Quantum time dynamics employing the Yang-Baxter equation for circuit compression

Peng, Bo; Gulania, Sahil; Alexeev, Yuri; Govind, Niranjan

doi:10.1103/physreva.106.012412

Title: Quantum time dynamics employing the Yang-Baxter equation for circuit compression

Journal Article · 08 July 2022 · Physical Review A

DOI: https://doi.org/10.1103/physreva.106.012412 · OSTI ID:1902649

^[1]; Gulania, Sahil ^[2]; Alexeev, Yuri ^[2];

^[1]

Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Argonne National Laboratory (ANL), Lemont, IL (United States)

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of one-dimensional (1D) integrable spin chains with nearest-neighbor interactions. We have proved the existence of a reflection symmetry in the quantum circuit employed for simulating the time evolution of certain classes of 1D Heisenberg model Hamiltonians by virtue of the quantum Yang-Baxter equation, and how this symmetry can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the depth of the compressed circuit is rigorously a linear function of the system size for the studied Heisenberg model Hamiltonians in the present work. As a consequence, the number of CNOT gates in the compressed circuit only scales quadratically with the system size, which allows for the simulations of time dynamics of very large 1D spin chains. We derive the compressed circuit representations for different special cases of the Heisenberg Hamiltonian. We compare and demonstrate the effectiveness of this approach by performing simulations on quantum computers.

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Research Organization:: Argonne National Laboratory (ANL), Lemont, IL (United States); Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1902649

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 1 Vol. 106; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (66)

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
Zur Theorie des Ferromagnetismus Heisenberg, W. Zeitschrift f�r Physik, Vol. 49, Issue 9-10 https://doi.org/10.1007/BF01328601	journal	September 1928
Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette Bethe, H. Zeitschrift f�r Physik, Vol. 71, Issue 3-4 https://doi.org/10.1007/BF01341708	journal	March 1931
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
Integrable quantum computation Zhang, Yong Quantum Information Processing, Vol. 12, Issue 1 https://doi.org/10.1007/s11128-012-0409-4	journal	April 2012
Yang–Baxter equations and quantum entanglements Ge, Mo-Lin; Xue, Kang; Zhang, Ruo-Yang Quantum Information Processing, Vol. 15, Issue 12 https://doi.org/10.1007/s11128-014-0765-3	journal	July 2014
Two soluble models of an antiferromagnetic chain Lieb, Elliott; Schultz, Theodore; Mattis, Daniel Annals of Physics, Vol. 16, Issue 3 https://doi.org/10.1016/0003-4916(61)90115-4	journal	December 1961
Partition function of the Eight-Vertex lattice model Baxter, Rodney J. Annals of Physics, Vol. 70, Issue 1 https://doi.org/10.1016/0003-4916(72)90335-1	journal	March 1972
Some exact calculations on a chain of spins Niemeijer, Th. Physica, Vol. 36, Issue 3 https://doi.org/10.1016/0031-8914(67)90235-2	journal	January 1967
Quantum Field Theory and Condensed Matter Shankar, Ramamurti Cambridge University Press https://doi.org/10.1017/9781139044349	book	January 2017
The One-Dimensional Hubbard Model Essler, Fabian H. L.; Frahm, Holger; Göhmann, Frank Cambridge University Press https://doi.org/10.1017/CBO9780511534843	book	January 2009
Quantum Phase Transitions Sachdev, Subir https://doi.org/10.1017/CBO9780511973765	book	January 2011
What Are the Physical Contents of Hubbard and Heisenberg Hamiltonian Interactions Extracted from Broken Symmetry DFT Calculations in Magnetic Compounds? David, Grégoire; Guihéry, Nathalie; Ferré, Nicolas Journal of Chemical Theory and Computation, Vol. 13, Issue 12 https://doi.org/10.1021/acs.jctc.7b00976	journal	November 2017
Time-dependent quantum-mechanical methods for molecular dynamics Kosloff, Ronnie The Journal of Physical Chemistry, Vol. 92, Issue 8 https://doi.org/10.1021/j100319a003	journal	April 1988
Fast-forwarding of Hamiltonians and exponentially precise measurements Atia, Yosi; Aharonov, Dorit Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-01637-7	journal	November 2017
Low-cost quantum circuits for classically intractable instances of the Hamiltonian dynamics simulation problem Nam, Yunseong; Maslov, Dmitri npj Quantum Information, Vol. 5, Issue 1 https://doi.org/10.1038/s41534-019-0152-0	journal	May 2019
Variational fast forwarding for quantum simulation beyond the coherence time Cîrstoiu, Cristina; Holmes, Zoë; Iosue, Joseph npj Quantum Information, Vol. 6, Issue 1 https://doi.org/10.1038/s41534-020-00302-0	journal	September 2020
Parallel quantum simulation of large systems on small NISQ computers Barratt, F.; Dborin, James; Bal, Matthias npj Quantum Information, Vol. 7, Issue 1 https://doi.org/10.1038/s41534-021-00420-3	journal	May 2021
Experimental realization of the Yang-Baxter Equation via NMR interferometry Vind, F. Anvari; Foerster, A.; Oliveira, I. S. Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep20789	journal	February 2016
A unified view of the theoretical description of magnetic coupling in molecular chemistry and solid state physics Moreira, Ibério de P. R.; Illas, Francesc Physical Chemistry Chemical Physics, Vol. 8, Issue 14 https://doi.org/10.1039/b515732c	journal	January 2006
Solution of a Three‐Body Problem in One Dimension Calogero, F. Journal of Mathematical Physics, Vol. 10, Issue 12 https://doi.org/10.1063/1.1664820	journal	December 1969
Ground State of a One‐Dimensional N‐Body System Calogero, F. Journal of Mathematical Physics, Vol. 10, Issue 12 https://doi.org/10.1063/1.1664821	journal	December 1969
Quantum Many‐Body Problem in One Dimension: Ground State Sutherland, Bill Journal of Mathematical Physics, Vol. 12, Issue 2 https://doi.org/10.1063/1.1665584	journal	February 1971
Quantum Many‐Body Problem in One Dimension: Thermodynamics Sutherland, Bill Journal of Mathematical Physics, Vol. 12, Issue 2 https://doi.org/10.1063/1.1665585	journal	February 1971
Solution of the One‐Dimensional N ‐Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials Calogero, F. Journal of Mathematical Physics, Vol. 12, Issue 3 https://doi.org/10.1063/1.1665604	journal	March 1971
Introduction to the Bethe Ansatz II Karbach, Michael; Hu, Kun; Müller, Gerhard Computers in Physics, Vol. 12, Issue 6 https://doi.org/10.1063/1.168740	journal	January 1998
The Bethe ansatz after 75 years Batchelor, Murray T. Physics Today, Vol. 60, Issue 1 https://doi.org/10.1063/1.2709557	journal	January 2007
Introduction to the Bethe Ansatz I Karabach, Michael; Müller, Gerhard; Gould, Harvey Computers in Physics, Vol. 11, Issue 1 https://doi.org/10.1063/1.4822511	journal	January 1997
Elucidating reaction mechanisms on quantum computers Reiher, Markus; Wiebe, Nathan; Svore, Krysta M. Proceedings of the National Academy of Sciences, Vol. 114, Issue 29 https://doi.org/10.1073/pnas.1619152114	journal	July 2017
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
Quantum-circuit design for efficient simulations of many-body quantum dynamics Raeisi, Sadegh; Wiebe, Nathan; Sanders, Barry C. New Journal of Physics, Vol. 14, Issue 10 https://doi.org/10.1088/1367-2630/14/10/103017	journal	October 2012
The generalized Gibbs ensemble for Heisenberg spin chains Pozsgay, Balázs Journal of Statistical Mechanics: Theory and Experiment, Vol. 2013, Issue 07 https://doi.org/10.1088/1742-5468/2013/07/P07003	journal	July 2013
Yang–Baxter integrable models in experiments: from condensed matter to ultracold atoms Batchelor, Murray T.; Foerster, Angela Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 17 https://doi.org/10.1088/1751-8113/49/17/173001	journal	March 2016
Simple Models of Magnetism Skomski, Ralph Oxford University Press https://doi.org/10.1093/acprof:oso/9780198570752.001.0001	book	January 2008
Real- and Imaginary-Time Evolution with Compressed Quantum Circuits Lin, Sheng-Hsuan; Dilip, Rohit; Green, Andrew G. PRX Quantum, Vol. 2, Issue 1 https://doi.org/10.1103/PRXQuantum.2.010342	journal	March 2021
Quantum Computer Systems for Scientific Discovery Alexeev, Yuri; Bacon, Dave; Brown, Kenneth R. PRX Quantum, Vol. 2, Issue 1 https://doi.org/10.1103/PRXQuantum.2.017001	journal	February 2021
Adaptive Variational Quantum Dynamics Simulations Yao, Yong-Xin; Gomes, Niladri; Zhang, Feng PRX Quantum, Vol. 2, Issue 3 https://doi.org/10.1103/PRXQuantum.2.030307	journal	July 2021
Linear Antiferromagnetic Chain with Anisotropic Coupling Orbach, R. Physical Review, Vol. 112, Issue 2 https://doi.org/10.1103/PhysRev.112.309	journal	October 1958
Statistical Mechanics of the Anisotropic Linear Heisenberg Model Katsura, Shigetoshi Physical Review, Vol. 127, Issue 5 https://doi.org/10.1103/PhysRev.127.1508	journal	September 1962
Statistical Mechanics of the Anisotropic Linear Heisenberg Model Katsura, Shigetoshi Physical Review, Vol. 129, Issue 6 https://doi.org/10.1103/PhysRev.129.2835.4	journal	March 1963
Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State Lieb, Elliott H.; Liniger, Werner Physical Review, Vol. 130, Issue 4 https://doi.org/10.1103/PhysRev.130.1605	journal	May 1963
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum Lieb, Elliott H. Physical Review, Vol. 130, Issue 4 https://doi.org/10.1103/PhysRev.130.1616	journal	May 1963
Algebraic compression of quantum circuits for Hamiltonian evolution Kökcü, Efekan; Camps, Daan; Bassman, Lindsay Physical Review A, Vol. 105, Issue 3 https://doi.org/10.1103/PhysRevA.105.032420	journal	March 2022
Quantum circuits for strongly correlated quantum systems Verstraete, Frank; Cirac, J. Ignacio; Latorre, José I. Physical Review A, Vol. 79, Issue 3 https://doi.org/10.1103/PhysRevA.79.032316	journal	March 2009
Vertical-Arrow Correlation Length in the Eight-Vertex Model and the Low-Lying Excitations of the X − Y − Z Hamiltonian Johnson, James D.; Krinsky, Samuel; McCoy, Barry M. Physical Review A, Vol. 8, Issue 5 https://doi.org/10.1103/PhysRevA.8.2526	journal	November 1973
Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation Babbush, Ryan; McClean, Jarrod; Wecker, Dave Physical Review A, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevA.91.022311	journal	February 2015
Solvable multistate model of Landau-Zener transitions in cavity QED Sinitsyn, Nikolai A.; Li, Fuxiang Physical Review A, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevA.93.063859	journal	June 2016
Eigenvalue spectrum of interacting massive fermions in one dimension Luther, A. Physical Review B, Vol. 14, Issue 5 https://doi.org/10.1103/PhysRevB.14.2153	journal	September 1976
Real-time dynamics in spin- 1 2 chains with adaptive time-dependent density matrix renormalization group Gobert, Dominique; Kollath, Corinna; Schollwöck, Ulrich Physical Review E, Vol. 71, Issue 3 https://doi.org/10.1103/PhysRevE.71.036102	journal	March 2005
Is the efficiency of classical simulations of quantum dynamics related to integrability? Prosen, Tomaž; Žnidarič, Marko Physical Review E, Vol. 75, Issue 1 https://doi.org/10.1103/PhysRevE.75.015202	journal	January 2007
Generalized Thermalization in an Integrable Lattice System Cassidy, Amy C.; Clark, Charles W.; Rigol, Marcos Physical Review Letters, Vol. 106, Issue 14 https://doi.org/10.1103/PhysRevLett.106.140405	journal	April 2011
Time Evolution of Local Observables After Quenching to an Integrable Model Caux, Jean-Sébastien; Essler, Fabian H. L. Physical Review Letters, Vol. 110, Issue 25 https://doi.org/10.1103/PhysRevLett.110.257203	journal	June 2013
Integrable Time-Dependent Quantum Hamiltonians Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y. Physical Review Letters, Vol. 120, Issue 19 https://doi.org/10.1103/PhysRevLett.120.190402	journal	May 2018
Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction Yang, C. N. Physical Review Letters, Vol. 19, Issue 23 https://doi.org/10.1103/PhysRevLett.19.1312	journal	December 1967
Efficient Approximation of the Dynamics of One-Dimensional Quantum Spin Systems Osborne, Tobias J. Physical Review Letters, Vol. 97, Issue 15 https://doi.org/10.1103/PhysRevLett.97.157202	journal	October 2006
Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons Rigol, Marcos; Dunjko, Vanja; Yurovsky, Vladimir Physical Review Letters, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevLett.98.050405	journal	February 2007
Quantum dynamics simulations beyond the coherence time on noisy intermediate-scale quantum hardware by variational Trotter compression Berthusen, Noah F.; Trevisan, Thaís V.; Iadecola, Thomas Physical Review Research, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevResearch.4.023097	journal	May 2022
Non-Abelian anyons and topological quantum computation Nayak, Chetan; Simon, Steven H.; Stern, Ady Reviews of Modern Physics, Vol. 80, Issue 3 https://doi.org/10.1103/RevModPhys.80.1083	journal	September 2008
Lecture Notes on Electron Correlation and Magnetism Fazekas, Patrick https://doi.org/10.1142/2945	book	January 1999
Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems Sutherland, Bill https://doi.org/10.1142/5552	book	June 2004
Introduction to the Yang-Baxter Equation Jimbo, Michio International Journal of Modern Physics A, Vol. 04, Issue 15 https://doi.org/10.1142/S0217751X89001503	journal	September 1989
Generalized Yang–Baxter Equations and Braiding Quantum Gates Chen, Rebecca S. Journal of Knot Theory and Its Ramifications, Vol. 21, Issue 09 https://doi.org/10.1142/S0218216512500873	journal	May 2012
One-Dimensional Heisenberg Model at Finite Temperature Takahashi, Minoru Progress of Theoretical Physics, Vol. 46, Issue 2 https://doi.org/10.1143/PTP.46.401	journal	August 1971
Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems: Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations Suzuki, M. Progress of Theoretical Physics, Vol. 56, Issue 5 https://doi.org/10.1143/PTP.56.1454	journal	November 1976
Constant-depth circuits for dynamic simulations of materials on quantum computers Bassman, Lindsay; Van Beeumen, Roel; Younis, Ed Materials Theory, Vol. 6, Issue 1 https://doi.org/10.1186/s41313-022-00043-x	journal	March 2022
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

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Title: Quantum time dynamics employing the Yang-Baxter equation for circuit compression

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