Optimization of algorithmic errors in analog quantum simulations

Zemlevskiy, Nikita A.; Froland, Henry F.; Caspar, Stephan

doi:10.1103/physreva.109.052425

Optimization of algorithmic errors in analog quantum simulations

Journal Article · Wed May 15 00:00:00 EDT 2024 · Physical Review A

DOI:https://doi.org/10.1103/physreva.109.052425· OSTI ID:2352117

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University of Washington, Seattle, WA (United States); UW
University of Washington, Seattle, WA (United States)

Due to rapidly improving quantum computing hardware, Hamiltonian simulations of relativistic lattice field theories have seen a resurgence of attention. Furthermore, this computational tool requires turning the formally infinite-dimensional Hilbert space of the full theory into a finite-dimensional one. For gauge theories, a widely used basis for the Hilbert space relies on the representations induced by the underlying gauge group, with a truncation that keeps only a set of the lowest dimensional representations. This works well at large bare gauge coupling, but becomes less efficient at small coupling, which is required for the continuum limit of the lattice theory. In this work, we develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge. In particular, we show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved, which allows for this basis to be used at all values of the coupling. Little prior knowledge is assumed, so this may also be used as an introduction to the subject of Hamiltonian formulations of lattice gauge theories.

View Accepted Manuscript (DOE)

Research Organization:: University of Washington, Seattle, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0020970

OSTI ID:: 2352117

Alternate ID(s):: OSTI ID: 2356919

Report Number(s):: IQuS@UW--21-059

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 5 Vol. 109; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (76)

Kernel Flows Emulation for NASA's Surface Biology and Geology Mission Braverman, Amy Root https://doi.org/10.48577/jpl.056uf9	dataset	January 2023
The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines Benioff, Paul Journal of Statistical Physics, Vol. 22, Issue 5 https://doi.org/10.1007/BF01011339	journal	May 1980
Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems Suzuki, Masuo Communications in Mathematical Physics, Vol. 51, Issue 2 https://doi.org/10.1007/BF01609348	journal	June 1976
Simulating physics with computers Feynman, Richard P. International Journal of Theoretical Physics, Vol. 21, Issue 6-7 https://doi.org/10.1007/BF02650179	journal	June 1982
Time-resolved observation of spin waves in a linear chain of nuclear spins Mádi, Z. L.; Brutscher, B.; Schulte-Herbrüggen, T. Chemical Physics Letters, Vol. 268, Issue 3-4 https://doi.org/10.1016/S0009-2614(97)00194-2	journal	April 1997
Quantum annealing with manufactured spins Johnson, M. W.; Amin, M. H. S.; Gildert, S. Nature, Vol. 473, Issue 7346 https://doi.org/10.1038/nature10012	journal	May 2011
Non-local propagation of correlations in quantum systems with long-range interactions Richerme, Philip; Gong, Zhe-Xuan; Lee, Aaron Nature, Vol. 511, Issue 7508 https://doi.org/10.1038/nature13450	journal	July 2014
Quasiparticle engineering and entanglement propagation in a quantum many-body system Jurcevic, P.; Lanyon, B. P.; Hauke, P. Nature, Vol. 511, Issue 7508 https://doi.org/10.1038/nature13461	journal	July 2014
Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems Ma, Xiao-song; Dakic, Borivoje; Naylor, William Nature Physics, Vol. 7, Issue 5 https://doi.org/10.1038/nphys1919	journal	February 2011
SU(2) hadrons on a quantum computer via a variational approach Atas, Yasar Y.; Zhang, Jinglei; Lewis, Randy Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-26825-4	journal	November 2021
Practical verification protocols for analog quantum simulators Shaffer, Ryan; Megidish, Eli; Broz, Joseph npj Quantum Information, Vol. 7, Issue 1 https://doi.org/10.1038/s41534-021-00380-8	journal	March 2021
Hamiltonian simulation in the low-energy subspace Şahinoğlu, Burak; Somma, Rolando D. npj Quantum Information, Vol. 7, Issue 1 https://doi.org/10.1038/s41534-021-00451-w	journal	July 2021
Many-body physics with individually controlled Rydberg atoms Browaeys, Antoine; Lahaye, Thierry Nature Physics, Vol. 16, Issue 2 https://doi.org/10.1038/s41567-019-0733-z	journal	January 2020
Quantum phases of matter on a 256-atom programmable quantum simulator Ebadi, Sepehr; Wang, Tout T.; Levine, Harry Nature, Vol. 595, Issue 7866 https://doi.org/10.1038/s41586-021-03582-4	journal	July 2021
Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms Scholl, Pascal; Schuler, Michael; Williams, Hannah J. Nature, Vol. 595, Issue 7866 https://doi.org/10.1038/s41586-021-03585-1	journal	July 2021
Practical quantum advantage in quantum simulation Daley, Andrew J.; Bloch, Immanuel; Kokail, Christian Nature, Vol. 607, Issue 7920 https://doi.org/10.1038/s41586-022-04940-6	journal	July 2022
Evidence for the utility of quantum computing before fault tolerance Kim, Youngseok; Eddins, Andrew; Anand, Sajant Nature, Vol. 618, Issue 7965 https://doi.org/10.1038/s41586-023-06096-3	journal	June 2023
Quantum simulation of fundamental particles and forces Bauer, Christian W.; Davoudi, Zohreh; Klco, Natalie Nature Reviews Physics, Vol. 5, Issue 7 https://doi.org/10.1038/s42254-023-00599-8	journal	June 2023
Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model Gong, Shou-Shu; Zhu, Wei; Sheng, D. N. Scientific Reports, Vol. 4, Issue 1 https://doi.org/10.1038/srep06317	journal	September 2014
Digital-Analog Quantum Simulation of Spin Models in Trapped Ions Arrazola, Iñigo; Pedernales, Julen S.; Lamata, Lucas Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep30534	journal	July 2016
Toward the first quantum simulation with quantum speedup Childs, Andrew M.; Maslov, Dmitri; Nam, Yunseong Proceedings of the National Academy of Sciences, Vol. 115, Issue 38 https://doi.org/10.1073/pnas.1801723115	journal	September 2018
Universal quantum Hamiltonians Cubitt, Toby S.; Montanaro, Ashley; Piddock, Stephen Proceedings of the National Academy of Sciences, Vol. 115, Issue 38 https://doi.org/10.1073/pnas.1804949115	journal	August 2018
Quantum phases of Rydberg atoms on a kagome lattice Samajdar, Rhine; Ho, Wen Wei; Pichler, Hannes Proceedings of the National Academy of Sciences, Vol. 118, Issue 4 https://doi.org/10.1073/pnas.2015785118	journal	January 2021
Digital-analog quantum simulations with superconducting circuits Lamata, Lucas; Parra-Rodriguez, Adrian; Sanz, Mikel Advances in Physics: X, Vol. 3, Issue 1 https://doi.org/10.1080/23746149.2018.1457981	journal	January 2018
Assembled arrays of Rydberg-interacting atoms Schlosser, Malte; Ohl de Mello, Daniel; Schäffner, Dominik Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 53, Issue 14 https://doi.org/10.1088/1361-6455/ab8b46	journal	June 2020
A concise review of Rydberg atom based quantum computation and quantum simulation* Wu, Xiaoling; Liang, Xinhui; Tian, Yaoqi Chinese Physics B, Vol. 30, Issue 2 https://doi.org/10.1088/1674-1056/abd76f	journal	February 2021
Higher order decompositions of ordered operator exponentials Wiebe, Nathan; Berry, Dominic; Høyer, Peter Journal of Physics A: Mathematical and Theoretical, Vol. 43, Issue 6 https://doi.org/10.1088/1751-8113/43/6/065203	journal	January 2010
Engineering an effective three-spin Hamiltonian in trapped-ion systems for applications in quantum simulation Andrade, Bárbara; Davoudi, Zohreh; Graß, Tobias Quantum Science and Technology, Vol. 7, Issue 3 https://doi.org/10.1088/2058-9565/ac5f5b	journal	April 2022
Propagation of errors and quantitative quantum simulation with quantum advantage Flannigan, S.; Pearson, N.; Low, G. H. Quantum Science and Technology, Vol. 7, Issue 4 https://doi.org/10.1088/2058-9565/ac88f5	journal	August 2022
Quantifying the Sensitivity to Errors in Analog Quantum Simulation Poggi, Pablo M.; Lysne, Nathan K.; Kuper, Kevin W. PRX Quantum, Vol. 1, Issue 2 https://doi.org/10.1103/PRXQuantum.1.020308	journal	November 2020
Digital-Analog Quantum Simulations Using the Cross-Resonance Effect Gonzalez-Raya, Tasio; Asensio-Perea, Rodrigo; Martin, Ana PRX Quantum, Vol. 2, Issue 2 https://doi.org/10.1103/PRXQuantum.2.020328	journal	May 2021
Trotter Errors from Dynamical Structural Instabilities of Floquet Maps in Quantum Simulation Chinni, Karthik; Muñoz-Arias, Manuel H.; Deutsch, Ivan H. PRX Quantum, Vol. 3, Issue 1 https://doi.org/10.1103/PRXQuantum.3.010351	journal	March 2022
Microwave Engineering of Programmable XXZ Hamiltonians in Arrays of Rydberg Atoms Scholl, P.; Williams, H. J.; Bornet, G. PRX Quantum, Vol. 3, Issue 2 https://doi.org/10.1103/PRXQuantum.3.020303	journal	April 2022
Quantum Simulation for High-Energy Physics Bauer, Christian W.; Davoudi, Zohreh; Balantekin, A. Baha PRX Quantum, Vol. 4, Issue 2 https://doi.org/10.1103/PRXQuantum.4.027001	journal	May 2023
Preparation for quantum simulation of the (1+1) -dimensional O(3) nonlinear σ model using cold atoms Ciavarella, Anthony N.; Caspar, Stephan; Singh, Hersh Physical Review A, Vol. 107, Issue 4 https://doi.org/10.1103/PhysRevA.107.042404	journal	April 2023
Simulating Heisenberg interactions in the Ising model with strong drive fields Ciavarella, Anthony N.; Caspar, Stephan; Singh, Hersh Physical Review A, Vol. 108, Issue 4 https://doi.org/10.1103/PhysRevA.108.042216	journal	October 2023
Higher-order methods for Hamiltonian engineering pulse sequence design Tyler, Matthew; Zhou, Hengyun; Martin, Leigh S. Physical Review A, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevA.108.062602	journal	December 2023
Boson-mediated quantum spin simulators in transverse fields: X Y model and spin-boson entanglement Wall, Michael L.; Safavi-Naini, Arghavan; Rey, Ana Maria Physical Review A, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevA.95.013602	journal	January 2017
Relationship between the transverse-field Ising model and the X Y model via the rotating-wave approximation Kiely, Thomas G.; Freericks, J. K. Physical Review A, Vol. 97, Issue 2 https://doi.org/10.1103/PhysRevA.97.023611	journal	February 2018
Digitization of scalar fields for quantum computing Klco, Natalie; Savage, Martin J. Physical Review A, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevA.99.052335	journal	May 2019
Quantum simulation of spin ordering with nuclear spins in a solid-state lattice Roumpos, Georgios; Master, Cyrus P.; Yamamoto, Yoshihisa Physical Review B, Vol. 75, Issue 9 https://doi.org/10.1103/PhysRevB.75.094415	journal	March 2007
Long-range Heisenberg models in quasiperiodically driven crystals of trapped ions Bermudez, A.; Tagliacozzo, L.; Sierra, G. Physical Review B, Vol. 95, Issue 2 https://doi.org/10.1103/PhysRevB.95.024431	journal	January 2017
Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis Ciavarella, Anthony; Klco, Natalie; Savage, Martin J. Physical Review D, Vol. 103, Issue 9 https://doi.org/10.1103/PhysRevD.103.094501	journal	May 2021
Classical and quantum evolution in a simple coherent neutrino problem Martin, Joshua D.; Roggero, A.; Duan, Huaiyu Physical Review D, Vol. 105, Issue 8 https://doi.org/10.1103/PhysRevD.105.083020	journal	April 2022
Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. I. Axial gauge Farrell, Roland C.; Chernyshev, Ivan A.; Powell, Sarah J. M. Physical Review D, Vol. 107, Issue 5 https://doi.org/10.1103/PhysRevD.107.054512	journal	March 2023
Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. II. Single-baryon β -decay in real time Farrell, Roland C.; Chernyshev, Ivan A.; Powell, Sarah J. M. Physical Review D, Vol. 107, Issue 5 https://doi.org/10.1103/PhysRevD.107.054513	journal	March 2023
Simple Hamiltonian for quantum simulation of strongly coupled (2+1)D SU(2) lattice gauge theory on a honeycomb lattice Müller, Berndt; Yao, Xiaojun Physical Review D, Vol. 108, Issue 9 https://doi.org/10.1103/PhysRevD.108.094505	journal	November 2023
Theta dependence, sign problems, and topological interference Ünsal, Mithat Physical Review D, Vol. 86, Issue 10 https://doi.org/10.1103/PhysRevD.86.105012	journal	November 2012
Digital Quantum Simulation of Spin Systems in Superconducting Circuits Heras, U. Las; Mezzacapo, A.; Lamata, L. Physical Review Letters, Vol. 112, Issue 20 https://doi.org/10.1103/PhysRevLett.112.200501	journal	May 2014
Analog Quantum Error Correction with Encoding a Qubit into an Oscillator Fukui, Kosuke; Tomita, Akihisa; Okamoto, Atsushi Physical Review Letters, Vol. 119, Issue 18 https://doi.org/10.1103/PhysRevLett.119.180507	journal	November 2017
Dynamical Topological Transitions in the Massive Schwinger Model with a θ Term Zache, T. V.; Mueller, N.; Schneider, J. T. Physical Review Letters, Vol. 122, Issue 5 https://doi.org/10.1103/PhysRevLett.122.050403	journal	February 2019
Nearly Optimal Lattice Simulation by Product Formulas Childs, Andrew M.; Su, Yuan Physical Review Letters, Vol. 123, Issue 5 https://doi.org/10.1103/PhysRevLett.123.050503	journal	August 2019
Quantum Algorithm for High Energy Physics Simulations Nachman, Benjamin; Provasoli, Davide; de Jong, Wibe A. Physical Review Letters, Vol. 126, Issue 6 https://doi.org/10.1103/PhysRevLett.126.062001	journal	February 2021
From Asymptotic Freedom to θ Vacua: Qubit Embeddings of the O(3) Nonlinear σ Model Caspar, Stephan; Singh, Hersh Physical Review Letters, Vol. 129, Issue 2 https://doi.org/10.1103/PhysRevLett.129.022003	journal	July 2022
Controlling Local Thermalization Dynamics in a Floquet-Engineered Dipolar Ensemble Martin, Leigh S.; Zhou, Hengyun; Leitao, Nathaniel T. Physical Review Letters, Vol. 130, Issue 21 https://doi.org/10.1103/PhysRevLett.130.210403	journal	May 2023
Real-Time Nonperturbative Dynamics of Jet Production in Schwinger Model: Quantum Entanglement and Vacuum Modification Florio, Adrien; Frenklakh, David; Ikeda, Kazuki Physical Review Letters, Vol. 131, Issue 2 https://doi.org/10.1103/PhysRevLett.131.021902	journal	July 2023
Robust Higher-Order Hamiltonian Engineering for Quantum Sensing with Strongly Interacting Systems Zhou, Hengyun; Martin, Leigh S.; Tyler, Matthew Physical Review Letters, Vol. 131, Issue 22 https://doi.org/10.1103/PhysRevLett.131.220803	journal	December 2023
Analog Quantum Error Correction Lloyd, Seth; Slotine, Jean-Jacques E. Physical Review Letters, Vol. 80, Issue 18 https://doi.org/10.1103/PhysRevLett.80.4088	journal	May 1998
Robust Dynamic Hamiltonian Engineering of Many-Body Spin Systems Choi, Joonhee; Zhou, Hengyun; Knowles, Helena S. Physical Review X, Vol. 10, Issue 3 https://doi.org/10.1103/PhysRevX.10.031002	journal	July 2020
Quantum Metrology with Strongly Interacting Spin Systems Zhou, Hengyun; Choi, Joonhee; Choi, Soonwon Physical Review X, Vol. 10, Issue 3 https://doi.org/10.1103/PhysRevX.10.031003	journal	July 2020
Theory of Trotter Error with Commutator Scaling Childs, Andrew M.; Su, Yuan; Tran, Minh C. Physical Review X, Vol. 11, Issue 1 https://doi.org/10.1103/PhysRevX.11.011020	journal	February 2021
Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms Cong, Iris; Levine, Harry; Keesling, Alexander Physical Review X, Vol. 12, Issue 2 https://doi.org/10.1103/PhysRevX.12.021049	journal	June 2022
Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics Salathé, Y.; Mondal, M.; Oppliger, M. Physical Review X, Vol. 5, Issue 2 https://doi.org/10.1103/PhysRevX.5.021027	journal	June 2015
Practical Quantum Error Mitigation for Near-Future Applications Endo, Suguru; Benjamin, Simon C.; Li, Ying Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031027	journal	July 2018
Quantum information with Rydberg atoms Saffman, M.; Walker, T. G.; Mølmer, K. Reviews of Modern Physics, Vol. 82, Issue 3 https://doi.org/10.1103/RevModPhys.82.2313	journal	August 2010
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
Programmable quantum simulations of spin systems with trapped ions Monroe, C.; Campbell, W. C.; Duan, L. -M. Reviews of Modern Physics, Vol. 93, Issue 2 https://doi.org/10.1103/RevModPhys.93.025001	journal	April 2021
Noisy intermediate-scale quantum algorithms Bharti, Kishor; Cervera-Lierta, Alba; Kyaw, Thi Ha Reviews of Modern Physics, Vol. 94, Issue 1 https://doi.org/10.1103/RevModPhys.94.015004	journal	February 2022
Quantum error mitigation Cai, Zhenyu; Babbush, Ryan; Benjamin, Simon C. Reviews of Modern Physics, Vol. 95, Issue 4 https://doi.org/10.1103/RevModPhys.95.045005	journal	December 2023
Quantum localization bounds Trotter errors in digital quantum simulation Heyl, Markus; Hauke, Philipp; Zoller, Peter Science Advances, Vol. 5, Issue 4 https://doi.org/10.1126/sciadv.aau8342	journal	April 2019
Quantum Algorithms for Quantum Field Theories Jordan, S. P.; Lee, K. S. M.; Preskill, J. Science, Vol. 336, Issue 6085 https://doi.org/10.1126/science.1217069	journal	May 2012
Floquet Hamiltonian engineering of an isolated many-body spin system Geier, Sebastian; Thaicharoen, Nithiwadee; Hainaut, Clément Science, Vol. 374, Issue 6571 https://doi.org/10.1126/science.abd9547	journal	November 2021
Simulating quantum field theory with a quantum computer Preskill, John Proceedings of The 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018) https://doi.org/10.22323/1.334.0024	conference	May 2019
Quantum computing with neutral atoms Henriet, Loïc; Beguin, Lucas; Signoles, Adrien Quantum, Vol. 4 https://doi.org/10.22331/q-2020-09-21-327	journal	September 2020
State Preparation in the Heisenberg Model through Adiabatic Spiraling Ciavarella, Anthony N.; Caspar, Stephan; Illa, Marc Quantum, Vol. 7 https://doi.org/10.22331/q-2023-04-06-970	journal	April 2023
Quantifying the sensitivity to errors in analog quantum simulation 2020, International conference for the quantum science and technology community; Kuper, Kevin; Lysne, Nathan Underline Science Inc. https://doi.org/10.48448/j30p-z596	audiovisual	January 2020

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