Quantum computation over continuous variables

This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromag netic held might be constructed using simple linear devices such as beam sp litters and phase shifters, together with squeezers and nonlinear devices s uch as Kerr-effect fibers and atoms in optical cavities. Such a device coul d in principle perform "quantum floating point" computations. Problems invo lving noise, finite precision, and error correction are discussed.