Quantum-Projected Semantic Retrieval: A Universal Low-Latency Backbone for Multi-Modal AI Systems

  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.