Representation of Classical Data on Quantum Computers

TL;DR

This paper addresses the challenge of representing classical data on gate-based quantum computers across diverse data modalities. It surveys and categorizes encoding schemes, including angle and amplitude encodings for vectors, quantum image representations (FRQI, NEQR, BRQI, QPIXL), qutrit-based approaches, QDCT/MPS non-standard methods, time-series encodings, and graph/state representations. Key contributions include a comprehensive catalog of methods, discussion of qubit counts and retrieval properties, and practical notes on state preparation and measurement. The work highlights the potential for exponential memory advantages offered by quantum representations and underscores the need to tailor data encodings to specific quantum algorithms and applications.

Abstract

Quantum computing is currently gaining significant attention, not only from the academic community but also from industry, due to its potential applications across several fields for addressing complex problems. For any practical problem which may be tackled using quantum computing, it is imperative to represent the data used onto a quantum computing system. Depending on the application, many different types of data and data structures occur, including regular numbers, higher-dimensional data structures, e.g., n-dimensional images, up to graphs. This report aims to provide an overview of existing methods for representing these data types on gate-based quantum computers.

Figures (2)

• Figure 1: Illustrative 2-by-2 image to be encoded on a quantum device.
• Figure 2: Quantum circuit for encoding a time series toy example.