Optimal compilation of parametrised quantum circuits

Understand

Parametrised quantum circuits contain phase gates whose phase is determined by a classical algorithm prior to running the circuit on a quantum device.

• Such circuits are used in variational algorithms like QAOA and VQE.
• In order for these algorithms to be as efficient as possible it is important that we use the fewest number of parameters.
• We show that, while the general problem of minimising the number of parameters is NP-hard, when we restrict to circuits that are Clifford apart from parametrised phase gates and where each parameter is used just once, we *can* efficiently find the optimal parameter count.