The question
Where do finite-size logical-error curves cross, and which error patterns explain those crossovers?
Why it matters
Physical devices need not produce X, Y, and Z errors equally often. Small codes make it possible to enumerate errors exactly and test whether familiar code rankings survive a change in the noise bias.
What you could investigate
- Compare tractable distance-three constructions, such as the five-qubit code, Steane seven-qubit code, Shor nine-qubit code, rotated surface-9, and XZZX-9.
- Assign syndromes and logical classes to Pauli errors and calculate exact logical-error probabilities across total-error and bias parameters.
- Map crossover regions and identify the logical mechanisms responsible for changes in performance.
What you could create
- Validated exact-enumeration code
- Crossover maps across noise parameters
- An explanation of dominant logical-error patterns