  We present COGNAC, a novel strategy for compiling quantum circuits based on
numerical optimization algorithms from scientific computing. Using a simple
noise model informed by the duration of entangling gates, our gradient-based
method can quickly converge to a local optimum that closely approximates the
target unitary. By iteratively and continuously decreasing a gate's duration to
zero, we reduce a circuit's gate count without the need for a large number of
explicit elimination rewrite rules. We have implemented this technique as a
general-purpose Qiskit compiler plugin and compared performance with
state-of-the-art optimizers on a variety of standard 4-qubit benchmarks. COGNAC
typically outperforms existing optimizers in reducing 2-qubit gate count,
sometimes significantly. Running on a low-end laptop, our plugin takes seconds
to optimize a small circuit, making it effective and accessible for a typical
quantum programmer.
