Realization of elementary operations for continuous-variable quantum computers

Abstract

Continuous-variable quantum computers encode information and perform calculations based on continuous degrees of freedoms, such as e.g. position or momentum. In this case, the elementary logical gates are characterized by continuous transformations such as displacement, rotation and shearing[1,2]. However, the implementation of these gates is limited to the experimentally available operations to manipulate continuous quantum states. Therefore, it is necessary to develop schemes that are applicable in a variety of physical systems. In this poster, we present a representation-free theory to realize the displacement, rotation and shearing operator for particles with non-vanishing mass. Our method is solely based on the application of linear and quadratic potentials that either act instantaneously or for a finite period of time, which makes our approach versatile for various continuous quantum systems. [1] S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003). [2] S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).