2024/05/14 by Dinesh Kumar E, Kumar, E. Dinesh, Steven H. Frankel +1 · 2 citations
Engineering · #FOS: Physical sciences #Lattice Boltzmann Simulation Studies #Quantum Physics (quant-ph) #Smart Grid Energy Management
paper · pdf · doi:10.48550/arxiv.2405.08669
openalex publication_date 2024/05/14 · openalex created_date 2024/05/16 · openalex updated_date 2026/07/28
We propose a quantum algorithm for the Lattice Boltzmann (LB) method to simulate fluid flows in the low Reynolds number regime. First, we encode the particle distribution functions (PDFs) as probability amplitudes of the quantum state and demonstrate the need to control the state of the ancilla qubit during the initial state preparation. Second, we express the LB algorithm as a matrix-vector product by neglecting the quadratic non-linearity in the equilibrium distribution function, wherein the vector represents the PDFs, and the matrix represents the collision and streaming operators. Third, we employ classical singular value decomposition (SVD) to decompose the non-unitary collision and streaming operators into a product of unitary matrices. Finally, we show the importance of having a Hadamard gate between the collision and the streaming operations. Our approach has been tested on linear/linearized flow problems such as the advection-diffusion of a Gaussian hill, Poiseuille flow, Couette flow, and lid-driven cavity problems. We provide counts for two-qubit controlled-NOT (CNOT) and single-qubit U gates for test cases involving 9 to 12 qubits, with grid sizes ranging from 24 to 216 points. While the gate count aligns closely with theoretical limits, the high number of two-qubit gates on the order of 107 necessitates careful attention to circuit synthesis.