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The Quantum Alternating Operator Ansatz for Satisfiability Problems

Conference · · 2023 IEEE International Conference on Quantum Computing and Engineering (QCE)
 [1];  [1];  [1];  [1]
  1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
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Here, we comparatively study, through large-scale numerical simulation, the performance across a large set of Quantum Alternating Operator Ansatz (QAOA) implementations for finding approximate and optimum solutions to unconstrained combinatorial optimization problems. Our survey includes over 100 different mixing unitaries, and we combine each mixer with both the standard phase separator unitary representing the objective function and a thresholded version. Our numerical tests for randomly chosen instances of the unconstrained optimization problems Max 2-SAT and Max 3-SAT reveal that the traditional transverse-field mixer with the standard phase separator performs best for problem sizes of 8 through 14 variables, while the recently introduced Grover mixer with thresholding wins at problems of size 6. This result (i) corrects earlier work suggesting that the Grover mixer is a superior mixer based only on results from problems of size 6, thus illustrating the need to push numerical simulation to larger problem sizes to more accurately predict performance; and (ii) it suggests that more complicated mixers and phase separators may not improve QAOA performance.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
DOE Contract Number:
89233218CNA000001
OSTI ID:
2310334
Report Number(s):
LA-UR-23-20702
Journal Information:
2023 IEEE International Conference on Quantum Computing and Engineering (QCE), Conference: 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), Bellevue, WA (United States), 17-22 Sep 2023; Related Information: https://ieeexplore.ieee.org/xpl/conhome/10313590/proceeding
Country of Publication:
United States
Language:
English

References (11)

Reachability Deficits in Quantum Approximate Optimization journal March 2020
Phase Transitions and Backbones of 3-SAT and Maximum 3-SAT book January 2001
Counterdiabaticity and the quantum approximate optimization algorithm journal January 2022
Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation conference October 2020
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz journal February 2019
Threshold-Based Quantum Optimization conference October 2021
The Quantum Alternating Operator Ansatz on Maximum k-Vertex Cover conference October 2020
Bridging Classical and Quantum with SDP initialized warm-starts for QAOA preprint January 2020
Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm journal May 2022
Warm-starting quantum optimization journal June 2021
Bridging Classical and Quantum with SDP initialized warm-starts for QAOA journal February 2023

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