Phase-Encoded Semantic Relationships: Noise-Robust Quantum Natural Language Processing

Quantum natural language processing (QNLP) promises to leverage quantum mechanical phenomena for computational linguistics, yet current implementations encode word meanings in quantum state amplitudes, making them highly susceptible to hardware noise. We introduce Phase-Encoded Semantic Relationships (PESR), a novel quantum encoding scheme that maps semantic similarity to relative quantum phase rather than amplitude. We prove that this mapping is bijective: cosine similarity between word embeddings corresponds one-to-one with phase values in [0, pi], enabling exact recovery of semantic information through interference measurements. Crucially, we demonstrate both theoretically and experimentally that phase-based encoding is inherently more robust to dephasing noise than amplitude-based encoding, since dephasing channels preserve phase while exponentially degrading amplitude information. Hardware experiments on Quantinuum's H1-1 trapped-ion processor validate our theoretical predictions, achieving phase recovery with mean error below 0.025 radians across five test configurations. Under controlled dephasing at 20% noise, PESR maintains 0.94 fidelity compared to 0.78 for amplitude encoding, a 1.21x advantage. These results establish phase encoding as a practical and noise-resilient paradigm for quantum natural language processing on near-term devices.