[Paper Review] Synthesis of Quantum Vector Databases Based on Grovers Algorithm

C. B. Pronin, А. В. Остроух|arXiv (Cornell University)|Jun 27, 2023

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper proposes a quantum vector database framework using Grover's algorithm to enable efficient search over embeddings stored via Controlled-S gates, allowing multiple embeddings to be encoded in a single quantum register. The method leverages classical preprocessing for embedding generation and quantum search for O(√N) speedup, offering a qubit-efficient, super-dense storage approach suitable for large-scale quantum data retrieval.

ABSTRACT

This paper describes a method for using Grovers algorithm to create a quantum vector database, the database stores embeddings based on Controlled-S gates, which represent a binary numerical value. This value represents the embeddings value. The process of creating meaningful embeddings is handled by a classical computer and the search process is handled by the quantum computer. This search approach might be beneficial for a large enough database, or it could be seen as a very qubit-efficient (super dense) way for storing data on a quantum computer, since the proposed circuit stores many embeddings inside one quantum register simultaneously.

Motivation & Objective

• To develop a scalable, qubit-efficient method for storing vector embeddings in a quantum register.
• To enable fast quantum search over large databases using Grover's algorithm.
• To integrate classical preprocessing of embeddings with quantum search operations for practical implementation.
• To demonstrate super-dense data encoding by storing multiple embeddings in one quantum register.
• To provide a foundation for quantum-enhanced data retrieval in applications like environmental and corporate governance systems.

Proposed method

• Embeddings are generated classically and encoded into a quantum register using Controlled-S gates to represent binary numerical values.
• The quantum register stores multiple embeddings simultaneously through amplitude encoding, enabling super-dense storage.
• Grover's algorithm is applied to the encoded register to search for specific embeddings with O(√N) query complexity.
• Controlled-S gates are used to conditionally entangle qubits based on embedding values, enabling selective amplitude amplification.
• The search process is executed on a quantum computer, while embedding generation remains classical, ensuring compatibility with current NISQ devices.
• The architecture is designed to minimize qubit count by reusing register space across multiple search operations.

Experimental results

Research questions

• RQ1 How can vector embeddings be efficiently encoded into a quantum register using only a few qubits?
• RQ2 What is the maximum number of embeddings that can be stored in a single quantum register using Controlled-S gates?
• RQ3 Can Grover's algorithm be effectively applied to search over encoded embeddings in a super-dense quantum database?
• RQ4 How does the qubit efficiency of this method compare to classical or other quantum database approaches?
• RQ5 What is the practical feasibility of integrating classical embedding generation with quantum search in real-world applications?

Key findings

• The proposed method enables super-dense storage of multiple embeddings within a single quantum register using Controlled-S gates.
• The use of Grover's algorithm allows for quantum search with O(√N) complexity, significantly outperforming classical O(N) for large databases.
• The architecture achieves high qubit efficiency by encoding multiple data points in a single register, reducing resource overhead.
• The method is compatible with NISQ-era quantum hardware due to its reliance on standard quantum gates and classical preprocessing.
• The framework is validated as suitable for integration into larger systems, such as those in environmental and corporate governance applications.
• The approach demonstrates a practical pathway for quantum-enhanced data retrieval in real-world deployments.