Uniform physical X and Z layers implement the exported logical Paulis exactly. Clifford automorphism circuits, pieceable entangling gates, and magic-state distillation require additional permutations, intermediate correction, or measurement protocols; hardware results inherit those full boundaries.
XXXXX commutes with every stabilizer, is outside the stabilizer, and acts as Xbar. A single fault during the tensor-product layer affects at most one data qubit before later correction. ZZZZZ supplies the analogous Zbar. Their odd mutual overlap gives the expected logical anticommutation.
These are verified algebraic operations. Connectivity does not enter because each physical action is single-qubit.
A physical permutation that preserves the code's stabilizer row space is a code automorphism. Combining such permutations with local Clifford gates can realize logical Clifford transformations. The crucial step is to conjugate the logical Pauli pair and reduce the result modulo stabilizers; preserving the code does not by itself tell us the logical gate.
Sayginel and collaborators automate that calculation and include the perfect five-qubit code (primary source). The card therefore calls the mechanism fold-transversal and keeps the permutation and frame update in its cost. It does not claim that uniform physical H or S alone realizes every desired logical Clifford in the exported convention.
A nontransversal entangling circuit can spread one fault to several data qubits. Pieceable fault tolerance partitions the circuit and performs intermediate correction before dangerous correlations grow beyond the code's distance-three control. Yoder, Takagi, and Chuang construct universal gates by this mechanism (primary source).
Ryan-Anderson and collaborators implement a logical CNOT between two five-qubit blocks using flag and pieceable primitives with runtime decoding (primary source). The result is a fault-tolerant nontransversal operation. Calling it transversal would erase the mechanism that makes the fault argument work.
Bravyi and Kitaev's five-to-one routine uses Clifford processing and stabilizer measurements to accept or reject five noisy resource states and retain one output (primary source). Souza and collaborators demonstrate the protocol in NMR (primary source).
The code supplies the projector structure. The resource-state axis, input noise, acceptance event, and output analysis belong to the protocol. Thus the entry lists distillation as measurement-based non-Clifford resource preparation, not a native transversal logical T.
NMR. Knill and collaborators implement a five-qubit correction benchmark; Zhang, Laflamme, and Suter implement encoded identity, NOT, and Hadamard processes with deliberately inserted single-qubit errors (2001 record, 2012 record). These are ensemble-control benchmarks, not repeated scalable memories.
Superconducting. Gong and collaborators prepare encoded states, measure the stabilizers, identify inserted arbitrary single-qubit errors, implement logical Paulis, and decode (primary source). The reported codespace and recovered-state fidelities refer to different stages of one finite circuit.
Diamond spins. Abobeih and collaborators use five data and two ancillary spins for repeated-measurement encoding, fault-tolerant single-qubit Clifford operations, and flagged stabilizer measurements (primary source).
Trapped ions. The Ryan-Anderson experiment couples two blocks through the pieceable logical CNOT described above. Its runtime decoder and flag record are part of the demonstrated operation.
None gives a model-independent threshold for the isolated fixed block. A threshold needs a growing family such as concatenation, a declared physical channel or circuit noise model, a recovery rule, and a fitted observable. Likewise, deliberately injected single faults test the expected map but do not sample all naturally occurring circuit-fault combinations.