Entanglement perspective on the quantum approximate optimization algorithm

Dupont, Maxime; Didier, Nicolas; Hodson, Mark J.; Moore, Joel E.; Reagor, Matthew J.

doi:10.1103/PhysRevA.106.022423

Entanglement perspective on the quantum approximate optimization algorithm

Journal Article · 22 August 2022 · Phys.Rev.A

DOI:https://doi.org/10.1103/PhysRevA.106.022423· OSTI ID:1988467

Dupont, Maxime ^[1]; Didier, Nicolas ^[2]; Hodson, Mark J. ^[2]; Moore, Joel E. ^[3]; Reagor, Matthew J. ^[2]

UC, Berkeley; LBNL, Berkeley; Rigetti Computing
Rigetti Computing
UC, Berkeley; LBNL, Berkeley

Many quantum algorithms seek to output a specific bitstring solving the problem of interest—or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit depth, which aims to solve quadratic unconstrained binary optimization problems. Hence, the expected final state for these algorithms is either a product state or a low-entangled superposition involving a few bitstrings. What happens in between the initial $N$ -qubit product state ${| 0 〉}^{\otimes N}$ and the final one regarding entanglement? Here, we consider the QAOA algorithm for solving the paradigmatic MaxCut problem on different types of graphs. We study the entanglement growth and spread resulting from randomized and optimized QAOA circuits and find that there is a volume-law entanglement barrier between the initial and final states. We also investigate the entanglement spectrum in connection with random matrix theory. In addition, we compare the entanglement production with a quantum annealing protocol aiming to solve the same MaxCut problems. Finally, we discuss the implications of our results for the simulation of QAOA circuits with tensor network-based methods relying on low-entanglement for efficiency, such as matrix product states.

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Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

DOE Contract Number:: AC02-07CH11359

OSTI ID:: 1988467

Report Number(s):: FERMILAB-PUB-22-973-SQMS-V; arXiv:2206.07024; oai:inspirehep.net:2096195

Journal Information:: Phys.Rev.A, Vol. 106, Issue 2

Country of Publication:: United States

Language:: English

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