Compressing the one-dimensional Clifford generating set

Compress the explicit constant-size one-dimensional nearest-neighbor generating set for the Clifford group while preserving its constant spectral gap and constant circuit depth.

Background

A central technical result constructs a system-size-independent generating set for the Clifford group with at most 451 generators, constant one-dimensional nearest-neighbor depth, and an Ω(1) Kazhdan constant. Although this set suffices for the unitary-design construction, the authors identify reducing its cardinality as an unresolved structural and practical problem.