Representation of Classical Data on Quantum Computers (2410.00742v3)

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.

• The paper presents innovative strategies for encoding classical data, focusing on methods for numbers, text, images, and graphs on quantum systems.
• It compares gate-based quantum computers with quantum annealers, emphasizing the trade-offs between universal functionality and optimization specializations.
• Advanced techniques like amplitude and angle encoding reduce qubit requirements, paving the way for more efficient quantum data processing.

Representation of Classical Data on Quantum Computers

The exploration of representing classical data on quantum computers is a timely and essential topic as quantum computing moves closer to practical applications across multiple domains. This paper, authored by researchers from the Fraunhofer Institute of Integrated Circuits IIS, Development Center X-ray Technology, provides a comprehensive overview of methods for representing different types of classical data on gate-based quantum computers.

Motivation and Context

Quantum computing, known for its potential to solve complex problems intractable for classical computers, necessitates efficient data representation strategies to handle various data types such as numbers, graphs, text, and images. This paper specifically caters to gate-based quantum systems, which are currently the primary universal quantum computing platforms.

Comparative Analysis: Gate-Based vs. Quantum Annealers

The paper contrasts gate-based quantum computers with quantum annealers. While theoretically equivalent, practical distinctions arise. Gate-based systems offer universal quantum computing capabilities, whereas quantum annealers specialize in optimization problems. The indirect encoding through quadratic unconstrained optimization problems (QUBO) distinguishes the latter.

Data Representation Methods

The paper categorizes data representation methods tailored for quantum systems as follows:

Text Representation

Textual data can be encoded simply as binary sequences or through embeddings like Bag-of-Words, word2vec, and BERT. These embeddings transform text into high-dimensional vector spaces, allowing quantum conversion via numerical vector encoding methods.

Categorical and Numerical Values

Categorical values deploy encoding strategies such as ordinal and one-hot encoding. Numerical data, on the other hand, necessitate binary representations or angle encoding schemes. Angle encoding stands out by mapping real numbers as phase angles in a quantum system, allowing compact qubit use.

Vectors and Matrices

For higher-dimensional data like vectors and matrices, the paper explores both simple Kronecker product formations and advanced amplitude encoding. The latter highlights its promise by enabling large data storage in exponentially fewer qubits.

Quantum Image Representation

Quantum image encoding is another focal point. The paper details several methods:

• FRQI and NEQR: These methods are foundational in encoding images, with NEQR achieving exact pixel retrieval.
• Advanced Techniques: Further advancements like QPIE and BRQI offer alternative encoding schemes with implications for efficient quantum image processing.

Each method balances between efficient storage and complexity of retrieval, critical for image processing tasks in quantum systems.

Time Series and Graph Data

Encoding strategies extend to time series and graph data. Quantum enhancement of traditional time series methods and direct transformation of graph adjacency matrices to quantum states are proposed, signifying the ability to represent interconnected systems effectively.

Implications and Future Directions

The examination of these representation methods outlines both current potential and challenges in adapting classical data to quantum systems—thereby directly impacting algorithm development and execution on quantum hardware. The continuous evolution in quantum algorithms will undoubtedly reciprocate with innovative data representation strategies, which remain a vibrant research frontier.

Conclusion

This paper effectively synthesizes methods for classical data encoding on quantum computers, focusing on exploiting quantum superposition and parallelism for efficient data processing. As quantum computing technology progresses, these foundational methods will be pivotal in bridging classical datasets with quantum algorithmic capabilities, warranting ongoing exploration and refinement in the field of quantum data representation.