Constant-depth QAC computation of parity

Determine whether polynomial-size, constant-depth QAC circuits can compute the parity function, equivalently implement an unbounded fan-out operation.

Background

The paper distinguishes QAC circuits, which allow unbounded fan-in but not unbounded fan-out, from QNC circuits. The construction targets QAC because it is believed to be substantially weaker than QNC, yet the computational power of polynomial-size constant-depth QAC remains poorly understood. Establishing whether such circuits can compute parity would resolve a fundamental question about the relationship between these shallow quantum circuit classes.