论文标题
NISQ时代的高级量子泊松求解器
Advanced Quantum Poisson Solver in the NISQ era
论文作者
论文摘要
泊松方程在整个科学和工程领域都有许多应用。到目前为止，大多数用于泊松求解器的量子算法要么缺乏准确性和/或仅限于非常小的问题，因此没有实际用途。在这里，我们提出了一种高级量子算法，用于以高精度和动态可调的问题大小求解泊松方程。通过有限的差异方法将泊松方程转换为线性系统后，我们采用了harrow-hassidim-lloyd（HHL）算法作为基本框架。特别是，在这项工作中，我们提出了一个高级电路，该电路通过通过特征值放大以及提高受控旋转角系数的准确性来确保解决方案的准确性，这是HHL算法中的关键因素。我们表明，我们的算法不仅提高了解决方案的准确性，而且还通过动态控制NISQ设备中的问题大小来构成更实用和可扩展的电路。我们介绍了模拟和实验解决方案，并得出结论，量子硬件上的总体结果由CNOT门中的误差主导。
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental solutions, and conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.
