Representing Data on a Quantum Computer

Thomas Lang, Anja Heim, Kilian Dremel +6 more

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.

Varun Puram, K. M. George, Johnson P. Thomas

Jincheng Zhang

Geometric data, encompassing complex geometric shapes and their associated properties, represents a significant challenge in various fields, from computer graphics and scientific visualization to data analysis and pattern recognition. Traditional data compression techniques often struggle to effectively handle the inherent complexities of geometric data, leading to limitations in compression ratios and computational efficiency. This paper explores the potential of leveraging quantum entanglement to revolutionize geometric data compression and acceleration. We introduce a novel algorithm, Quantum Geometric Compression (QGC), that utilizes entanglement to efficiently transfer and manipulate geometric data, resulting in significantly improved compression ratios and accelerated geometric computations. The core mechanism centers on exploiting the correlated properties of entangled qubits to represent and manipulate geometric data in a fundamentally different manner than conventional methods. We demonstrate the effectiveness of QGC through extensive experimental analysis, showcasing substantial compression gains and speedups in key geometric operations. The research contributes to a paradigm shift in data compression and computation, paving the way for more efficient and robust geometric processing.

Jesse Van Griensven Thé, Roydon Andrew Fraser, José R. Rosas-Bustos

Manuela Weigold, Johanna Barzen, Frank Leymann +1 more

Abstract As quantum computers are based on the laws of quantum mechanics, they are capable of solving certain problems faster than their classical counterparts. However, quantum algorithms with a theoretical speed‐up often assume that data can be loaded efficiently. In general, the runtime complexity of the loading routine depends on (i) the data encoding that defines how the data is represented by the state of the quantum computer and (ii) the data itself. In some cases, loading the data requires at least exponential time that destroys a potential speed‐up. And especially for the first generation of devices that are currently available, the resources (qubits and operations) needed to encode the data are limited. In this work, we, therefore, present six patterns that describe how data is handled by quantum computers.

Rüdiger Schack