A Study on Variational Quantum Algorithms for Constrained Combinatorial Optimization

Abstract

Combinatorial optimization has many real-world applications. As the amount of data circulation increases due to technology development, high-performance computers for larger-scale combinatorial optimizations are required. Currently, quantum computers are attracting attention as the solvers for such problems. Especially, variational quantum algorithms (VQA) are expected to work on noisy intermediate-scale quantum devices. In VQA, quantum circuits to sample combinatorial solutions are obtained by learning their variational parameters. However, in constrained optimization problems, there is a possibility that infeasible solutions appear because VQA is likely to fail to learn the proper parameters. In this report, we propose a new architecture for circuit models to enhance the learning ability. The circuit consists of three layers: initializing-layer to encode the approximate solutions, learning-constraint-layer to search for the feasible ones, and minimizing-objective-layer for the global ones. We carried out Qiskit simulations and found that proposed method showed high possibilities to sample feasible and global solutions.