Extension of a quantum lattice Boltzmann method to multiple time steps without reinitialization

Kurzfassung

The computational power to resolve large complex aerospace flow problems has increased over the past decades but is still yet not able to simulate these problems sufficiently accurate to a scale resolved level. At the same time, the interest in quantum computing has recently increased rapidly due to the massive improvements of the quantum computer hardware technology. Many fields of research explore the possible advantages that quantum computing can offer in their respective fields. For fluid flow problems, the exponentially increasing storage capacity of flow properties by quantum amplitude encoding offers an approach to efficiently deal with highly resolved flow fields. Within the DLR-QCI project ToQuaFlics, we adjust and extend the quantum lattice Boltzmann method (QLBM) from the literature for single time steps and present our extension to multiple time steps. The structure of our algorithm is shown in Fig. 1. Our extended QLBM can perform all time steps of a simulation without having to extract the quantum state or parts of it at any time. Therefore, with our algorithm there is no need to measure any qubit during or at the end of the simulation. This saves the computationally expensive read out and reinitialization after every time step and enables an efficient time stepping scheme. We verify our algorithm on 1D and 2D test cases simulating a linear advection-diffusion process with periodic boundary conditions. The algorithm is simulated using the IBM simulator package Qiskit with the shot method. For verification reasons, we measure the entire flow field at the end of the simulation to demonstrate the agreement with the reference solution given by the classic lattice Boltzmann solution. The results show excellent agreement and arbitrary convergence towards the reference. We further discuss the inherent amplitude decay of a QLBM time step and how that effects our solution in terms of signal loss of the quantum state. An outlook to include a body with a surface interaction model and to capture nonlinearities is given and briefly sketched.