Journal Article

FZJ-2023-05387

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Mean-Field Approximate Optimization Algorithm

Misra-Spieldenner, A.FZJ* ; Bode, T. (Corresponding author)FZJ* ; Schuhmacher, P. K. ; Stollenwerk, T.FZJ* ; Bagrets, D.FZJ* ; Wilhelm-Mauch, F.FZJ*

2023
American Physical Society College Park, MD

This record in other databases:    

Please use a persistent id in citations: doi:10.1103/PRXQuantum.4.030335  doi:10.34734/FZJ-2023-05387

Abstract: The quantum approximate optimization algorithm (QAOA) is suggested as a promising application on early quantum computers. Here a quantum-inspired classical algorithm, the mean-field approximate optimization algorithm (mean-field AOA), is developed by replacement of the quantum evolution of the QAOA with classical spin dynamics through the mean-field approximation. Because of the alternating structure of the QAOA, this classical dynamics can be found exactly for any number of QAOA layers. We benchmark its performance against the QAOA on the Sherrington-Kirkpatrick model and the partition problem, and find that the mean-field AOA outperforms the QAOA in both cases for most instances. Our algorithm can thus serve as a tool to delineate optimization problems that can be solved classically from those that cannot, i.e., we believe that it will help to identify instances where a true quantum advantage can be expected from the QAOA. To quantify quantum fluctuations around the mean-field trajectories, we solve an effective scattering problem in time, which is characterized by a spectrum of time-dependent Lyapunov exponents. These provide an indicator for the hardness of a given optimization problem relative to the mean-field AOA.

---

Contributing Institute(s):

1. Quantum Computing Analytics (PGI-12)

Research Program(s):

1. 5223 - Quantum-Computer Control Systems and Cryoelectronics (POF4-522) (POF4-522)
2. Verbundprojekt: Digital-Analoge Quantencomputer (DAQC) - Teilvorhaben: DAQC Kontrolle, Kalibrierung und Charakterisierung (13N15688) (13N15688)
3. Verbundprojekt, Quantum Artificial Intelligence for the Automotive Industry (Q(AI)2) - Teilvorhaben: Implementierung, Benchmarking, und Management (13N15584) (13N15584)

Appears in the scientific report 2023

---

Database coverage:
; ; ; ; Article Processing Charges ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; DOAJ Seal ; Essential Science Indicators ; Fees ; IF >= 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

---