Possible simplification for threaded gradients

[rrtucci]

Stairs circuit is currently defined so that, in its full generality (i.e., where it includes all possible parents for each U(2)), it has as final state, a completely general n-qubit state. The stairs circuit as currently defined uses multi-controlled U(2) gates. Can one replace each U(2) by exp(i*alpha) Ry(beta) for real numbers alpha, beta? Hence reduce from four to two parameters per gate string. This would simplify calculation of derivatives. Would it still produce a completely general n-qubit state at the end?

[rrtucci]

No. But replacing each U(2) by R(t1, t2, t3) with 1 out of the 3 parameters (t1, t2, t3) equal to zero, would work. So you really only need 2 parameters per U(2), not 4.