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This is of particular relevance to hybrid, NISQ-era algorithms for dynamical simulation or eigensolving. The user initially specifies B<\/mml:mi><\/mml:mrow><\/mml:math> as a blank template: a layout of parameterised unitary gates configured to the identity. The compilation then proceeds using quantum hardware to perform an isomorphic energy-minimisation task, and an optional gate elimination phase to compress the circuit. If B<\/mml:mi><\/mml:mrow><\/mml:math> is insufficient for perfect recompilation then the method will result in an approximate solution. We optimise using imaginary time evolution, and a recent extension of quantum natural gradient for noisy settings. We successfully recompile a 7<\/mml:mn><\/mml:math>-qubit circuit involving 186<\/mml:mn><\/mml:math> gates of multiple types into an alternative form with a different topology, far fewer two-qubit gates, and a smaller family of gate types. Moreover we verify that the process is r<\/mml:mi>o<\/mml:mi>b<\/mml:mi>u<\/mml:mi>s<\/mml:mi>t<\/mml:mi><\/mml:math>, finding that per-gate noise of up to 1<\/mml:mn>&#x0025;<\/mml:mi><\/mml:math> can still yield near-perfect recompilation. We test the scaling of our algorithm on up to 20<\/mml:mn><\/mml:math> qubits, recompiling into circuits with up to 400<\/mml:mn><\/mml:math> parameterized gates, and incorporate a custom adaptive timestep technique. We note that a classical simulation of the process can be useful to optimise circuits for today's prototypes, and more generally the method may enable `blind' compilation i.e. harnessing a device whose response to control parameters is deterministic but unknown.The code and resources used to generate our results are openly available online \\cite{githubLink} \\cite{mmaGithubLink}. 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