基于密度矩阵编码的量子格子玻尔兹曼方法用于带壁面边界条件的流体模拟

中文摘要 AI 辅助

量子格子玻尔兹曼方法（QLBM）有望实现高效的流体模拟，然而对现实边界条件的处理，特别是具有任意几何形状的固体壁面边界，仍然是一个关键且悬而未决的挑战。我们提出了一种QLBM算法，该算法纳入了壁面边界以及入口/出口速度条件。在现有的采用系综变换的QLBM基础上，我们采用了密度矩阵编码，这种编码在电路设计上提供了更大的灵活性，并能够通过Kraus算子实现非酉操作。对于边界强制执行，我们设计了半步反弹格式的量子实现，并在流步之前引入了一个组分交换步骤，该步骤在不修改输运操作的情况下自然地强制执行无滑移条件。入口和出口条件通过受控SWAP操作结合预先制备在指定速度态的辅助寄存器来实现。我们的QLBM通过对经过后向台阶、圆柱体和具有复杂几何形状的障碍物的二维流动进行模拟，得到了定量验证，证明了我们边界算法的准确性和可扩展性。

英文摘要

The quantum lattice Boltzmann method (QLBM) holds promise for efficient fluid simulations, yet the treatment of realistic boundary conditions, particularly solid wall boundary with arbitrary geometry, remains a critical open challenge. We propose a QLBM algorithm that incorporates wall boundaries as well as inlet/outlet velocity conditions. Building upon the existing QLBM with ensemble transformations, we adopt a density-matrix encoding that offers greater flexibility in circuit design and enables the implementation of non-unitary operations through Kraus operators. For boundary enforcement, we design a quantum implementation of the half-way bounce-back scheme and introduce a component exchange step prior to the streaming step, which naturally enforces the no-slip condition without modifying the transport operation. Inlet and outlet conditions are imposed via controlled SWAP operations combined with ancilla registers prepared in the prescribed velocity states. Our QLBM is quantitatively validated through simulations of two-dimensional flows past a backward-facing step, a cylinder, and an obstacle with complex geometry, demonstrating both accuracy and extensibility of our boundary algorithm.

发表机构

• State Key Laboratory for Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University（北京大学力学与工程科学学院湍流与复杂系统国家重点实验室）
• HEDPS-CAPT, Peking University（北京大学高能量密度物理研究中心）

机构由 AI 辅助整理，请以论文原文为准。