推广量子虚时演化以求解线性偏微分方程
Generalising quantum imaginary time evolution to solve linear partial differential equations
AI总结：
本文推广量子虚时演化方法，利用其跟踪状态向量规模的能力，提出一种求解线性偏微分方程的量子数值算法，并通过数值模拟成功求解一维和二维热方程。
摘要：
量子虚时演化（QITE）方法是为了克服在量子计算机上实现虚时演化时非酉性这一关键问题而提出的。QITE此后被用于近似各种物理系统的基态。在本文中，我们展示了QITE作为线性偏微分方程的量子数值求解器的实际应用。我们的算法灵感来源于QITE，两种算法中量子态遵循相同的归一化轨迹。然而，正是我们QITE方法能够随时间跟踪状态向量规模的能力，使得我们的算法能够求解微分方程。我们通过数值模拟展示了我们的方法，并使用六量子比特和十量子比特分别求解了一维和二维热方程。
英文摘要：
The quantum imaginary time evolution (QITE) methodology was developed to overcome a critical issue as regards non-unitarity in the implementation of imaginary time evolution on a quantum computer. QITE has since been used to approximate ground states of various physical systems. In this paper, we demonstrate a practical application of QITE as a quantum numerical solver for linear partial differential equations. Our algorithm takes inspiration from QITE in that the quantum state follows the same normalised trajectory in both algorithms. However, it is our QITE methodology's ability to track the scale of the state vector over time that allows our algorithm to solve differential equations. We demonstrate our methodology with numerical simulations and use it to solve the heat equation in one and two dimensions using six and ten qubits, respectively.
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