Q where A; G and Q are real matrices. A number of applications from n£n control theory and related areas lead to eigenvalue problems involving such matrices, with a stronger emphasis …

Problem: Consider a quantum system for which the exact Hamiltonian is H. Assume the quantum system is of bounded spatial extend, so that it is known rigorously that the eigenstates of H, …

Find the eigenvalues and (normalized) eigenvectors of H, A, and B. Suppose the system starts out in the generic state c1 S(0) = c2 , c3

We will discuss the relation of structured and unstructured condition numbers for these problems as well as algorithms exploiting the given matrix structures. Applications of Hamiltonian and …

It provides subroutines for computing eigenvalues, eigenvectors, and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices, as well as structured Schur forms and several …

We develop a universal algorithm that deterministically implements any desired (suitably differentiable) function on the eigenvalues of any unknown Hamiltonian, whose positive-time …

In one of the problems of the previous section we discussed that an important operator used in quantum computation is the Hadamard gate, which is represented by the matrix: Determine …

May 12, 2022 · I would like to solve an eigenvalue problem of a Hamiltonian. I was able to find the lowest eigenvalue by converting the Hamiltonian into a matrix and applying linear algebra …

Solving large Hamiltonian eigenvalue problems David S. Watkins [email protected] Department of Mathematics Washington State University

As an example consider problems with Hamiltonian eigensymmetry. It has been shown in Freiling, Mehrmann & Xu (2002) and Ran & Rodman (1988, 1989) that the problem may be well …