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DOE OSTI · 1852863

Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems

Brady, Lucas T.·Baldwin, Christopher L.·Bapat, Aniruddha·Kharkov, Yaroslav·Gorshkov, Alexey V.
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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. Futher, the general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS97 MATHEMATICS AND COMPUTINGPhysics

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Brady, Lucas T., Baldwin, Christopher L., Bapat, Aniruddha, Kharkov, Yaroslav, Gorshkov, Alexey V.. 2021-02-19. Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems. https://doi.org/10.1103/physrevlett.126.070505

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