Improved Lower Bounds for QAC0

In this work, we establish the strongest known lower bounds against QAC0, while allowing its full power of polynomially many ancillae and gates. Our two main results show that: (1) Depth 3 QAC0 circuits cannot compute PARITY regardless of size, and require at least Ω(exp(√n)) many gates to compute MAJORITY. (2) Depth 2 circuits cannot approximate high-influence Boolean functions (e.g., PARITY) with non-negligible advantage, regardless of size.