Improved hand-derived syndrome-extraction schedules

Determine whether hand-derived syndrome-extraction schedules for the even-distance Generalized Superfast Encoding can reduce circuit depth or provide a better starting point for AlphaSyndrome.

Background

The paper uses AlphaSyndrome to generate bare-ancilla syndrome-extraction schedules for the proposed non-CSS Generalized Superfast Encoding codes. Although the stabilizers can be partitioned into four qubit-wise commuting groups and have weight at most 6, the synthesized schedules do not necessarily attain the resulting structural depth bound because AlphaSyndrome optimizes decoder-conditioned logical error rate rather than minimal circuit depth.

The authors identify unresolved potential benefits from deriving schedules manually, including lower circuit depth and improved initialization of the AlphaSyndrome optimization procedure. Establishing either benefit would help reduce circuit-level noise and possibly improve the observed memory performance.