1 research outputs found
Quantum-Informed Recursive Optimization Algorithms
We propose and implement a family of quantum-informed recursive optimization
(QIRO) algorithms for combinatorial optimization problems. Our approach
leverages quantum resources to obtain information that is used in
problem-specific classical reduction steps that recursively simplify the
problem. These reduction steps address the limitations of the quantum component
and ensure solution feasibility in constrained optimization problems.
Additionally, we use backtracking techniques to further improve the performance
of the algorithm without increasing the requirements on the quantum hardware.
We demonstrate the capabilities of our approach by informing QIRO with
correlations from classical simulations of shallow (depth ) circuits of
the quantum approximate optimization algorithm (QAOA), solving instances of
maximum independent set and maximum satisfiability problems with hundreds of
variables. We also demonstrate how QIRO can be deployed on a neutral atom
quantum processor available online on Amazon Braket to find large independent
sets of graphs. In summary, our scheme achieves results comparable to classical
heuristics, such as simulated annealing and greedy algorithms, even with
relatively weak quantum resources. Furthermore, enhancing the quality of these
quantum resources improves the performance of the algorithms, highlighting the
potential of QIRO. Notably, the modular nature of QIRO offers various avenues
for modifications, positioning our work as a blueprint for designing a broader
class of hybrid quantum-classical algorithms for combinatorial optimization.Comment: 17 pages, 10 figures. Revised Figs. 1 and