Quantum Computation with Generalized Binomial States in Cavity Quantum Electrodynamics

Cavity quantum electrodynamics (CQED) has been shown to be suitable to quantum computation processing1 thanks to the high quality factors Q of cavities, control of atom-cavity interactions and long lifetimes of Rydberg atoms2. In this context, the information can be stored and processed by atoms and photons representing the quantum bits (qubits)3 and two approaches can be distinct: the “microwave way”, where photons are confined in cavities and atoms are used to carry out the information between the cavities; the “optical way”, where atoms are very slow or even trapped within the cavities and information is carried out by photons4. Following the first approach, a CQED scheme to obtain two-bit universal quantum logic gates has been proposed5 and a quantum phase gate realized6, while a controlled-NOT (CNOT) gate was constructed by the optical approach7,8. These schemes use resonant interactions between two-level Rydberg atoms and cavities having zero or one photon only. Recently, interest has arisen to the coherent states and their usefulness to realize universal quantum computation in the quantum optics context9,10,11. There, the qubit is represented by two coherent states |α〉 and | − α〉 of π-phase difference and the quantum logic operations, based on quantum teleportation, are realized by beam-splitters, non-linear crystals and phase-shifters9. Apart the difficulty of performing a teleportation protocol, a drawback of using coherent states is their intrinsic non orthogonality, with the consequent request of a large photon number.