Conjecture 2: Measurement-Free Fault Tolerance and Cooling Capacity¶
Big Picture¶
Conjecture 2 asks whether measurement-free fault tolerance is governed by a cooling-capacity inequality: ambient nonunital dynamics must supply enough usable purity to beat the architecture-specific refresh demand.
Current Status¶
No conjecture-local research nodes exist yet. The first pass should make the cooling-capacity definition and one concrete architecture mathematically precise before widening to general thresholds.
Minimal Theorem Targets¶
- Compute \(C_{\mathrm{cool}}\) for finite-memory primitive reset processes with commuting fixed points.
- Upper-bound \(C_{\mathrm{req}}\) for one measurement-free architecture on a 2D grid and on a reconfigurable array.
- Prove the sufficient direction \(C_{\mathrm{cool}}>C_{\mathrm{req}}\) for that concrete setting first.
Technical Tools¶
The first research pass should expect to use algorithmic cooling, entropy-rate methods, purity distillation, approximate QEC criteria, and non-Markovian threshold techniques.
Next Actions¶
- Create the first theorem/gap nodes under research/ using the bounded graph workflow.
- Add Zotero source checks only after a concrete target theorem is selected.
- Keep learning and manuscript material as stubs until a durable research spine exists.