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Title: Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle

Abstract

We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale of the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Moreover, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.

Authors:
 [1];  [2];  [3];  [3];  [1]
  1. Boston Univ., Boston, MA (United States)
  2. Univ. of British Columbia, Vancouver, BC (Canada); Western Washington Univ., Bellingham, WA (United States)
  3. Google Inc., Venice, CA (United States)
Publication Date:
Research Org.:
Boston Univ., MA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1357856
Alternate Identifier(s):
OSTI ID: 1389776
Grant/Contract Number:  
FG02-06ER46316
Resource Type:
Journal Article: Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Volume: 7; Journal Issue: 2; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Yang, Zhi -Cheng, Rahmani, Armin, Shabani, Alireza, Neven, Hartmut, and Chamon, Claudio. Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle. United States: N. p., 2017. Web. doi:10.1103/PhysRevX.7.021027.
Yang, Zhi -Cheng, Rahmani, Armin, Shabani, Alireza, Neven, Hartmut, & Chamon, Claudio. Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle. United States. doi:10.1103/PhysRevX.7.021027.
Yang, Zhi -Cheng, Rahmani, Armin, Shabani, Alireza, Neven, Hartmut, and Chamon, Claudio. Thu . "Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle". United States. doi:10.1103/PhysRevX.7.021027.
@article{osti_1357856,
title = {Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle},
author = {Yang, Zhi -Cheng and Rahmani, Armin and Shabani, Alireza and Neven, Hartmut and Chamon, Claudio},
abstractNote = {We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale of the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Moreover, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.},
doi = {10.1103/PhysRevX.7.021027},
journal = {Physical Review. X},
number = 2,
volume = 7,
place = {United States},
year = {Thu May 18 00:00:00 EDT 2017},
month = {Thu May 18 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevX.7.021027

Citation Metrics:
Cited by: 4 works
Citation information provided by
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