TY  - JOUR
AU  - Misra-Spieldenner, Aditi
AU  - Bode, Tim
AU  - Schuhmacher, Peter K.
AU  - Stollenwerk, Tobias
AU  - Bagrets, Dmitry
AU  - Wilhelm-Mauch, Frank
TI  - Mean-Field Approximate Optimization Algorithm
JO  - PRX quantum
VL  - 4
IS  - 3
SN  - 2691-3399
CY  - College Park, MD
PB  - American Physical Society
M1  - FZJ-2023-05387
SP  - 030335
PY  - 2023
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001123002800001
DO  - DOI:10.1103/PRXQuantum.4.030335
UR  - https://juser.fz-juelich.de/record/1019430
ER  -