Several literatures use the same row/column structure for different purposes. This ledger states what each picture preserves and what it does not license.
| picture | exact object retained | insight gained | boundary |
|---|---|---|---|
| gauge-center quotient | symplectic gauge rows, center rows, protected quotient | why noncommuting local checks can protect one qubit | canonical executable view |
| perpendicular repetition | row and column parity quotients | sector distances, degeneracy, and perfect-readout decoding | does not define a noisy extraction circuit |
| quantum compass Hamiltonian | local XX/ZZ interaction pattern and line symmetries | center strips as rigid symmetries | does not make the static model topological or self-correcting |
| surface-tensor leg reassignment | tensor-network operator-pushing dictionary | how physical/logical leg bookkeeping exposes weight-two gauges | not an exact constructor replay or equality of stabilizer row order |
| frustration graph | pairwise anticommutation of gauge terms | which perpendicular links obstruct simultaneous gauge values | ordinary Bacon–Shor is the obstructed relative, not labeled free-fermion solvable |
| autonomous gauge dynamics | gauge interactions plus a chosen dissipative/control model | how the disposable subsystem affects dynamical correction | dynamics claim, not a new static code parameter |
| period-four Floquet descendant | scheduled measurement graph, detectors, time-dependent logicals | how related pair measurements define a dynamical qubit | not the static CheckMatrix rendered at landing |
The first two rows are recomputed. The other rows are curated dictionaries with registered primary references.
Assign the pair operators as local Hamiltonian terms. The same vertical-X and horizontal-Z pattern becomes the square quantum compass model. Products along complete lines commute with the Hamiltonian and mirror the center-strip symmetries. This makes the energetic role of gauge degrees of freedom visible.
It does not follow that local pair terms produce a topologically ordered or self-correcting memory. dorier2005compass, bacon2006operator, and sarma2013gauge discuss the interaction/symmetry and autonomous-dynamics questions with their own model assumptions. The static code entry exports no Hamiltonian gap, bath, lifetime, or thermal scaling claim.
cao2022quantumlego obtains a Bacon–Shor description by reorganizing a surface-code tensor network and declaring selected dangling legs logical rather than physical. Operator pushing then exposes the pair-gauge structure.
This is a useful explanation of subsystem bookkeeping: changing which tensor legs count as protected versus disposable can turn a stabilizer presentation into a gauge presentation. It is not an exact operation-tree adapter in this repository. A contraction or leg reassignment can also create a new code whose parameters must be recomputed rather than inherited.
Build a graph whose vertices are gauge terms and whose edges connect anticommuting pairs. For the rectangular compass pattern, a vertical X edge is adjacent to each horizontal Z edge sharing exactly one endpoint. The graph is constructor-derivable and exposes the nonabelian measurement conflicts.
chapman2022freefermion uses Bacon–Shor as the obstructed comparison when constructing a related free-fermion subsystem model. The fetched source does not establish that ordinary Bacon–Shor is itself free-fermion solvable. The card therefore labels this view a boundary, not a free-fermion realization.
| platform/result | code object | established | not established |
|---|---|---|---|
thirteen-qubit trapped-ion processor (egan2021fault) | nine data qubits in a static Bacon–Shor logical block plus four ancillas | fault-tolerant preparation, measurement, corrected rotations, and stabilizer-extraction primitives on a fixed block | increasing-distance below-threshold memory scaling |
superconducting processor (sun2025floquetbacon) | scheduled Floquet–Bacon–Shor descendant | operations on a time-dependent dynamical logical qubit | realization of this card's static center/checkmatrix experiment |
bias-preserving teleportation architecture (brooks2013asymmetric) | proposed strongly rectangular blocks inside a larger protocol | architecture and resource analysis under biased elementary operations | hardware demonstration or a code-only optimum aspect ratio |
The static trapped-ion experiment is the direct realization attached to this card. The superconducting result is recorded as descendant evidence because its logical qubit and detectors depend on a schedule absent from the static constructor.
As of the 2026-08-02 realization sweep, no increasing-distance below-threshold Bacon–Shor hardware scaling demonstration was found. That dated negative result does not diminish the demonstrated fixed-block primitive suite; it prevents the two evidence levels from being merged.
Use the following test before transferring a claim:
r and c preserves the rectangular pair-gauge grammar but changes sector distances and gauge count;Matching words such as "compass," "Bacon–Shor," or "subsystem" do not prove these objects have interchangeable distances, thresholds, operations, or hardware evidence.
bacon2006operator, dorier2005compass, sarma2013gauge.cao2022quantumlego.chapman2022freefermion.egan2021fault.alam2025board, sun2025floquetbacon.brooks2013asymmetric.The 2026-08-02 representation sweep found no source calling the ordinary two-dimensional compass Hamiltonian a self-correcting topological memory, and no source making the base code free-fermion solvable. Bibliographic identity, queries, and correction notes are retained in the six local literature files.