Efficient block-encodings require structure

Abstract

Block-encodings are ubiquitous in quantum computing as a way to represent data within a unitary operator. While several unstructured methods are applicable to arbitrary data, these techniques are burdened by hidden costs and poor accuracy. In this paper, we demonstrate that, even for a small 6-qubit encoding, these structure-agnostic techniques require wildly intractable resources. We compare these resources with an encoding method which respects a mathematical representation of the block, leading to the conclusion that unstructured encoding mehtods should only be used in the most extenuating circumstances. This finding runs contrary to existing literature on quantum algorithms which often employ structure-agnostic methods.