Abstract

Gaussian graph states represent the basic resource for measurement-based quantum computation with continuous variables. I will present two approaches for obtaining them. The first [1] involves a family of Hamiltonians whose ground states are Gaussian graph states, thus opening the way for their adiabatic preparation in physical settings beyond the standard optical ones. Regarding the second approach [2] I will present a general scheme, applying both to discrete- and continuous-variable systems, for sequential one-way quantum computation, where both the generation of the graph state and its consumption by measurements are carried out simultaneously. Finally, I will introduce a minimal scheme to reconstruct those states (and any arbitrary state) in the case of quantum networks composed of interacting continuous variables [3].

[1] Leandro Aolita, Augusto J. Roncaglia, Alessandro Ferraro, and Antonio Acín, Phys. Rev. Lett. 106, 090501 (2011). [2] Augusto J. Roncaglia, Leandro Aolita, Alessandro Ferraro, and Antonio Acín, Phys. Rev. A 83 , 062332 (2011). [3] Tommaso Tufarelli, Alessandro Ferraro, M. S. Kim, and Sougato Bose, Phys. Rev. A 85 , 032334 (2012).