Inputs and the fixed gate alphabet

For an integer $N\ge 2$, let

Input bits are least significant first:

The source's padded parameter is

This padding must not be silently replaced by $\ell$ in numerical probability claims.

The primitive gates are

together with CNOT and Toffoli. The alphabet also contains their inverses and their singly controlled versions. Its maximum arity is four. The description has twenty gate names if inverse and control flags are counted separately; some names represent the same unitary.

The gate alphabet is fixed once and for all. It does not contain an instruction specifying a rotation angle as part of the input. A conjunction of many controls must be synthesized into the allowed bounded-arity gates, rather than counted as one gate SourceModel,LeanTarget279.