Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large-scale eigenvalue problems using quantum computers. Unfortunately, these require the solution ill-conditioned generalized problem, with a matrix pencil corrupted by nonnegligible amount noise that is far above machine precision. Despite pessimistic predictions from classical worst-case perturbation...

A new procedure to diagonalize quadratic Hamiltonians is introduced. We show that one can find a unitary transformation such the transformed Hamiltonian diagonal but still written in terms of original position and momentum observables. give general method an arbitrary derive few simplest special cases detail.

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant ...

To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource. It allows one, in principle, to diagonalize hermitean (N × N) matrices by quantum mechanical measurements only. To do so, one considers the given matrix as an observable of a single spin wit...

the optical spectrum band positions and epr parameters (g factors g//, g^ and hyperfine structure constants a// and a^) for vo2+ ions in zn(antipyrine)2(no3)2 are theoretically studied from the complete diagonalization (of energy matrix) method (cdm) and the perturbation theory method (ptm). in the two methods, the contributions from the spin–orbit (so) coupling of central 3dn ion and ligand ar...

Of the many approaches to non-perturbative quantum field theory, we can identify two general computational strategies. The first is the method of Monte Carlo. The main advantages of this approach is that it can treat many higher dimensional field theories, requires relatively little storage, and can be performed with massively parallel computers. The other strategy is the method of explicit dia...

The two-by-two Sp(2) matrix has three parameters with unit determinant. Yet, there are no established procedures for diagonalizing this matrix. It is shown that this matrix can be written as a similarity transformation of the two-by-two Wigner matrix, derivable from Wigner’s little group which dictates the internal space-time symmetries of relativistic particles. The Wigner matrix can be diagon...

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with high-order filter polynomials obtained from a regularized Chebyshev expansion of a window function. After a short discussion of the conceptual foun...