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Faster Digital Quantum Simulation by Symmetry Protection

Tran, Minh C. and Su, Yuan and Carney, Daniel and Taylor, Jacob M. (2021) Faster Digital Quantum Simulation by Symmetry Protection. PRX Quantum, 2 (1). Art. No. 010323. ISSN 2691-3399. doi:10.1103/prxquantum.2.010323.

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Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection. We derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We prove a bound on this approximation error, exponentially improving a recent result of Burgarth, Facchi, Gramegna, and Pascazio. We apply the symmetry-protection technique to the simulations of the XXZ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory. For both systems, the technique can reduce the simulation error by several orders of magnitude over the unprotected simulation. Finally, we provide numerical evidence suggesting that the technique can also protect simulation against other types of coherent, temporally correlated errors, such as the 1/f noise commonly found in solid-state experiments.

Item Type:Article
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URLURL TypeDescription Paper
Tran, Minh C.0000-0001-7599-9160
Su, Yuan0000-0003-1144-3563
Additional Information:© 2021 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 6 July 2020; accepted 12 January 2021; published 12 February 2021. We thank Ryan Babbush, Andrew Childs, Su-Kuan Chu, Zohreh Davoudi, Jens Eisert, Mária Kieferová, Natalie Klco, Hank Lamm, Guang Hao Low, Nhung Nguyen, Alexander Shaw, and Nathan Wiebe for helpful discussions. Partial support for this research is provided by the Princeton Center for Complex Materials, a MRSEC supported by NSF Grant DMR No. 1420541 and by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Quantum Algorithms Teams and Quantum Testbed Pathfinder programs (Award No. DE-SC0019040). M.C.T. and Y.S. acknowledge additional funding by ARO MURI, NSF (Grant No. CCF-1813814) and Accelerated Research in Quantum Computing (Award No. DE-SC0020312) program. M.C.T also acknowledges DoE BES Materials and Chemical Sciences Research for Quantum Information Science program (Award No. DESC0019449), NSF PFCQC program, AFOSR, AFOSR MURI, ARL CDQI, and NSF PFC at JQI. Y.S. is supported by the Google Ph.D. Fellowship program. He also acknowledges the National Science Foundation RAISE-TAQS 1839204 and Amazon Web Services, AWS Quantum Program. The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center PHY-1733907. Fermilab is operated by Fermi Research Alliance, LLC, under Contract No. DEAC02-07CH11359 with the US Department of Energy. The authors acknowledge the University of Maryland supercomputing resources ( made available for conducting the research reported in this paper.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0019040
Army Research Office (ARO)UNSPECIFIED
Department of Energy (DOE)DE-SC0020312
Department of Energy (DOE)DE-SC0019449
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Army Research LaboratoryUNSPECIFIED
Amazon Web ServicesUNSPECIFIED
Department of Energy (DOE)DE-AC02-07CH11359
Issue or Number:1
Record Number:CaltechAUTHORS:20210212-131356210
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108039
Deposited By: Tony Diaz
Deposited On:12 Feb 2021 21:22
Last Modified:16 Nov 2021 19:08

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