Block-encoding structured matrices for data input in quantum computing

Understand

The cost of data input can dominate the run-time of quantum algorithms.

• Here, we consider data input of arithmetically structured matrices via block encoding circuits, the input model for the quantum singular value transform and related algorithms.
• We demonstrate how to construct block encoding circuits based on an arithmetic description of the sparsity and pattern of repeated values of a matrix.
• We present schemes yielding different subnormalisations of the block encoding; a comparison shows that the best choice depends on the specific matrix.