Quantum algorithm for the advection–diffusion equation simulated with the lattice Boltzmann method

L. Budinski · 2021 · Quantum Information Processing 20, 57

| 编号 QC046 | 主题 量子格子玻尔兹曼 | 链接 10.1007/s11128-021-02996-3 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

A novel quantum algorithm for solving advection–diffusion equation by the lattice Boltzmann method is proposed. The presented quantum algorithm is composed of two major segments. In the first segment, equilibrium distribution function, presented in the form of a non-unitary diagonal matrix, is quantum circuit implemented by using a standard-form encoding approach. For the second segment, the quantum walk procedure as a method for implementing the propagation step is applied. The constructed algorithm is presented as a series of single- and two-qubit gates, as well as multiple-input controlled-NOT gates. In order to demonstrate the validity of the proposed quantum algorithm, the unsteady one-dimensional (1D) and two-dimensional (2D) advection–diffusion equations are solved by using the IBM’s quantum computing software development framework Qiskit, while the analytic solution and the classic code are used for verification. Finally, the complexity analysis and directions for future work are discussed.

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