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.
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.
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.
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.
Although the performance of LLMs on a wide variety of natural language processing problems demonstrates remarkable ability, hallucinated responses are introduced as one of the key weaknesses of LLMs, especially in knowledge-intensive applications, where fidelity to facts is paramount. While effective in reducing hallucinations, the context retrieved during the RAG operations is still very often suboptimal with respect to the external documents used in the retrieval stage, and being based on cosine similarity and nearest-neighbour search, these models typically do not return optimal context to support factual generation. The authors propose a five-stage solution, called Quantum-Enhanced Retrieval-Augmented Generation (QERAG), which combines the use of a quantum-inspired probability amplitude document ranking, a Context Utility Score (CUS) optimisation engine, and a Hallucination Verification Agent (HVA) based on a formal Hallucination Reduction Index (HRI). The Quantum Relevance Score (QRS) uses interference based, Amplitude Encoding on candidate Document Sets to yield a normalised relevance distribution that emphasises the relatively higher value generated in the discriminative context as compared to other locally similar passages in a document set. QERAG outperforms Standard LLM and Traditional RAG models on all five Natural benchmark across response accuracy, with a score of 92.8% vs. 74.3%, and hallucination rate, 4.3% vs. 18.2%, respectively. They achieve a significant overall improvement by using quantum-inspired retrieval layer, which achieves a 3.5-percentage-point reduction in hallucination rate when compared to cosine-similarity RAG, with this single layer showing more reduction than the rest of the pipeline layers. The results of an ablation study show the individual contribution of every pipeline stage, and the quantum-inspired retrieval layer exhibits the greatest reduction of a 3.5 percentage points over cosine-similarity RAG.
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.
Over the last decade, representation learning, which embeds complex information extracted from large amounts of data into dense vector spaces, has emerged as a key technique in machine learning. Among other applications, it has been a key building block for large language models and advanced computer vision systems based on contrastive learning. A core component of representation learning systems is the projection head, which maps the original embeddings into different, often compressed spaces, while preserving the similarity relationship between vectors. In this paper, we propose a quantum-inspired projection head that includes a corresponding quantum-inspired similarity metric. Specifically, we map classical embeddings onto quantum states in Hilbert space and introduce a quantum circuit-based projection head to reduce embedding dimensionality. To evaluate the effectiveness of this approach, we extended the BERT language model by integrating our projection head for embedding compression. We compared the performance of embeddings, which were compressed using our quantum-inspired projection head, with those compressed using a classical projection head on information retrieval tasks using the TREC 2019 and TREC 2020 Deep Learning benchmarks. The results demonstrate that our quantum-inspired method achieves competitive performance relative to the classical method while utilizing 32 times fewer parameters. Furthermore, when trained from scratch, it notably excels, particularly on smaller datasets. This work not only highlights the effectiveness of the quantum-inspired approach but also emphasizes the utility of efficient, ad hoc low-entanglement circuit simulations within neural networks as a powerful quantum-inspired technique.