Abstract Modern AI systems rely on fast, accurate document retrieval at every step — from answering questions to generating responses grounded in real knowledge. Yet today's best retrieval methods treat text as flat numerical coordinates, ignoring the richer geometry that quantum mechanics provides. We present QuantumRAG : a system that maps neural text embeddings into complex quantum states in Hilbert space and retrieves documents using quantum fidelity — a similarity measure that sees both the magnitude and the phase (orientation angle) of semantic meaning. On the MATH benchmark (12,500 problems, 7 categories, 500 test queries), Quantum Q-CSD achieves P@1 = 0.698 and NDCG@10 = 0.825, matching BERT-cosine accuracy while running 3.6× faster (8.4 ms vs 29.9 ms per query). The system is modality-agnostic: the same quantum backbone retrieves mathematics, natural language documents, and video content without any architectural changes. All experiments run on standard CPU hardware — no quantum computer required.
Abstract Modern AI systems rely on fast, accurate document retrieval at every step — from answering questions to generating responses grounded in real knowledge. Yet today's best retrieval methods treat text as flat numerical coordinates, ignoring the richer geometry that quantum mechanics provides. We present QuantumRAG : a system that maps neural text embeddings into complex quantum states in Hilbert space and retrieves documents using quantum fidelity — a similarity measure that sees both the magnitude and the phase (orientation angle) of semantic meaning. On the MATH benchmark (12,500 problems, 7 categories, 500 test queries), Quantum Q-CSD achieves P@1 = 0.698 and NDCG@10 = 0.825, matching BERT-cosine accuracy while running 3.6× faster (8.4 ms vs 29.9 ms per query). The system is modality-agnostic: the same quantum backbone retrieves mathematics, natural language documents, and video content without any architectural changes. All experiments run on standard CPU hardware — no quantum computer required.
Modern AI systems rely on fast, accurate document retrieval at every step — from answering questions to generating responses grounded in real knowledge. Yet today's best retrieval methods treat text as flat numerical coordinates, ignoring the richer geometry that quantum mechanics provides. We present QuantumRAG: a system that maps neural text embeddings into complex quantum states in Hilbert space and retrieves documents using quantum fidelity — a similarity measure that captures both the magnitude and the phase (orientation angle) of semantic meaning. Built on BERT-projected quantum encoding (8 qubits, 256-dimensional Hilbert space) with a Fisher discriminant category mask, QuantumRAG achieves P@1=0.698 and NDCG@10=0.825 on the MATH benchmark (12,500 problems, 7 categories, 500 test queries), matching BERT-cosine accuracy while running 3.6× faster (8.4 ms vs 29.9 ms per query). The system is modality-agnostic: the same quantum backbone retrieves mathematics, natural language documents, and video content without any architectural changes. A Grover-inspired Quantum Amplitude Amplification (QAA) reranker provides a secondary scoring pass using quantum interference principles. All experiments run on standard CPU hardware — no quantum computer required. QuantumRAG serves as the universal retrieval backbone for a multi-modal AI pipeline spanning gesture recognition, mathematical reasoning, and document question answering — demonstrating that quantum-projected representations are a practical, deployable alternative to classical similarity search today, with a clear scaling path as quantum hardware matures.
Text embeddings are central to modern information retrieval and Retrieval-Augmented Generation (RAG). While dense models derived from Large Language Models (LLMs) dominate current practice, recent work has explored quantum-inspired alternatives motivated by the geometric properties of Hilbert-like spaces and their potential to encode richer semantic structure.
This paper presents an experimental framework for constructing quantum-inspired 1024-dimensional document embeddings based on overlapping windows and multi-scale aggregation. The pipeline combines semantic projections (e.g., EigAngle), circuit-inspired feature mappings, and optional teacher-student distillation, together with a fingerprinting mechanism for reproducibility and controlled evaluation.
We introduce a set of diagnostic tools for hybrid retrieval, including static and dynamic interpolation between BM25 and embedding-based scores, candidate union strategies, and a conceptual alpha-oracle that provides an upper bound for score-level fusion.
Experiments on controlled corpora of Italian and English documents across technical, narrative, and legal domains, using synthetic queries, show that BM25 remains a strong baseline, teacher embeddings provide stable semantic structure, and standalone quantum-inspired embeddings exhibit weak and unstable ranking signals. Distillation yields mixed effects, improving alignment in some cases but not consistently enhancing retrieval performance, while hybrid retrieval can recover competitive results when lexical and embedding-based signals are combined.
Overall, the results highlight structural limitations in the geometry of quantum-inspired embeddings, including distance compression and ranking instability, and clarify their role as auxiliary components rather than standalone retrieval representations.
We demonstrate how word and text embeddings as n-dimensional real vectors used in classical Natural Language Processing (NLP)/AI applications can be mapped to quantum states or quantum embedding representations in Quantum Applications using NLP and AI. Models like fastText [1], [2], GloVe [3], Numberbatch [4], or BERT [5] are common NLP embedding vectors or models that encode semantic properties of words or text fragments. We use these models to evaluate mapping properties and compression rate, as well as information preservation in quantum embeddings. For mapping embedding vectors to quantum states, we use encoding strategies, such as Amplitude Encoding. The encoding strategies allow us to map large dense vectors from the embedding models to compact quantum states using different compression ratios. The compression with Amplitude Encoding can be2ntoN, resulting in a mapping of a 1,024-dimensional vector of reals in the classical environment to a 10-qubit state. The goal of this work is to evaluate these strategies with respect to their compression ratio and measure the preservation of semantic information using similarity scores. We show that the resulting quantum embeddings based on mapped classical computing embeddings exhibit the same relational properties and that there is no significant loss of semantic information in the conversion from classical n-dimensional real vector embeddings to qubit states. We conclude that the experimental results allow us to quantum compute semantic similarities of words or text, reusing existing and freely available embedding models from classical NLP/AI computing.
Abstract Retrieval-Augmented Generation (RAG) has emerged as a powerful framework in natural language processing (NLP), integrating retrieval mechanisms with generative models to enhance information accuracy and contextual relevance. However, classical retrieval techniques face scalability bottlenecks and computational inefficiencies when handling large datasets. In this work, we introduce GroQ-Enhanced RAG (QRAG), a hybrid quantum-classical framework that leverages Grover’s search algorithm and GroQ-Rank (QAOA-based ranking) to enhance retrieval efficiency and optimization. QRAG employs Grover’s algorithm to accelerate query processing and utilizes GroQ for combinatorial ranking optimization, significantly reducing computational overhead. Empirical evaluations demonstrate that QRAG reduces retrieval latency by 40–50% compared to traditional RAG while improving response accuracy and scalability. By integrating quantum search and optimization techniques, GroQ-powered QRAG sets a new benchmark for efficient, high-fidelity information retrieval in NLP. While this study applies QRAG to RAG-based architectures, the proposed framework can be extended to other AI-driven retrieval-intensive applications, highlighting the transformative potential of quantum computing in large-scale language processing and information retrieval tasks.
While having enhanced NLP, deep learning and pre-trained language models requires a lot of processing power.The work showcases the potential of quantum computing by mapping linguistic data into vast, high-dimensional Hilbert spaces through entanglement and superposition.It focuses on mathematical concepts that set quantum approaches apart from classical ones, among them being the fidelity-based similarity and quantum probability.Various quantum machine learning models are considered in this article, including Quantum Neural Networks and Quantum Support Vector Machines, each discussing the computational advantages in pattern recognition.In addition, it considers retrieval techniques like Grover's algorithm, showing how quantum similarity functions give better semantic search.Indeed, the comparison does show that quantum techniques might yield advantages regarding expressiveness and scalability, despite obstacles such as hardware noise and data encoding.Notwithstanding that quantum technology is still in its infancy, future improvements might advance language understanding.
Quantum-inspired algorithms represent an important direction in modern software information technologies that use heuristic methods and approaches of quantum science. This work presents a quantum approach for document search, retrieval, and ranking based on the Bell-like test, which is well-known in quantum physics. We propose quantum probability theory in the hyperspace analog to language (HAL) framework exploiting a Hilbert space for word and document vector specification. The quantum approach allows for accounting for specific user preferences in different contexts. To verify the algorithm proposed, we use a dataset of synthetic advertising text documents from travel agencies generated by the OpenAI GPT-4 model. We show that the "entanglement" in two-word document search and retrieval can be recognized as the frequent occurrence of two words in incompatible query contexts. We have found that the user preferences and word ordering in the query play a significant role in relatively small sizes of the HAL window. The comparison with the cosine similarity metrics demonstrates the key advantages of our approach based on the user-enforced contextual and semantic relationships between words and not just their superficial occurrence in texts. Our approach to retrieving and ranking documents allows for the creation of new information search engines that require no resource-intensive deep machine learning algorithms.