论文标题
组合通过变分量子功率法优化
Combinatorial optimization through variational quantum power method
论文作者
论文摘要
功率方法（或迭代）是一种众所周知的经典技术，可用于找到矩阵的主要特征台。在这里，我们提出了一种用于电源迭代的变异量子电路方法，该方法可用于查找单一矩阵的特征矩阵以及与其相关的汉密尔顿人。我们讨论了如何将电路应用于组合作为二次无约束二进制优化的组合优化问题并讨论其复杂性。此外，我们运行了最多21个参数的随机问题实例的数值模拟，并观察到该方法可以在仅少量迭代的优化问题上生成解决方案，并且迭代次数的增长是参数数量的多项式。因此，可以轻松地在近期量子计算机上模拟电路。
The power method (or iteration) is a well-known classical technique that can be used to find the dominant eigenpair of a matrix. Here, we present a variational quantum circuit method for the power iteration, which can be used to find the eigenpairs of unitary matrices and so their associated Hamiltonians. We discuss how to apply the circuit to combinatorial optimization problems formulated as a quadratic unconstrained binary optimization and discuss its complexity. In addition, we run numerical simulations for random problem instances with up to 21 parameters and observe that the method can generate solutions to the optimization problems with only a few number of iterations and the growth in the number of iterations is polynomial in the number of parameters. Therefore, the circuit can be simulated on the near term quantum computers with ease.
