Combinatorial Optimization with Few Qubits
Rudy Raymond
Abstract: The potential of quantum computing for Combinatorial Optimization (CO) is significant, but current quantum computers lack the necessary physical resources, particularly the number of qubits, to tackle problem instances on the same scale as classical computers. Various methods have been developed to scale problem instances that can be addressed with a limited number of qubits, showing promise. Here, we introduce a method for CO using few qubits, involving the application of Quantum Random Access Code (QRAC) for encoding variables into few qubits, Classical Shadow (CS) for decoding the variables efficiently, and Coordinate Descent (CD) for optimizing quantum circuits to generate desirable quantum states for CO instances. The effectiveness of the proposed method is demonstrated through experiments on parameterized quantum circuits for solving instances of NP-hard problems such as the minimum bisection.