Details

Autor(en) / Beteiligte

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

Titel

Entanglement perspective on the quantum approximate optimization algorithm

Ist Teil von

• Physical review. A, 2022-08, Vol.106 (2), Article 022423

Ort / Verlag

United States: American Physical Society (APS)

Erscheinungsjahr

2022

Link zum Volltext

Quelle

American Physical Society Journals

Beschreibungen/Notizen

• 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$\rangle$ⓍN and the final one regarding entanglement? Here, in this study, 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.