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We present an algorithm for compiling arbitrary unitaries into a sequence ofgates native to a quantum processor. As accurate CNOT gates are hard for theforeseeable Noisy- Intermediate-Scale Quantum devices era, our A* inspiredalgorithm attempts to minimize their count, while accounting for connectivity.We discuss the search strategy together with metrics to expand the solutionfrontier. For a workload of circuits with complexity appropriate for the NISQera, we produce solutions well within the best upper bounds published inliterature and match or exceed hand tuned implementations, as well as otherexisting synthesis alternatives. In particular, when comparing againststate-of-the-art available synthesis packages we show 2.4x average (up to 5.3x)reduction in CNOT count. We also show how to re-target the algorithm for adifferent chip topology and native gate set, while obtaining similar qualityresults. We believe that empirical tools like ours can facilitate algorithmicexploration, gate set discovery for quantum processor designers, as well asproviding useful optimization blocks within the quantum compilation tool-chain.

Heuristics for Quantum Compiling with a Continuous Gate Set