Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems

Lucas T. Brady, Christopher L. Baldwin, Aniruddha Bapat, Yaroslav Kharkov, and Alexey V. Gorshkov
Phys. Rev. Lett. 126, 070505 – Published 19 February 2021
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Abstract

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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  • Received 22 March 2020
  • Revised 21 December 2020
  • Accepted 26 January 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.070505

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Lucas T. Brady1,2,*, Christopher L. Baldwin1,2, Aniruddha Bapat1,2, Yaroslav Kharkov1,2, and Alexey V. Gorshkov1,2

  • 1Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
  • 2Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA

  • *Lucas.Brady@nist.gov

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Issue

Vol. 126, Iss. 7 — 19 February 2021

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