Equality of bounded-error and exact QAC^0

Determine whether the bounded-error and exact constant-depth quantum circuit classes satisfy BQAC^0 = EQAC^0.

Background

The exactification construction shows that every Boolean function known in BQAC0 is also computable in EQAC0 when sufficiently many classical copies of the input are supplied. This establishes a substantial inclusion for the relevant lifted setting but does not provide a generic exactification procedure for all bounded-error QAC0 computations.

The authors explicitly leave open whether every bounded-error QAC0 computation can be made exact without changing the class, emphasizing that the limited current understanding of which Boolean functions belong to BQAC0 makes the question difficult.

References

So, we leave open the question of whether $\BQAC0 = \EQAC0$. It is quite unclear how a generic exactification procedure might be implemented, given that it is still quite unclear which types of Boolean functions are even in $\BQAC0$.

— The Robustness of QAC0  (2610.02154 - Grier et al., 1 Oct 2026) in Section 3, “Future directions”