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 : vertical bar x >vertical bar y >vertical bar 0 >(k) -> vertical bar x >vertical bar y circle plus f(x)>vertical bar 0 >(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.