标题： 约束组合优化的变分量子电路的归纳构造 显示英文标题

标题： Inductive Construction of Variational Quantum Circuit for Constrained Combinatorial Optimization

摘要： 在本研究中，我们提出了一种使用变分量子电路的约束组合优化新方法。量子计算机被认为比经典计算机更有潜力更快地解决大规模组合优化问题。变分量子算法，如变分量子本征求解器（VQE），由于预计可以在噪声中等规模设备上运行而受到广泛研究。不幸的是，许多优化问题都有约束条件，这会导致VQE过程中产生不可行的解。最近，通过设计仅输出满足约束条件状态的量子电路，已经提出了几种高效解决约束组合优化问题的方法。然而，可用的约束类型仍然有限。因此，我们开始开发能够处理更广泛约束的变分量子电路。所提出的方法利用了一种前向操作，该操作将子问题的可行状态映射到更大子问题的可行状态。只要可以定义适当的前向操作，该过程的迭代可以归纳地构建出即使在多个和复杂约束情况下也能输出可行状态的变分电路。在本文中，所提出的方法被应用于设施定位问题，并发现可以提高测量可行解或最优解的概率。此外，所得电路的成本与传统变分电路相当。 显示英文摘要

摘要： 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.