Autonomous Quantum Error Correction via Fibonacci-Hopfield Networks: A Photonic Implementation Proposal

Current quantum error correction (QEC) schemes require extensive classical processing overhead: ancilla measurement, syndrome decoding, and active feedback represent ~99% of the computational cost. We propose a fundamentally different approach: autonomous QEC via Fibonacci-Hopfield networks, in which error correction emerges from the natural dynamics of the system without external intervention. The key insight, formalized in the recently proven phinary framework (Harnessing the Phinary System, 2026), is that Fibonacci-structured quantum codes have error-detection properties that are logically necessary consequences of the non-adjacent-ones constraint — not engineering choices. We demonstrate that a quantum Hopfield network with Fibonacci-spaced energy levels realizes these properties naturally: the attractor states (logical codewords) correspond to stable harmonic modes, and errors (decoherence events) are automatically corrected by the system’s tendency to relax toward its Fibonacci attractors. We propose a concrete implementation on photonic qubits using time-bin encoding, where temporal modes |𝑡𝑛⟩ at Fibonacci time-delays Δ𝑡_𝑛 = 𝑇₀/𝜑^𝑛 constitute the physical register. This architecture achieves: (i) room-temperature operation (photons maintain coherence at 300 K); (ii) autonomous correction without classical feedback; (iii) content-addressable storage (robustness to partial errors); and (iv) natural integration with the Extended Integrated Information Theory (EIIT) framework, wherein a system achieving Φ_EIIT > Φ_threshold generates self-sustaining phase coherence. We provide threshold error rates, capacity bounds, and a 5-step experimental protocol toward a 10-logical-qubit proof-of-concept.