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 Hμ called HYPs (Hermitian Young Projectors) for n particles with d colors or, equivalently, for n qu(d)its. Hμ projects out n particle irrep μ of U(d).

主权项

1. A method of operating a classical computer to calculate a total SEO, with the purpose of using said total SEO to operate a quantum computer, and to induce said quantum computer to undergo a unitary transformation U that acts on n qu(d)its, wherein U simultaneously diagonalizes a set of operators Hμ, that satisfies the H-properties, wherein said U can be expressed in the formU=∑μHμDμ,wherein each operator Dμ lives in μ with respect to a set of Jμ operators that satisfies the J-properties, wherein said total SEO comprises a product of unitary operators Λμ554 , wherein each Λμ is designed to diagonalize for the matrix to which it is applied, all rows or columns corresponding to index μ.