Deutsch-Jozsa algorithm for continuous variables
  We present an idealized quantum continuous variable analog of the Deutsch-Jozsa algorithm which can be implemented on a perfect continuous variable quantum computer. Using the Fourier transformation and XOR gate appropriate for continuous spectra we show that under ideal operation to infinite precision that there is an infinite reduction in number of query calls in this scheme. 
Arun K. Pati and Samuel L. Braunstein