Qubit-efficient quantum local search for combinatorial optimization

TL;DR

This paper introduces a qubit-efficient quantum local search algorithm for combinatorial optimization that can handle larger neighborhoods with fewer qubits, showing promising results on graph coloring problems.

Contribution

The paper presents a novel variational quantum algorithm that uses logarithmic qubits for local search, enabling larger neighborhood exploration on near-term quantum devices.

Findings

Successfully solved large graph coloring instances with quantum methods.

Demonstrated the advantage of increasing quantum resources for better solutions.

Highlighted potential for large-scale combinatorial optimization on near-term quantum hardware.

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.