Recursive Fidelity Decay

Recursive Fidelity Decay is the model of how the fidelity of a quantum operation falls as it is repeated over many recursive cycles, combining a fixed per-cycle degradation with exponential decoherence. It answers the question behind the Sustained Performance Requirements: how many cycles a qubit can run before its information integrity is lost. Two mechanisms act together, a linear degradation that removes a small fraction of fidelity every cycle, and an exponential decoherence term with a characteristic number of cycles; their combined effect sets a fundamental limit on how deep reliable recursive processing can go. The book stresses that PulseCore-Validated Qubits are judged by exactly this capacity to sustain recursive, self-correcting processing. Fℜ(n) = F₀ × (1 − α)ⁿ × exp(−n/n⨶), where Fℜ(n) is the fidelity after n cycles, F₀ is the single-operation fidelity (0.999), α is the degradation factor per cycle (0.001 ± 0.0005), n is the number of recursive cycles and n⨶ is the exponential decay scale (100 ± 20 cycles). All quantities are [∅]. It sets the Sustained Performance Requirements and connects to Quantum Pulse Fidelity, Persistence Fidelity Condition, PulseCore-Validated Qubits and Operational Coherence Time.