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Conjecture 4: Logical Survival Versus Efficient Decodability

Big Picture

Conjecture 4 asks whether logical quantum information can survive information-theoretically while every useful decoder remains computationally intractable.

Current Status

No conjecture-local research nodes exist yet. The first pass should choose an exact model where survival can be certified independently from decoder runtime.

Minimal Theorem Targets

  1. Prove an exact-decoding separation before approximate decoding.
  2. Replace average-case hardness by a cleaner worst-case hardness target if needed.
  3. Use coherent information or another decoder-independent survival certificate as the first weaker theorem.

Technical Tools

The first research pass should expect to use approximate Knill-Laflamme conditions, coherent information, LDPC decoding hardness, tensor-network contraction hardness, and syndrome-decoding reductions.

Next Actions

  1. Create the first theorem/gap nodes under research/ using the bounded graph workflow.
  2. Add Zotero source checks only after a concrete target theorem is selected.
  3. Keep learning and manuscript material as stubs until a durable research spine exists.

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