Efficient and Fail-Safe Collisionless Quantum Boltzmann Method

Blaga N. Todorova, R. Steijl

Blaga N. Todorova, R. Steijl

Soichiro Yamazaki, Fumio Uchida, Kotaro Fujisawa +2 more

The collisionless Boltzmann equation (CBE) is a fundamental equation that governs the dynamics of a broad range of astrophysical systems from space plasma to star clusters and galaxies. It is computationally expensive to integrate the CBE directly in a multi-dimensional phase space, and thus the applications to realistic astrophysical problems have been limited so far. Recently, Todorova & Steijl (2020) proposed an efficient quantum algorithm to solve the CBE with significantly reduced computational complexity. We extend the algorithm to perform quantum simulations of self-gravitating systems, incorporating the method to calculate gravity with the major Fourier modes of the density distribution extracted from the solution-encoding quantum state. Our method improves the dependency of time and space complexities on N v , the number of grid points in each velocity coordinate, compared to the classical simulation methods. We then conduct some numerical demonstrations of our method. We first run a 1+1 dimensional test calculation of free streaming motion on 64 × 64 grids using 13 simulated qubits and validate our method. We then perform simulations of Jeans collapse, and compare the result with analytic and linear theory calculations. It will thus allow us to perform large-scale CBE simulations on future quantum computers. • We propose a quantum algorithm for solving Boltzmann equation. • Reservoir method is improved to be able to simulate variable force field systems. • Quantum Fourier transform and tomography enables efficient information extraction. • Test calculations assuming noiseless 13 qubits have been conducted.

Aaron Nagel, Leo Basov

The simulation of gas flows for reentry problems can require to resolve a larger range of spatial scales in order to accurately model the physics of the flow field. In hypersonic flows, the modeling additionally requires to cover a large range in the velocity subspace of the phase space. Scale resolving methods like the Direct Simulation Monte Carlo (DSMC) method have been developed but can become computationally very expensive and unfeasible. Therefore, approximation methods allowing coarser grids are used which, however, may not be sufficiently accurate. To enable more efficient simulation methods, first approaches of a quantum lattice-gas model have been developed but these model do not scale efficiently with the grid resolution. Building on these quantum algorithms, promising modeling approaches using a quantum lattice Boltzmann method (QLBM) with amplitude encoding have shown to efficiently deal with very large grids and fine discretizations. Fine resolution of position and velocity space in the context of lattice Boltzmann methods (LBM) translate to many grid cells and a large set of velocity vectors in the LBM velocity discretization stencil, which can be encoded to scale efficiently in a qubit representation using the QLBM. For the investigation of collisionless flows a method based on Todorova et al. has been adopted and extended (cf. Fig. 1) to build upon our previous publication. The streaming and boundary interaction are modeled as two independent modular blocks, where the streaming block is adapted to be performed independently of the boundary. Additionally, our quantum algorithm includes the summation of the velocity distribution functions to calculate the mass density distribution directly in the quantum simulation. In contrast to a summation by classical post processing, the quantum summation block enables further development to extract reduced data from the quantum computer. This is a key point to not having to extract the entire high dimensional quantum state vector. In this study, a hypersonic collisionless flow around a flat plate with specular reflection is simulated using a quantum lattice Boltzmann method and compared with results using the established DSMC method for modeling rarefied flows. The quantum simulation is performed using a quantum algorithm simulator. Further approaches on how to extend the specular reflection model to a diffusive reflecting model are sketched out.

Sauro Succi A

Higuchi Hayato, Juan W. Pedersen, Akimasa Yoshikawa