qubitTypeCount
plain-language theorem explainer
The declaration fixes the number of superconducting qubit types at five in the Recognition Science enumeration. Quantum computing researchers applying RS decoherence predictions would cite the count when classifying architectures for phi-ladder scaling. The proof is a one-line wrapper that invokes the decide tactic on the decidable Fintype instance of the inductive type.
Claim. The finite set of superconducting qubit types has cardinality five: $|S| = 5$ where $S = $ {transmon, fluxonium, capacitively shunted flux, quantum dot hybrid, spin qubit}.
background
The module derives superconducting qubit properties from J-cost within Recognition Science, predicting phi-ladder decoherence suppression with T1 and T2 times scaling as phi^k and optimal anharmonicity at ladder positions. Five canonical types are defined: transmon, fluxonium, capacitively shunted flux, quantum dot hybrid, and spin qubit, corresponding to configDim D = 5. The RS qubit ladder states T2(k+1) = T2(k) * phi. The upstream inductive definition lists these five constructors and equips the type with DecidableEq, Repr, BEq, and Fintype.
proof idea
The proof is a one-line wrapper that applies the decide tactic to evaluate Fintype.card on the inductive type with five constructors.
why it matters
This supplies the five_types field inside scQubitCert, completing the certification object for RS_PAT_043 on phi-ladder decoherence suppression. It anchors the qubit enumeration inside the Recognition Science framework, linking to the phi-ladder and configDim = 5. The result enables downstream coherence ratio calculations without introducing new hypotheses.
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