Principal Investigator Isaac Chuang
We have developed a new polytime quantum algorithm for converting from the computational basis to the Schur basis, which is the basis on n qudits which simultaneously reduces the actions of S_n and U(d) to their irreducible representations. This is useful for a number of problems in information theory, and we hope it will have algorithmic applications. Current work includes looking for applications and connections to other transforms, such as the Fourier transform over S_n.