Inductive Construction of Variational Quantum Circuit for Constrained Combinatorial Optimization

TL;DR

This paper introduces an inductive method for constructing variational quantum circuits capable of solving constrained combinatorial optimization problems, expanding the range of constraints that can be efficiently handled.

Contribution

It proposes a novel inductive circuit construction technique that manages complex constraints in variational quantum algorithms for optimization.

Findings

Increased probability of measuring feasible or optimal solutions.

Circuit complexity comparable to conventional variational circuits.

Effective application to facility location problem.

Abstract

In this study, we propose a new method for constrained combinatorial optimization using variational quantum circuits. Quantum computers are considered to have the potential to solve large combinatorial optimization problems faster than classical computers. Variational quantum algorithms, such as Variational Quantum Eigensolver (VQE), have been studied extensively because they are expected to work on noisy intermediate scale devices. Unfortunately, many optimization problems have constraints, which induces infeasible solutions during VQE process. Recently, several methods for efficiently solving constrained combinatorial optimization problems have been proposed by designing a quantum circuit so as to output only the states that satisfy the constraints. However, the types of available constraints are still limited. Therefore, we have started to develop variational quantum circuits that can handle a wider range of constraints. The proposed method utilizes a forwarding operation that maps from feasible states for subproblems to those for larger subproblems. As long as appropriate forwarding operations can be defined, iteration of this process can inductively construct variational circuits outputting feasible states even in the case of multiple and complex constraints. In this paper, the proposed method was applied to facility location problem and was found to increase the probability for measuring feasible solutions or optimal solutions. In addition, the cost of the obtained circuit was comparable to that of conventional variational circuits.