Related papers: The operator sum-difference representation for qua…
The so-called Lindblad equation, a typical master equation describing the dissipative quantum dynamics, is shown to be solvable for finite-level systems in a compact form without resort to writing it down as a set of equations among matrix…
In quantum computation, amplitude estimation is a fundamental subroutine that is utilized in various quantum algorithms. A general important task of such estimation problems is to characterize the estimation lower bound, which is referred…
In this paper, we examine the non-relativistic stationary Schr\"odinger equation from a differential Galois-theoretic perspective. The main algorithmic tools are pullbacks of second order ordinary linear differential operators, so as to…
We show that the time evolution of density operator of open qubit system can always be described in terms of the Kraus representation. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can…
We investigate the second-order von Neumann approach from a diagrammatic point-of-view and demonstrate its equivalence with the resonant tunneling approximation. Investigation of higher-order diagrams shows that the method correctly…
Undergraduate quantum mechanics focuses on teaching through a wavefunction approach in the position-space representation. This leads to a differential equation perspective for teaching the material. However, we know that abstract…
Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large\rev{-}scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized…
This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…
We introduce a new superintegrable Kepler-Coulomb system with non-central terms in $N$-dimensional Euclidean space. We show this system is multiseparable and allows separation of variables in hyperspherical and hyperparabolic coordinates.…
The representation theory of the generalized deformed oscillator algebras (GDOA's) is developed. GDOA's are generated by the four operators ${1,a,a^{\dag},N}$. Their commutators and Hermiticity properties are those of the boson oscillator…
The Brownian dynamics of the density operator for a quantum system interacting with a classical heat bath is described using a stochastic, non-linear Liouville equation obtained from a variational principle. The environment's degrees of…
In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods…
Given a quantum channel it is possible to define the non-commutative operator graph whose properties determine a possibility of error-free transmission of information via this channel. The corresponding graph has a straight definition…
Given a list of n complex numbers, when can it be the spectrum of a quantum channel, i.e., a completely positive trace preserving map? We provide an explicit solution for the n=4 case and show that in general the characterization of the…
Quadratic Unconstrained Binary Optimization (QUBO) problems are prevalent in real-world applications, such as portfolio optimization, but pose significant computational challenges for large-scale instances. We propose a hybrid…
Theoretical tools used in processing continuous measurement records from real experiments to obtain quantum trajectories can easily lead to numerical errors due to a non-infinitesimal time resolution. In this work, we propose a systematic…
We study quantum tunneling through a potential barrier whose height fluctuates in time and is modeled by Gaussian white noise. We map the stochastic dynamics onto an equivalent time-independent Lindblad equation for the density matrix,…
A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical…
We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a…
In a remarkable paper, T. Koslowski introduced kinematical representations for loop quantum gravity in which there is a non-degenerate spatial background metric present. He also considered their properties, and showed that Gauss and…