Figure 1. Controlling arbitrary quantum operations using additional degrees of freedom.

(a) Logic circuit in which quantum operation O is implemented on a register of qubits (target register), conditional on the logical state of a single control qubit. (b) Our approach to implementing the circuit in (a). The target information carriers are four dimensional systems with logical states |0〉,|1〉,|2〉 and |3〉. Initially and finally, only the bottom two 'qubit' levels (|0〉 and |1〉) are populated. Controlled-X_a gates (equations 1 and 2) swap information between the qubit levels and the upper levels (|2〉 and |3〉), on which O does not act. In this way, conditional on the state of the control qubit, the entire quantum state of the target register is temporarily moved into an effective quantum memory on which O does not act.