Robust quantum compilation and circuit optimisation via energy minimisation

We explore a method for automatically recompiling quantum circuit A into target B, with the goal that both circuits have same action on specific input i.e. B|in> = A|in>. This is of particular relevance to hybrid, NISQ-era algorithms dynamical simulation or eigensolving. The user initially specifies B as blank template: layout parameterised unitary gates configured identity. compilation then proceeds using hardware perform an isomorphic energy-minimisation task, and optional gate elimination phase compress circuit. If insufficient perfect recompilation will result in approximate solution. optimise imaginary time evolution, recent extension natural gradient noisy settings. successfully recompile 7-qubit involving 186 multiple types alternative form different topology, far fewer two-qubit gates, smaller family types. Moreover we verify process robust, finding per-gate noise up 1% can still yield near-perfect recompilation. test scaling our algorithm 20 qubits, 400 parameterized incorporate custom adaptive timestep technique. note classical be useful today's prototypes, more generally may enable 'blind' harnessing device whose response control parameters deterministic but unknown.