  L-QLES is an open source python code for generating 1D, 2D and 3D Laplacian
operators and associated Poisson equations and their classical solutions. Its
goal is to provide quantum algorithm developers with a flexible test case
framework where features of industrial applications can be incorporated without
the need for end-user domain knowledge or reliance on inflexible one-off
industry supplied matrix sets. A sample set of 1, 2, and 3 dimensional
Laplacians are suggested and used to compare the performance of the
Prepare-Select and FABLE block encoding techniques. Results show that large
matrices are not needed to investigate industrial characteristics. A matrix
with a condition number of 17,000 can be encoded using 13 qubits. L-QLES has
also been produced to enable algorithm developers to investigate and optimise
both the classical and quantum aspects of the inevitable hybrid nature of
quantum linear equation solvers. Prepare-Select encoding that takes over an
hour of classical preprocessing time to decompose a 4,096x4,096 matrix into
Pauli strings can be can investigated using L-QLES matrices. Similarly,
row-column query oracles that have success probabilities $\le 10^{-7}$ for the
same matrix can be investigated.
