Applications of the Schur Basis to Quantum Algorithms
Isaac L. Chuang, Aram W. Harrow · 2011
Abstract : Quantum computation offers a promising avenue to high performance computing, for certain applications, but depends on development of new quantum algorithms. Thus far, all major quantum algorithms which are exponentially fast compared with classical counterparts are based on the quantum Fourier transform. This project seeks to develop new quantum algorithms, based on a different mathematical transform known as the Schur transform. The Schur transform (or Schur-Weyl duality) arises naturally in many areas of mathematics, chemistry, and physics, and many applications of it have now been found in quantum coding and information theory. This project has also led to the efficient quantum circuits for the Schur transform, and a new quantum algorithm for superpolynomial speedups based on quantum circuits.