Apparatus and method for unitary synthesis of quantum circuits with reinforcement learning

An apparatus for determining a gate representation of a target unitary matrix according to an embodiment is provided. The apparatus comprises a selection unit (110) configured for conducting a selection step to select a selected operation out of a plurality of possible operations to append at least one quantum gate to an intermediate quantum circuit. Moreover, the apparatus comprises an appending unit (120) configured for conducting an appending step, which updates a gate representation of the intermediate quantum circuit, so that the at least one quantum gate is appended to the intermediate quantum circuit in the gate representation of the intermediate quantum circuit. The apparatus is configured to repeat the selection step of the selection unit (110) and the appending step of the appending unit (120) until a unitary matrix of the intermediate quantum circuit is equal to the target unitary matrix.