IndisputableMonolith.Physics.QuantumComputingGatesFromRS
Module linking single-qubit Clifford gates to the Recognition Science dimension count: the Clifford group on one qubit has order 8, identified with 2^D. Physicists working the RS-to-quantum-computing bridge cite it for the gate census and the certificate that the count matches the forced spatial dimension. Structure is definitional plus a short equality proof for the count.
claimThe single-qubit Clifford group has cardinality $8 = 2^D$, where $D$ is the spatial dimension forced by Recognition Science. The module introduces a canonical gate type, a gate count, the Clifford single-qubit set, the equality $8 = 2^D$, and a quantum-computing gate certificate packaging that fact.
background
Recognition Science forces $D = 3$ spatial dimensions (forcing chain T8) and an eight-tick octave of period $2^3$ (T7). In the quantum-computing layer those two facts meet the standard single-qubit Clifford group, whose order is classically 24 when including global phases, but the projective or Pauli-normalized census used here is 8.
The module sits in the Physics domain and imports only Mathlib. It introduces a canonical gate datatype, a numeric gate count, an explicit Clifford single-qubit collection, and a certificate record that packages the equality between that count and $2^D$. The local claim is purely combinatorial: the RS-forced dimension reproduces the Clifford order on one qubit.
proof idea
Definitional core: CanonicalGate, canonicalGateCount, cliffordSingleQubit, and the certificate type QCGateCert are introduced by direct construction. The sole nontrivial statement is clifford_eq_8, an equality proof that the enumerated single-qubit Clifford set has cardinality 8, written as $2^D$. The certificate qcGateCert simply packages that equality for downstream consumers. No deep tactic work; the argument is enumeration plus the already-forced value of $D$.
why it matters in Recognition Science
Gives the RS side of the quantum-computing gate dictionary: once $D = 3$ is forced, the single-qubit Clifford order is no longer an external input but a derived $2^D$. Downstream physics and computing layers can cite the certificate rather than re-prove the count. Ties directly to forcing-chain landmarks T7 (eight-tick / $2^3$) and T8 ($D = 3$). Does not yet address multi-qubit Cliffords or universality; it only locks the one-qubit census to the RS dimension.
scope and limits
- Does not treat multi-qubit Clifford groups or their orders.
- Does not prove gate universality or generate a full gate set beyond the Clifford census.
- Does not derive $D = 3$ internally; assumes the forcing-chain value.
- Does not address continuous gate groups or non-Clifford magic states.