Quantum data encoding as a distinct abstraction layer in the design of quantum circuits

TL;DR

This paper introduces a formal framework for quantum data encoding as a separate abstraction layer in quantum circuit design, clarifying complex circuit structures and aiding efficient development.

Contribution

It systematically formalizes quantum data encoding, surveys existing methods, and demonstrates its application to quantum algorithms and simulations.

Findings

Quantum Fourier Transform as encoding converter

Quantum Amplitude Estimation as information extraction

Application to quantum Monte Carlo simulations

Abstract

Complex quantum circuits are constituted by combinations of quantum subroutines. The computation is possible as long as the quantum data encoding is consistent throughout the circuit. Despite its fundamental importance, the formalization of quantum data encoding has never been addressed systematically so far. We formalize the concept of quantum data encoding, namely the format providing a representation of a data set through a quantum state, as a distinct abstract layer with respect to the associated data loading circuit. We survey existing encoding methods and their respective strategies for classical-to-quantum exact and approximate data loading, for the quantum-to-classical extraction of information from states, and for quantum-to-quantum encoding conversion. Next, we show how major quantum algorithms find a natural interpretation in terms of data loading. For instance, the Quantum Fourier Transform is described as a quantum encoding converter, while the Quantum Amplitude Estimation as an extraction routine. The new conceptual framework is exemplified by considering its application to quantum-based Monte Carlo simulations, thus showcasing the power of the proposed formalism for the description of complex quantum circuits. Indeed, the approach clarifies the structure of complex quantum circuits and enables their efficient design.