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Quantum Imaginary Time Evolution, Quantum Lanczos, and Quantum Thermal Averaging

Motta, Mario and Sun, Chong and Tan, Adrian T. K. and O'Rourke, Matthew J. and Ye, Erika and Minnich, Austin J. and Brandão, Fernando G. S. L. and Chan, Garnet Kin-Lic (2019) Quantum Imaginary Time Evolution, Quantum Lanczos, and Quantum Thermal Averaging. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20190801-134541389

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Abstract

An efficient way to compute Hamiltonian ground-states on a quantum computer stands to impact many problems in the physical and computer sciences, ranging from quantum simulation to machine learning. Unfortunately, existing techniques, such as phase estimation and variational algorithms, display formal and practical disadvantages, such as requirements for deep circuits and high-dimensional optimization. We describe the quantum imaginary time evolution and quantum Lanczos algorithms, analogs of classical algorithms for ground (and excited) states, but with exponentially reduced space and time requirements per iteration, and without deep circuits, ancillae, or high-dimensional non-linear optimization. We further discuss quantum imaginary time evolution as a natural subroutine to generate Gibbs averages through an analog of minimally entangled typical thermal states. We implement these algorithms with exact classical emulation as well as in prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit, demonstrating the power of quantum elevations of classical algorithms.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1901.07653arXivDiscussion Paper
ORCID:
AuthorORCID
Motta, Mario0000-0003-1647-9864
Sun, Chong0000-0002-8299-9094
O'Rourke, Matthew J.0000-0002-5779-2577
Minnich, Austin J.0000-0002-9671-9540
Brandão, Fernando G. S. L.0000-0003-3866-9378
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:MM, GKC, FGSLB, ATKT, AJM were supported by the US NSF via RAISE-TAQS CCF 1839204. MJO’R was supported by an NSF graduate fellowship via grant No. DEG-1745301; the tensor network algorithms were developed with the support of the US DOD via MURI FA9550-18-1-0095. EY was supported by a Google fellowship. CS was supported by the Simons Collaboration on the Many-Electron Problem. The Rigetti computations were made possible by a generous grant through Rigetti Quantum Cloud services supported by the CQIA-Rigetti Partnership Program. We thank GH Low, JR McClean, R Babbush for discussions, and the Rigetti team for help with the QVM and QPU simulations.
Group:Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFCCF-1839204
NSF Graduate Research FellowshipDGE-1745301
Air Force Office of Scientific Research (AFOSR)FA9550-18-1-0095
Google PhD FellowshipUNSPECIFIED
Simons FoundationUNSPECIFIED
CQIA-Rigetti Partnership ProgramUNSPECIFIED
Record Number:CaltechAUTHORS:20190801-134541389
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190801-134541389
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97601
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:01 Aug 2019 21:41
Last Modified:04 Jun 2020 10:14

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