Codes MOC

Curated map of Zoo entries in the Codes family.

Entries

Entry	Type	Status
bacon-shor-code	encoding	demonstrated
floquet-codes	encoding	proposed
qldpc-codes	encoding	proposed

Composition

• encoding: 3

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

• bacon-shor-code, floquet-codes, and qldpc-codes live here because their identity is primarily code-theoretic: subsystem structure, measurement schedule, or parity-check sparsity is the main story.
• surface-code-logical-qubit, color-code-logical-qubit, and erasure-qubit stay in cross-platform-moc because they function as architecture-level roadmapping concepts as much as code families.
• 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.

Editorial note

This MOC is still narrow. It currently captures only families with stable Zoo-level identity. Keep generic code-theory papers in References/ unless they materially change the hardware-facing story.