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arXiv · 2502.02245

Qubit-efficient quantum local search for combinatorial optimization

M. Podobrii·V. Kuzmin·V. Voloshinov·M. Veshchezerova·M. R. Perelshtein
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Abstract

An essential component of many sophisticated metaheuristics for solving combinatorial optimization problems is some variation of a local search routine that iteratively searches for a better solution within a chosen set of immediate neighbors. The size $l$ of this set is limited due to the computational costs required to run the method on classical processing units. We present a qubit-efficient variational quantum algorithm that implements a quantum version of local search with only $\lceil \log_2 l \rceil$ qubits and, therefore, can potentially work with classically intractable neighborhood sizes when realized on near-term quantum computers. Increasing the amount of quantum resources employed in the algorithm allows for a larger neighborhood size, improving the quality of obtained solutions. This trade-off is crucial for present and near-term quantum devices characterized by a limited number of logical qubits. Numerically simulating our algorithm, we successfully solved the largest graph coloring instance that was tackled by a quantum method. This achievement highlights the algorithm's potential for solving large-scale combinatorial optimization problems on near-term quantum devices.

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M. Podobrii, V. Kuzmin, V. Voloshinov, M. Veshchezerova, M. R. Perelshtein. 2025-02-04. Qubit-efficient quantum local search for combinatorial optimization. https://arxiv.org/abs/2502.02245

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