I-13 H1.0-FINAL — a frozen, hashed release. Its VH2 CUBI hypothesis test ran and was verified 10/10: the counting below is the skeleton that survived.
This seat carries no fidelities of its own; it fixes what the freeze asserts and hands the counts to the centre. cited from the freeze
The perfect five-qubit code [[5,1,3]]: 5 physical qubits, Hilbert dimension 25 = 32; the logical (code) space has dimension 2 (rank 2); distance 3.
| quantity | value |
|---|---|
| physical qubits n | 5 |
| Hilbert dim 25 | 32 |
| code dim (rank) | 2 |
| distance d | 3 |
| corrects ƒ((d−1)/2) | 1 |
Distance 3 corrects any single-qubit error. computed
The perfect five-qubit code is Laflamme, Miquel, Paz & Zurek, 1996 — the smallest code correcting an arbitrary single-qubit error.
The amplitude-level fidelities of 1.0 are cited from the frozen VH2 test (verified 10/10), not re-simulated here. cited, verified 10/10
Ties: quantum-linear-algebra · the transmon universe.
The model that survived: a 3-mode ternary CONTROLLER governing one protected [[5,1,3]] qubit. The controller is dimension 3; the protected register stays rank 2.
Inject one single-qubit error and route it through the engine — the code turns it into a syndrome:
Count the errors; count the syndromes; check the matching. Exact integers — no amplitudes.
| set | count |
|---|---|
| single-qubit Paulis (5×3) | 15 |
| stabilizer generators (n−k) | 4 |
| nonzero 4-bit syndromes (24−1) | 15 |
The 15 single-qubit Paulis map one-to-one onto the 15 nonzero syndromes — every nonzero syndrome used exactly once, none left over. That is what “perfect” means. matching, LIT
The model that failed: a ternary (dimension-3) logical basis inside one [[5,1,3]] block. To hold three orthogonal logical states it needs rank ≥ 3 — but the code space is rank 2.
3 > 2 is impossible. The ternary basis does not fit inside the block. tested & disproven
“Ternary logic lives inside the 5-qubit code.”
REJECTED — a rank-2 code cannot carry a dimension-3 basis (2 < 3). The corpus keeps the falsification rather than hiding it.
I-13 runs a MEASURED DEAD register; this headstone stays lit. DEAD kept
Claim the ternary (dim-3) basis fits inside the block — that rank 2 suffices for dimension 3: