Method For Projecting Out Irreducible Representations From a Quantum State of n Particles with d Colors

摘要

We describe a method for using a classical computer to generate a particular sequence of elementary operations (SEO), an instruction set for a quantum computer. Such a SEO will induce a quantum computer to perform a unitary transformation U that we call an Irreps Gen U. This U simultaneously diagonalizes a set of operators H_μ called HYPs (Hermitian Young Projectors) for n particles with d colors or, equivalently, for n qu(d)its. H_μ projects out n particle irrep μ of U(d).