Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems

Quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we analytically apply the fra...

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Bibliographic Details
Published in:Physical review letters Vol. 126; no. 7; p. 070505
Main Authors: Brady, Lucas T., Baldwin, Christopher L., Bapat, Aniruddha, Kharkov, Yaroslav, Gorshkov, Alexey V.
Format: Journal Article
Language:English
Published: United States American Physical Society 19.02.2021
American Physical Society (APS)
Subjects:
Algorithms
Annealing
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Control theory
Ising model
Optimal control
Optimization
Optimization algorithms
Physics
ISSN:0031-9007, 1079-7114, 1079-7114
Online Access:Get full text
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Summary:Quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we analytically apply the framework of optimal control theory to show that generically, given a fixed amount of time, the optimal procedure has the pulsed (or "bang-bang") structure of QAOA at the beginning and end but can have a smooth annealing structure in between. This is in contrast to previous works which have suggested that bang-bang (i.e., QAOA) protocols are ideal. To support this theoretical work, we carry out simulations of various transverse field Ising models, demonstrating that bang-anneal-bang protocols are more common. The general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.
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SC0019139; SC0019449
National Institute of Standards and Technology (NIST)
USDOE Office of Science (SC)
ISSN:0031-9007
1079-7114
1079-7114
DOI:10.1103/PhysRevLett.126.070505