An access model for quantum encoded data

TL;DR

This paper introduces a new quantum data access model based on approximate sampling and querying, demonstrating its compositionality and computational power, with applications to distributed inner product estimation and quantum circuit analysis.

Contribution

It proposes a novel quantum data access model applicable to various contexts and shows how it improves sample and computational complexity for specific tasks.

Findings

Polynomial improvements in distributed inner product estimation

New interpretation of Pauli sampling's usefulness

Partial characterization of time-limited fault-tolerant quantum circuits

Abstract

We introduce and investigate a data access model (approximate sample and query) that is satisfiable by the preparation and measurement of block encoded states, as well as in contexts such as classical quantum circuit simulation or Pauli sampling. We illustrate that this abstraction is compositional and has some computational power. We then apply these results to obtain polynomial improvements over the state of the art in the sample and computational complexity of distributed inner product estimation. By doing so, we provide a new interpretation for why Pauli sampling is useful for this task. Our results partially characterize the power of time-limited fault-tolerant quantum circuits aided by classical computation. They are a first step towards extending the classical data Quantum Singular Value Transform dequantization results to a quantum setting.