Related papers: Extended Power Method to Calculate Pre-Selectable …
The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is applied to the $H_\alpha \equiv P^2 + iX^3 + i\alpha X$ Hamiltonian, enabling the algebraic/numerical generation of converging bounds to the complex energies of the…
We demonstrate the application of the recently introduced parametric projector operator technique to a calculation of the second order non-linear optical response of a multilevel molecular system. We derive a parametric quantum master…
We study the simultaneous estimation of multiple phases as a discretised model for the imaging of a phase object. We identify quantum probe states that provide an enhancement compared to the best quantum scheme for the estimation of each…
In this paper, we consider the operator properties of various phononic eigenvalue problems. We aim to answer some fundamental questions about the eigenvalues and eigenvectors of phononic operators. These include questions about the…
The large moment method can be used to compute a large number of moments of physical quantities that are described by coupled systems of linear differential equations. Besides these systems the algorithm requires a certain number of initial…
We investigate how the choice of decision makers can be varied under the presence of risk and uncertainty. Our analysis is based on the approach we have previously applied to individual decision makers, which we now generalize to the case…
Quantum mechanical methods have been devised for the elucidation and clarification of reaction paths of chemical processes over decades. While they are typically deployed in routine calculations on systems for which some insights have…
We study quantum equivalents of non-commutative operators in quantum mechanics. Any matrix "$B$" satisfying the non-commuting relation $[A,B]\neq 0$ with "$A$", can be used via $B^{-1} AB$ to reproduce eigenvalues of "$A$". This…
Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated…
The advantage that many quantum algorithms have over their classical counterparts may be lost when the results are extracted as classical data (output problem). One example are eigenpair solvers, which encode the eigenpairs in a quantum…
The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take…
Solving eigenvalue problems is crucially important for both classical and quantum applications. Many well-known numerical eigensolvers have been developed, including the QR and the power methods for classical computers, as well as the…
We delineate the scope of research on the completeness of eigenstates in quantum mechanics. Based on the limit of the potential function at infinity, the proof of completeness is divided into eight cases, and theoretical proofs or numerical…
The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bi-partite quantum state-space. When the…
We study the maximal amount of energy that can be extracted from a finite quantum system by means of projective measurements. For this quantity we coin the expression "metrotropy" $\mathcal{M}$, in analogy with "ergotropy" $\mathcal{W}$,…
We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate…
VQE is currently one of the most widely used algorithms for optimizing problems using quantum computers. A necessary step in this algorithm is calculating the expectation value given a state, which is calculated by decomposing the…
An iterative algorithm for the reconstruction of an unknown quantum state from the results of incompatible measurements is proposed. It consists of Expectation-Maximization step followed by a unitary transformation of the eigenbasis of the…
A well-known method of transferring the population of a quantum system from an eigenspace of the free Hamiltonian to another is to use a periodic control law with an angular frequency equal to the difference of the eigenvalues. For finite…
Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper…