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Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems

Journal Article · · Physical Review Letters
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  1. Joint Center for Quantum Information and Computer Science, College Park, MD (United States); National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States); Univ. of Maryland, College Park, MD (United States); Joint Quantum Institute, College Park, MD (United States)

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. Futher, the general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.

Research Organization:
Univ. of Iowa, Iowa City, IA (United States); Duke Univ., Durham, NC (United States)
Sponsoring Organization:
USDOE Office of Science (SC); National Institute of Standards and Technology (NIST)
Grant/Contract Number:
SC0019139; SC0019449
OSTI ID:
1852863
Alternate ID(s):
OSTI ID: 2280947
Journal Information:
Physical Review Letters, Vol. 126, Issue 7; ISSN 0031-9007
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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