Schurly Your Joking Drs. Bacon, Chuang, and Harrow?

What better way to start the new year than with the new paper dance. You can dance, you can dance, everyone publish their rants.
Thanks to the hard work and good timing of coauthor Aram Harrow, we were able to get the first paper of the new year on quant-ph: quant-ph/0601001. Happy new year!
The Quantum Schur Transform: I. Efficient Qudit Circuits
Authors: Dave Bacon, Isaac L. Chuang, Aram W. Harrow
Comments: 24 pages

We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis to a labelling related to the representation theory of the symmetric and unitary groups. If we desire to implement the Schur transform to an accuracy of epsilon, then our circuit construction uses a number of gates which is polynomial in n, d and log(1/epsilon). The important insights we use to perform this construction are the selection of the appropriate subgroup adapted basis and the Wigner-Eckart theorem. Our efficient circuit construction renders numerous protocols in quantum information theory computationally tractable and is an important new efficient quantum circuit family which goes significantly beyond the standard paradigm of the quantum Fourier transform.