Bulletin of the American Physical Society
APS March Meeting 2024
Monday–Friday, March 4–8, 2024; Minneapolis & Virtual
Session PP01: V: Quantum Annealing and Quantum Foundations
11:30 AM–1:30 PM,
Thursday, March 7, 2024
Room: Virtual Room 01
Sponsoring
Unit:
DQI
Chair: Jonte Hance, Newcastle University; Ilon Joseph, Lawrence Livermore Natl Lab
Abstract: PP01.00002 : Mean-field Approximate Optimization Algorithm for Max-q-XORSAT problems on d-regular graphs
11:42 AM–11:54 AM
Presenter:
Aditi Misra-Spieldenner
(Universität des Saarlandes)
Authors:
Aditi Misra-Spieldenner
(Universität des Saarlandes)
Dmitry Bagrets
(Forschungszentrum Jülich, PGI-12)
Frank K Wilhelm-Mauch
(Universität des Saarlandes, Forschungszentrum Jülich, PGI-12)
In our previous work on the Mean-Field Approximate Optimization Algorithm (MFAOA) we benchmarked it against the QAOA and we saw that it outperforms the QAOA for the Sherrington-Kirkpatrick (SK) model and the number partitioning problem where the underlying graphs are complete. In this work, we have extended our new algorithm for d-regular and q-uniform hypergraphs which represent the Max-q-XORSAT problems for d= 2.
Mean-Field Approximate Optimization Algorithm (MFAOA) can be thought of as the semi-classical counterpart of the quantum annealing. We analyzed the Gaussian quantum fluctuations around mean-field spin trajectories corresponding to the classical path and came up with a spectrum of time-dependent positive Lyapunov exponents. Analysis of the local maxima of the largest Lyapunov exponent enables one to identify the critical point of the ergodic to many-body localization phase transition in the presence of a transverse magnetic field as we have verified it from the level-spacing statistics. By processing the largest Lyapunov exponent over time we came up with a novel population annealing based recursive version of the MFAOA which runs in polynomial time $O(N4p)$ and improves the results significantly.
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