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Measurement reduction in variational quantum algorithms

Zhao, Andrew and Tranter, Andrew and Kirby, William M. and Ung, Shu Fay and Miyake, Akimasa and Love, Peter J. (2020) Measurement reduction in variational quantum algorithms. Physical Review A, 101 (6). Art. No. 062322. ISSN 2469-9926. https://resolver.caltech.edu/CaltechAUTHORS:20200615-084304768

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Abstract

Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The number of terms can become overwhelmingly large for problems at the scale of NISQ hardware that may soon be available. We use unitary partitioning (developed independently by Izmaylov et al. [J. Chem. Theory Comput. 16, 190 (2020)]) to define variational quantum eigensolver procedures in which additional unitary operations are appended to the ansatz preparation to reduce the number of terms. This approach may be scaled to use all coherent resources available after ansatz preparation. We also study the use of asymmetric qubitization to implement the additional coherent operations with lower circuit depth. Using this technique, we find a constant factor speedup for lattice and random Pauli Hamiltonians. For electronic structure Hamiltonians, we prove that linear term reduction with respect to the number of orbitals, which has been previously observed in numerical studies, is always achievable. For systems represented on 10–30 qubits, we find that there is a reduction in the number of terms by approximately an order of magnitude. Applied to the plane-wave dual-basis representation of fermionic Hamiltonians, however, unitary partitioning offers only a constant factor reduction. Finally, we show that noncontextual Hamiltonians may be reduced to effective commuting Hamiltonians using unitary partitioning.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/physreva.101.062322DOIArticle
https://arxiv.org/abs/1908.08067arXivDiscussion Paper
ORCID:
AuthorORCID
Zhao, Andrew0000-0002-0299-0277
Tranter, Andrew0000-0002-0299-3478
Kirby, William M.0000-0002-2778-1703
Ung, Shu Fay0000-0001-8977-1749
Additional Information:© 2020 American Physical Society. Received 11 October 2019; accepted 14 May 2020; published 12 June 2020. The authors would like to thank A. Ralli for productive discussions. This work was supported by the National Science Foundation STAQ project (Grant No. PHY-1818914). W.M.K. additionally acknowledges support from the National Science Foundation (Grant No. DGE-1842474).
Funders:
Funding AgencyGrant Number
NSFPHY-1818914
NSFDGE-1842474
Issue or Number:6
Record Number:CaltechAUTHORS:20200615-084304768
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200615-084304768
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103906
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:15 Jun 2020 15:59
Last Modified:15 Jun 2020 15:59

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