Quantum Benchmarking (QB): Analysis of Matrices

This work is supplemental material for the white paper ``Feasibility of accelerating incompressible computational fluid dynamics simulations with fault-tolerant quantum computers'' (https://arxiv.org/abs/2406.06323). This includes Python analysis of $F$-matrices (collision matrices) of lattice Boltzmann method (LBM) and the Carleman-linearized $A$-matrix.

In example_A_norm.ipynb we establish an upper bound on the spectral norm of the $A$-matrix. This should be run first to save various matrices in .npz format.

In example_A_norm.py the actual spectral norm for a very small $A$-matrix is calculated. You can view the results in example_A_norm.results.txt instead of actually running the script. This was split out into a separate script because it tends to crash a default-sized Jupyter kernel.

May/June 2025 updates:

1. The lattice velocity vector table used was updated to reflect Tabl 15
2. The bounding_A_norm.ipynb was rearranged and some matrix plots were added, but the results are the same.
3. Added time_domain_convergence.ipynb to estimate the physical evolution time $T$ that the truncated Carleman linearized system accurately evolve to.

$F_1$ matrix:

$F_2$ matrix:

$F_3$ matrix: