Codes MOC

Curated map of Zoo entries in the Codes family.

Entries

Entry	Type	Status
bacon-shor-code	encoding	demonstrated
color-code-logical-qubit	encoding	demonstrated
erasure-qubit	encoding	demonstrated
floquet-codes	encoding	proposed
qldpc-codes	encoding	proposed
surface-code-logical-qubit	encoding	demonstrated

Composition

• encoding: 6

Curated synthesis

The cleanest way to read this family is that each entry makes a different bet about where to spend complexity in fault tolerance, and that bet matters more than the shared label “code.”

1. bacon-shor-code spends complexity in redundancy, not check hardware

   • The main win is subsystem structure: measure only weight-2 gauge operators, then reconstruct the heavier stabilizer information classically.
   • Route here when the hardware can do repeated local parity checks reliably but deeper ancilla-mediated stabilizer extraction is still the bottleneck.

2. floquet-codes spend complexity in time ordering

   • The code is not static; logical protection emerges over a measurement cycle.
   • Route here when the key question is whether a platform would rather keep checks two-body and local, even if that means accepting a stroboscopic decoder and schedule-aware syndrome logic.

3. qldpc-codes spend complexity in connectivity and decoding

   • The prize is asymptotically lower overhead, but the cost is sparse nonlocal check structure plus more demanding decoders.
   • Route here only once the discussion has already moved beyond nearest-neighbor patch layouts and toward modular links, shuttling, or otherwise nonlocal hardware.

Taken together, this family is best seen as the place where the Zoo asks which bottleneck is actually dominant: measurement weight, measurement schedule, or architectural connectivity. Once the answer becomes mostly about decoder assumptions or logical-overhead comparisons across many hardware families, hand off to cross-platform-moc.

Conceptual anchors

• threshold-theorem is the top-level reason these entries matter architecturally.
• erasure-error-vs-pauli-error is useful for separating codes that assume ordinary Pauli noise from hardware paths with flagged loss / erasure structure.

Scope boundary

• This is the authoritative code-family map. bacon-shor-code, floquet-codes, and qldpc-codes are primary members because code structure is their main identity.
• surface-code-logical-qubit, color-code-logical-qubit, and erasure-qubit appear here through explicit MOC facets while remaining primary members of cross-platform-moc, where their architectural consequences are compared.
• qldpc-codes should usually be read together with quantum-transduction and modular-hardware notes, since its long-range-check promise matters most once distributed connectivity enters the design.

Zoo coverage is intentionally selective: a code appears here when it has a stable hardware-facing identity, demonstrated logical role, or materially different overhead/noise tradeoff. Generic code-theory papers remain in References/.