Beijing Academy of Quantum Information Sciences, Beijing 100193, China.
Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
Sci Bull (Beijing). 2023 Mar 15;68(5):494-502. doi: 10.1016/j.scib.2023.02.016. Epub 2023 Feb 16.
Heat conduction, driven by thermal non-equilibrium, is the transfer of internal thermal energy through physical contacts, and it exists widely in various engineering problems, such as spacecraft and state-of-the-art dilution refrigerators. The mathematical equation for heat conduction is a prototypical partial differential equation. Here we report a quantum algorithm for heat conduction (QHC) that significantly outperforms classical algorithms. We represent the original heat conduction system by a symmetric system with an ancilla qubit so that the quantum circuit complexity is polylogarithmic in the number of discretized grid points. Compared with the existing algorithms based on solving linear equations via the Harrow-Hassidim-Lloyd (HHL) algorithm, our method evolves the linear process directly without phase estimation, which involves complex quantum operations and large output error. Therefore, this algorithm is experimental-friendly and without output error after the discretization procedure. We experimentally implemented the algorithm for a one-dimensional thermal conduction process with two-edge constant temperatures and adiabatic conditions on a nuclear spin quantum processor. The spatial and temporal distributions of the temperature are accurately determined from the experimental results. Our work can be naturally applied to any physical processes that can be reduced to the heat equation.
热传导是由热不平衡驱动的，通过物理接触传递内部热能，广泛存在于各种工程问题中，如航天器和最先进的稀释致冷机。热传导的数学方程是典型的偏微分方程。在这里，我们报告了一种量子热传导算法（QHC），它显著优于经典算法。我们通过引入辅助量子比特来表示原始的热传导系统，使得量子电路的复杂度对数级依赖于离散化网格点的数量。与现有的基于求解线性方程组的 Harrow-Hassidim-Lloyd（HHL）算法的算法相比，我们的方法直接演化线性过程，无需相位估计，这涉及复杂的量子操作和较大的输出误差。因此，这种算法实验友好，且在离散化后没有输出误差。我们在核自旋量子处理器上，通过实验实现了具有双边恒温和绝热条件的一维热传导过程的算法。从实验结果中准确地确定了温度的时空分布。我们的工作可以自然地应用于任何可以简化为热方程的物理过程。
