like alloys with Ga addition Zhu, Qianke; Chen, Zhe; Zhang, Shuling Journal of Magnetism and Magnetic Materials, Vol. 487 https://doi.org/10.1016/j.jmmm.2019.165297	journal	October 2019

Similar Records

Simulating the Shastry-Sutherland Ising Model Using Quantum Annealing

Journal Article · Mon Dec 14 00:00:00 EST 2020 · PRX Quantum · OSTI ID:1905415

Kairys, Paul; King, Andrew D.; Ozfidan, Isil; +4 more

High-field magnetotransport in microstructures of the frustrated antiferromagnet Yb₂Pt₂Pb

Technical Report · Mon Mar 06 00:00:00 EST 2017 · OSTI ID:1905415

Helm, T.; Moll, P. J. W.; Chan, Mun Keat; +2 more

Frustrated ground state in the metallic Ising antiferromagnet

{Nd}_{2} {Ni}_{2} In

Journal Article · Sun Oct 01 00:00:00 EDT 2017 · Physical Review Materials · OSTI ID:1905415

Sala, G.; Mašková, S.; Stone, M. B.

Related Subjects

97 MATHEMATICS AND COMPUTING
quantum approximate optimization
Ising
quantum computing
frustrated magnetism
quantum simulation

Title: Simulations of frustrated Ising Hamiltonians using quantum approximate optimization

Citation Formats

References (74)

Linked Research (1)

Similar Records

Related Subjects