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This study demonstrates that the Feedback-Based Algorithm for Quantum Optimization (FALQON) combined with an XY mixer outperforms conventional X-mixer approaches in solving small-scale graph coloring problems. By leveraging iterative measurement feedback to bypass variational parameter optimization, this method offers a more efficient pathway for addressing constrained combinatorial optimization tasks on quantum hardware.
Solving Graph Coloring Problems Using Feedback-Based Algorithm for Quantum Optimization
arXiv:2609.30991v1 Announce Type: new Abstract: The feedback-based algorithm for quantum optimization (FALQON), which is an extension of the quantum approximate optimization algorithm (QAOA), is a promising approach for finding approximate solutions to combinatorial optimization problems. The FALQON avoids the optimization of variational parameters by using information derived from iterative measurements. To solve a constrained combinatorial optimization problem, it is sometimes more efficient to use an XY mixer rather than the conventional X mixer. We applied the FALQON with the XY mixer to graph coloring and investigated the expectation value of the problem Hamiltonian, success probability of graph coloring, and fair sampling for several small-scale problems. The FALQON with the XY mixer exhibited better performance than that with the X mixer.
Abstract:The feedback-based algorithm for quantum optimization (FALQON), which is an extension of the quantum approximate optimization algorithm (QAOA), is a promising approach for finding approximate solutions to combinatorial optimization problems. The FALQON avoids the optimization of variational parameters by using information derived from iterative measurements. To solve a constrained combinatorial optimization problem, it is sometimes more efficient to use an XY mixer rather than the conventional X mixer. We applied the FALQON with the XY mixer to graph coloring and investigated the expectation value of the problem Hamiltonian, success probability of graph coloring, and fair sampling for several small-scale problems. The FALQON with the XY mixer exhibited better performance than that with the X mixer.
arXiv:2609.30991 [quant-ph]
(or arXiv:2609.30991v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.30991 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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