Efficient block encodings for computational-fluid-dynamics operators

Construct efficient block encodings for practically relevant computational-fluid-dynamics operators to enable implementation of the QSVT-based quantum Jacobi algorithm and integration into larger quantum CFD workflows.

Background

The proposed quantum Jacobi algorithm assumes access to a block encoding of the iteration matrix. Although the paper demonstrates the algorithm using generic block encodings and analyzes its resource requirements in terms of block-encoding queries, it does not provide concrete, efficient constructions for the practically relevant sparse operators arising in computational fluid dynamics.

Efficient block encodings are therefore a prerequisite for realizing the algorithm on early fault-tolerant quantum computers and for incorporating it into broader CFD workflows. The unresolved issue concerns how to construct such encodings with favorable implementation costs for realistic discretized differential operators, rather than merely assuming their availability.