Quantum synthesis of arbitrary unitary operators - art. no. 022102

Nature provides us with a restricted set of microscopic interactions. The q uestion is whether we can synthesize out of these fundamental interactions an arbitrary unitary operator. In this paper we present a constructive algo rithm for realization of any unitary operator which acts on a (truncated) H ilbert space of a single bosonic mode. The algorithm itself is not unitary because it involves a conditional measurement. However, it does yield a con stant probability of the conditional measurement which does not depend on t he input state of the bosonic system. We consider a physical implementation of unitary transformations acting on one-dimensional vibrational states of a trapped ion. As an example we present an algorithm which realizes the di screte Fourier transform.