Dequantizability from inputs

TL;DR

This paper introduces a scheme to verify dequantizability of input models, especially sparse-access models, by leveraging recent dequantization techniques, challenging the notion that such models are inherently un-dequantizable.

Contribution

It proposes a method to extract dequantizability from existing constructions and applies it to the sparse-access input model, providing a new perspective on its potential dequantization.

Findings

Dequantizability can be verified using the proposed scheme.

Sparse-access input models may be dequantizable despite previous beliefs.

The scheme is applicable to various input matrices in quantum algorithms.

Abstract

By comparing constructions of block encoding given by [1-4], we propose a way to extract dequantizability from advancements in dequantization techniques that have been led by Tang, as in [5]. Then we apply this notion to the sparse-access input model that is known to be BQP-complete in general, thereby conceived to be un-dequantizable. Our goal is to break down this belief by examining the sparse-access input model's instances, particularly their input matrices. In conclusion, this paper forms a dequantizability-verifying scheme that can be applied whenever an input is given.