Hybrid quantum computation in quantum optics

We propose a hybrid quantum computing scheme where qubit degrees of freedom for computation are combined with quantum continuous variables for communication. In particular, universal two-qubit gates can be implemented deterministically through qubit-qubit communication, mediated by a continuous-variable bus mode (“qubus”), without direct interaction between the qubits and without any measurement of the qubus. The key ingredients are controlled rotations of the qubus and unconditional qubus displacements. The controlled rotations are realizable through typical atom-light interactions in quantum optics. For such interactions, our scheme is universal and works in any regime, including the limits of weak and strong nonlinearities.

Figure 1

(Color online) (a) Circuit diagram of a universal two-qubit gate based on controlled displacements between the qubits and the probe bus. (b) Schematic phase-space evolution of a coherent qubus amplitude (with the $\beta$’s chosen real), depending on the four basis states of the two qubits.

Figure 2

(Color online) (a) Circuit diagram for an effective controlled displacement constructed from uncontrolled displacements and controlled rotations. (b) Schematic phase-space evolution of a coherent qubus amplitude during the controlled displacement.