Compilation flow for classically defined quantum operations

We present a flow for synthesizing quantum operations that are defined by classical combinational functions. The discussion will focus on out-of-place computation, i.e., $U_{f}$: $\vert x\rangle\vert y\rangle\vert 0\rangle^{k}\rightarrow\vert x\rangle\vert y\oplus f(x)\rangle\vert 0\rangle^{k}$. Our flow allows users to express this function at a high level of abstraction. At its core, there is an improved version of the current state-of-the-art algorithm for synthesizing oracles [1]. As a result, our synthesized circuits use up to 25 % fewer qubits and up to 43 % fewer Clifford gates. Crucially, these improvements are possible without increasing the number of $T$ gates nor the execution time.