Parallelization techniques for quantum simulation of fermionic systems

Bringewatt, Jacob; Davoudi, Zohreh

doi:10.22331/q-2023-04-13-975

Parallelization techniques for quantum simulation of fermionic systems

Journal Article · Thu Apr 13 00:00:00 EDT 2023 · Quantum

DOI:https://doi.org/10.22331/q-2023-04-13-975· OSTI ID:2420913

Bringewatt, Jacob ^[1]; Davoudi, Zohreh ^[2]

Univ. of Maryland, College Park, MD (United States); National Inst. of Standards and Technology (NIST), College Park, MD (United States)
Univ. of Maryland, College Park, MD (United States)

Mapping fermionic operators to qubit operators is an essential step for simulating fermionic systems on a quantum computer. We investigate how the choice of such a mapping interacts with the underlying qubit connectivity of the quantum processor to enable (or impede) parallelization of the resulting Hamiltonian-simulation algorithm. It is shown that this problem can be mapped to a path coloring problem on a graph constructed from the particular choice of encoding fermions onto qubits and the fermionic interactions onto paths. The basic version of this problem is called the weak coloring problem. Taking into account the fine-grained details of the mapping yields what is called the strong coloring problem, which leads to improved parallelization performance. A variety of illustrative analytical and numerical examples are presented to demonstrate the amount of improvement for both weak and strong coloring-based parallelizations. Our results are particularly important for implementation on near-term quantum processors where minimizing circuit depth is necessary for algorithmic feasibility.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Maryland, College Park, MD (United States); Krell Institute, Ames, IA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Air Force Office of Scientific Research (AFOSR); US Army Research Office (ARO); National Science Foundation (NSF); Simons Foundation; Heising-Simons Foundation

Grant/Contract Number:: SC0019040; SC0019323; SC0020271; SC0020312; OMA-2120757; PHY-1748958; 216179

OSTI ID:: 2420913

Journal Information:: Quantum, Vol. 7; ISSN 2521-327X

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

References (63)

An introduction to the SYK model Rosenhaus, Vladimir Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 32 https://doi.org/10.1088/1751-8121/ab2ce1	journal	July 2019
Series expansions for the massive Schwinger model in Hamiltonian lattice theory Hamer, C. J.; Weihong, Zheng; Oitmaa, J. Physical Review D, Vol. 56, Issue 1 https://doi.org/10.1103/PhysRevD.56.55	journal	July 1997
Hybridized Methods for Quantum Simulation in the Interaction Picture Rajput, Abhishek; Roggero, Alessandro; Wiebe, Nathan arXiv https://doi.org/10.48550/arXiv.2109.03308	text	January 2021
Fermions without Fermion Fields Ball, R. C. Physical Review Letters, Vol. 95, Issue 17 https://doi.org/10.1103/PhysRevLett.95.176407	journal	October 2005
Non-Abelian gauge invariance from dynamical decoupling Kasper, Valentin; Zache, Torsten V.; Jendrzejewski, Fred arXiv https://doi.org/10.48550/arXiv.2012.08620	preprint	January 2020
Quantum Computation and Quantum Information Nielsen, Michael A.; Chuang, Isaac L. Cambridge University Press https://doi.org/10.1017/CBO9780511976667	book	January 2011
Hamiltonian Simulation by Qubitization Low, Guang Hao; Chuang, Isaac L. Quantum, Vol. 3 https://doi.org/10.22331/q-2019-07-12-163	journal	July 2019
Quantum Algorithm for Simulating Hamiltonian Dynamics with an Off-diagonal Series Expansion Kalev, Amir; Hen, Itay Quantum, Vol. 5 https://doi.org/10.22331/q-2021-04-08-426	journal	April 2021
Search for efficient formulations for Hamiltonian simulation of non-Abelian lattice gauge theories Davoudi, Zohreh; Raychowdhury, Indrakshi; Shaw, Andrew Physical Review D, Vol. 104, Issue 7 https://doi.org/10.1103/PhysRevD.104.074505	journal	October 2021
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
Gapless spin-fluid ground state in a random quantum Heisenberg magnet Sachdev, Subir; Ye, Jinwu Physical Review Letters, Vol. 70, Issue 21 https://doi.org/10.1103/PhysRevLett.70.3339	journal	May 1993
Simulating Hamiltonian Dynamics with a Truncated Taylor Series Berry, Dominic W.; Childs, Andrew M.; Cleve, Richard Physical Review Letters, Vol. 114, Issue 9 https://doi.org/10.1103/PhysRevLett.114.090502	journal	March 2015
Clifford Algebras, Spin Groups and Qubit Trees Vlasov, Alexander Yurievich Quanta, Vol. 11, Issue 1 https://doi.org/10.12743/quanta.v11i1.199	journal	December 2022
Suppressing Coherent Gauge Drift in Quantum Simulations Lamm, Henry; Lawrence, Scott; Yamauchi, Yukari arXiv https://doi.org/10.48550/arXiv.2005.12688	preprint	January 2020
Fermion-to-qubit mappings with varying resource requirements for quantum simulation Steudtner, Mark; Wehner, Stephanie New Journal of Physics, Vol. 20, Issue 6 https://doi.org/10.1088/1367-2630/aac54f	journal	June 2018
Simulating lattice gauge theories on a quantum computer Byrnes, Tim; Yamamoto, Yoshihisa Physical Review A, Vol. 73, Issue 2 https://doi.org/10.1103/PhysRevA.73.022328	journal	February 2006
Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure Tranter, Andrew; Love, Peter J.; Mintert, Florian Entropy, Vol. 21, Issue 12 https://doi.org/10.3390/e21121218	journal	December 2019
Lattice Quantum Chromodynamics and Electrodynamics on a Universal Quantum Computer Kan, Angus; Nam, Yunseong arXiv https://doi.org/10.48550/arXiv.2107.12769	preprint	January 2021
Faster quantum simulation by randomization Childs, Andrew M.; Ostrander, Aaron; Su, Yuan Quantum, Vol. 3 https://doi.org/10.22331/q-2019-09-02-182	journal	September 2019
Exact bosonization in two spatial dimensions and a new class of lattice gauge theories Chen, Yu-An; Kapustin, Anton; Radičević, Đorđe Annals of Physics, Vol. 393 https://doi.org/10.1016/j.aop.2018.03.024	journal	June 2018
Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions Nguyen, Nhung H.; Tran, Minh C.; Zhu, Yingyue PRX Quantum, Vol. 3, Issue 2 https://doi.org/10.1103/PRXQuantum.3.020324	journal	May 2022
General theory of fractal path integrals with applications to many‐body theories and statistical physics Suzuki, Masuo Journal of Mathematical Physics, Vol. 32, Issue 2 https://doi.org/10.1063/1.529425	journal	February 1991
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
On colouring the nodes of a network Brooks, R. L. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 37, Issue 2 https://doi.org/10.1017/S030500410002168X	journal	April 1941
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
General methods for digital quantum simulation of gauge theories Lamm, Henry; Lawrence, Scott; Yamauchi, Yukari Physical Review D, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevD.100.034518	journal	August 2019
Exact bosonization in arbitrary dimensions Chen, Yu-An Physical Review Research, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevResearch.2.033527	journal	September 2020
An upper bound for the chromatic number of a graph and its application to timetabling problems Welsh, D. J. A. The Computer Journal, Vol. 10, Issue 1 https://doi.org/10.1093/comjnl/10.1.85	journal	January 1967
A Compact Fermion to Qubit Mapping Part 2: Alternative Lattice Geometries Derby, Charles; Klassen, Joel arXiv https://doi.org/10.48550/arXiv.2101.10735	preprint	January 2021
Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics Gilyén, András; Su, Yuan; Low, Guang Hao Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019 https://doi.org/10.1145/3313276.3316366	conference	January 2019
Optimal Hamiltonian Simulation by Quantum Signal Processing Low, Guang Hao; Chuang, Isaac L. Physical Review Letters, Vol. 118, Issue 1 https://doi.org/10.1103/PhysRevLett.118.010501	journal	January 2017
Quantum Algorithms for Quantum Chemistry and Quantum Materials Science Bauer, Bela; Bravyi, Sergey; Motta, Mario Chemical Reviews, Vol. 120, Issue 22 https://doi.org/10.1021/acs.chemrev.9b00829	journal	October 2020
Hamiltonian simulation algorithms for near-term quantum hardware Clinton, Laura; Bausch, Johannes; Cubitt, Toby Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-25196-0	journal	August 2021
Chiral effective field theory and nuclear forces Machleidt, R.; Entem, D. R. Physics Reports, Vol. 503, Issue 1 https://doi.org/10.1016/j.physrep.2011.02.001	journal	June 2011
The Bravyi-Kitaev transformation: Properties and applications Tranter, Andrew; Sofia, Sarah; Seeley, Jake International Journal of Quantum Chemistry, Vol. 115, Issue 19 https://doi.org/10.1002/qua.24969	journal	July 2015
Quantum algorithms for fermionic simulations Ortiz, G.; Gubernatis, J. E.; Knill, E. Physical Review A, Vol. 64, Issue 2 https://doi.org/10.1103/PhysRevA.64.022319	journal	July 2001
Removing staggered fermionic matter in U ( N ) and S U ( N ) lattice gauge theories Zohar, Erez; Cirac, J. Ignacio Physical Review D, Vol. 99, Issue 11 https://doi.org/10.1103/PhysRevD.99.114511	journal	June 2019
Geometric quantum information structure in quantum fields and their lattice simulation Klco, Natalie; Savage, Martin J. Physical Review D, Vol. 103, Issue 6 https://doi.org/10.1103/PhysRevD.103.065007	journal	March 2021
Suppressing nonperturbative gauge errors in the thermodynamic limit using local pseudogenerators Van Damme, Maarten; Mildenberger, Julius; Grusdt, Fabian arXiv https://doi.org/10.48550/arXiv.2110.08041	preprint	January 2021
Reducibility among Combinatorial Problems Karp, Richard M. Complexity of Computer Computations https://doi.org/10.1007/978-1-4684-2001-2_9	book	January 1972
Low-Depth Quantum Simulation of Materials Babbush, Ryan; Wiebe, Nathan; McClean, Jarrod Physical Review X, Vol. 8, Issue 1 https://doi.org/10.1103/PhysRevX.8.011044	journal	March 2018
The Power of Block-Encoded Matrix Powers: Improved Regression Techniques via Faster Hamiltonian Simulation Chakraborty, Shantanav; Gilyén, András; Jeffery, Stacey Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany https://doi.org/10.4230/LIPIcs.ICALP.2019.33	text	January 2019
Oracles for Gauss's law on digital quantum computers Stryker, Jesse R. Physical Review A, Vol. 99, Issue 4 https://doi.org/10.1103/PhysRevA.99.042301	journal	April 2019
Fermionic Quantum Computation Bravyi, Sergey B.; Kitaev, Alexei Yu. Annals of Physics, Vol. 298, Issue 1 https://doi.org/10.1006/aphy.2002.6254	journal	May 2002
Simulating 2D Effects in Lattice Gauge Theories on a Quantum Computer Paulson, Danny; Dellantonio, Luca; Haase, Jan F. PRX Quantum, Vol. 2, Issue 3 https://doi.org/10.1103/PRXQuantum.2.030334	journal	August 2021
Operator locality in the quantum simulation of fermionic models Havlíček, Vojtěch; Troyer, Matthias; Whitfield, James D. Physical Review A, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevA.95.032332	journal	March 2017
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
Bravyi-Kitaev Superfast simulation of electronic structure on a quantum computer Setia, Kanav; Whitfield, James D. The Journal of Chemical Physics, Vol. 148, Issue 16 https://doi.org/10.1063/1.5019371	journal	April 2018
Über das Paulische Äquivalenzverbot Jordan, P.; Wigner, E. P. The Collected Works of Eugene Paul Wigner https://doi.org/10.1007/978-3-662-02781-3_9	book	January 1993
Faster Digital Quantum Simulation by Symmetry Protection Tran, Minh C.; Su, Yuan; Carney, Daniel PRX Quantum, Vol. 2, Issue 1 https://doi.org/10.1103/PRXQuantum.2.010323	journal	February 2021
Quantum supremacy using a programmable superconducting processor Arute, Frank; Arya, Kunal; Babbush, Ryan Nature, Vol. 574, Issue 7779 https://doi.org/10.1038/s41586-019-1666-5	journal	October 2019
Quantum Simulation for High Energy Physics Bauer, Christian W.; Davoudi, Zohreh; Balantekin, A. Baha arXiv https://doi.org/10.48550/arXiv.2204.03381	text	January 2022
Compact fermion to qubit mappings Derby, Charles; Klassen, Joel; Bausch, Johannes Physical Review B, Vol. 104, Issue 3 https://doi.org/10.1103/PhysRevB.104.035118	journal	July 2021
A Comparison of the Bravyi–Kitaev and Jordan–Wigner Transformations for the Quantum Simulation of Quantum Chemistry Tranter, Andrew; Love, Peter J.; Mintert, Florian Journal of Chemical Theory and Computation, Vol. 14, Issue 11 https://doi.org/10.1021/acs.jctc.8b00450	journal	September 2018
Fault-tolerant quantum computation by anyons Kitaev, A. Yu. Annals of Physics, Vol. 303, Issue 1 https://doi.org/10.1016/S0003-4916(02)00018-0	journal	January 2003
Gauge-Symmetry Protection Using Single-Body Terms Halimeh, Jad C.; Lang, Haifeng; Mildenberger, Julius PRX Quantum, Vol. 2, Issue 4 https://doi.org/10.1103/PRXQuantum.2.040311	journal	October 2021
Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning Jiang, Zhang; Kalev, Amir; Mruczkiewicz, Wojciech Quantum, Vol. 4 https://doi.org/10.22331/q-2020-06-04-276	journal	June 2020
Quantum Algorithms for Simulating the Lattice Schwinger Model Shaw, Alexander F.; Lougovski, Pavel; Stryker, Jesse R. Quantum, Vol. 4 https://doi.org/10.22331/q-2020-08-10-306	journal	August 2020
The complexity of path coloring and call scheduling Erlebach, Thomas; Jansen, Klaus Theoretical Computer Science, Vol. 255, Issue 1-2 https://doi.org/10.1016/S0304-3975(99)00152-8	journal	March 2001
Local spin operators for fermion simulations Whitfield, James D.; Havlíček, Vojtěch; Troyer, Matthias Physical Review A, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevA.94.030301	journal	September 2016
Constrained Dynamics via the Zeno Effect in Quantum Simulation: Implementing Non-Abelian Lattice Gauge Theories with Cold Atoms Stannigel, K.; Hauke, P.; Marcos, D. Physical Review Letters, Vol. 112, Issue 12 https://doi.org/10.1103/PhysRevLett.112.120406	journal	March 2014
Quantum Simulation of Electronic Structure with Linear Depth and Connectivity Kivlichan, Ian D.; McClean, Jarrod; Wiebe, Nathan Physical Review Letters, Vol. 120, Issue 11 https://doi.org/10.1103/PhysRevLett.120.110501	journal	March 2018
Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits Chamberland, Christopher; Zhu, Guanyu; Yoder, Theodore J. Physical Review X, Vol. 10, Issue 1 https://doi.org/10.1103/PhysRevX.10.011022	journal	January 2020

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