论文标题
一种基于高斯 - 纽顿的量子算法，用于组合优化
A Gauss-Newton based Quantum Algorithm for Combinatorial Optimization
论文作者
论文摘要
在这项工作中，我们提出了一种基于高斯 - 纽顿的量子算法（GNQA），用于组合优化问题，在最佳条件下，该问题在最佳条件下迅速收敛到其中一种最佳解决方案，而不会被困在局部最小值或高原中。量子优化算法已经探讨了数十年，但是最近的研究是关于各种量子算法的研究，这些算法通常遭受上述问题的困扰。我们的方法通过采用张量产品状态来缓解那些能够准确代表最佳解决方案的张量产品状态，并为哈密顿量提供了适当的函数，其中包含二进制变量的所有组合。这里提出的数值实验证明了我们方法的有效性，它们表明，对于此处考虑的所有问题，GNQA在收敛属性和准确性中都优于其他优化方法。最后，我们简要讨论方法对其他问题的潜在影响，包括量子化学和高阶二元优化的问题。
In this work, we present a Gauss-Newton based quantum algorithm (GNQA) for combinatorial optimization problems that, under optimal conditions, rapidly converges towards one of the optimal solutions without being trapped in local minima or plateaus. Quantum optimization algorithms have been explored for decades, but more recent investigations have been on variational quantum algorithms, which often suffer from the aforementioned problems. Our approach mitigates those by employing a tensor product state that accurately represents the optimal solution, and an appropriate function for the Hamiltonian, containing all the combinations of binary variables. Numerical experiments presented here demonstrate the effectiveness of our approach, and they show that GNQA outperforms other optimization methods in both convergence properties and accuracy for all problems considered here. Finally, we briefly discuss the potential impact of the approach to other problems, including those in quantum chemistry and higher order binary optimization.
