基于旋转碰撞的量子格子玻尔兹曼方法
Rotation Collision based Quantum Lattice Boltzmann Methods
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中文总结 AI 辅助
针对量子格子玻尔兹曼方法中BGK碰撞算子的幺正性问题，提出基于旋转碰撞算子的新方法，用幺正旋转替代非幺正松弛，并构造门级电路，通过数值实验验证了其准确性和有效性。
中文摘要 AI 辅助
在现有的格子玻尔兹曼方法量子算法中，从第一性原理解决BGK碰撞算子的幺正性问题仍然是一个基本挑战，并且在文献中尚未建立一种系统构造的、能够在领头阶重现BGK松弛结构的幺正替代方案。在本工作中，我们提出了一种基于旋转碰撞算子的新型量子格子玻尔兹曼方法（QLBM），其中非幺正的BGK松弛被替换为分布函数振幅空间中的幺正旋转，并相应地构造了门级量子电路。具体而言，旋转碰撞算子分别针对对流-扩散方程的D2Q5模型和不可压缩Navier-Stokes方程的D2Q9模型进行了开发。值得注意的是，对于D2Q5模型，平衡态制备电路可以被预编译并重用，并且一旦指定了依赖于状态的碰撞参数，所得到的幺正块可以顺序组合。最后，进行了一些数值实验来验证所开发的QLBM，证明了其准确性和有效性。
英文摘要
In the existing quantum algorithms for the lattice Boltzmann method, resolving the unitarity problem of the BGK collision operator from first principles remains a fundamental challenge, and a systematically constructed unitary alternative that reproduces the BGK relaxation structure to leading order has not yet been established in the literature. In this work, we propose a novel quantum lattice Boltzmann method (QLBM) based on the rotation collision operator, in which the non-unitary BGK relaxation is replaced by a unitary rotation in the amplitude space of the distribution function, and the corresponding gate-level quantum circuits are also constructed. Specifically, the rotation collision operator is developed for both the D2Q5 model of the convection-diffusion equation and the D2Q9 model of the incompressible Navier--Stokes equations. It is worth noting that, for the D2Q5 model, the equilibrium-state preparation circuit can be precompiled and reused, and the resulting unitary blocks can be sequentially composed once the state-dependent collision parameters are specified. Finally, some numerical experiments are performed to validate the developed QLBM, demonstrating its accuracy and effectiveness.
发表机构
- School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院）
- College of Engineering, Shantou University（汕头大学工学院）
- Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology（华中科技大学数学与应用科学交叉研究院）
- Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology（华中科技大学工程建模与科学计算湖北省重点实验室）
- The State Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology（华中科技大学智能装备制造与技术国家重点实验室）
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