quantumComputingDepthCert
plain-language theorem explainer
Quantum computing depth in the Recognition Science model is certified by five gate types, an eight-element Pauli group, and three universal gates. Researchers linking quantum gates to J-cost minimization would cite this certificate to anchor standard quantum computing primitives in the framework. The definition constructs the structure by direct assignment from three upstream lemmas established by decision and reflexivity.
Claim. The quantum computing depth certificate is the structure satisfying $|QuantumGateType| = 5$, $pauliGroupSize = 2^3$, and $universalGates = 3$.
background
In Recognition Science, quantum computation consists of sequences of J-cost-minimizing recognition operations. The module specifies five canonical quantum gate types corresponding to configuration dimension D = 5. It further notes that the single-qubit Pauli group has eight elements equal to 2^D with D = 3, and that the universal gate set has three elements also matching D.
proof idea
This definition constructs an instance of the QuantumComputingDepthCert structure. It sets the five_gates field to quantumGateTypeCount, the pauli_8 field to pauliGroupSize_2cubed, and the universal_D field to universalGates_eq_D. The construction uses no tactics beyond the structure literal.
why it matters
This definition completes the RS_PAT_043 / B15 module by providing the explicit certificate for quantum computing depth derived from Recognition Science. It ties the five gate types and three universal gates to D, and the eight Pauli elements to the eight-tick octave with period 2^3. With no further declarations depending on it, the certificate stands as a self-contained witness for the connection between recognition operations and quantum gate universality.
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