Related papers: Improved transfer matrix methods for calculating q…
The transmission eigenvalues corresponding to the half-line Schr\"odinger equation with the general selfadjoint boundary condition is analyzed when the potential is real valued, integrable, and compactly supported. It is shown that a…
This article proposes a Variational Quantum Algorithm to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in…
Quantum tomography is a widely applicable tool for complete characterization of quantum states and processes. In the present work, we develop a method for precision-guaranteed quantum process tomography. With the use of the…
Free-space Quantum key distribution (QKD) allows two parties to share a random key with unconditional security, between ground stations, between mobile platforms, and even in satellite-ground quantum communications. Atmospheric turbulence…
We present a high-order shifted Gegenbauer pseudospectral method (SGPM) to solve numerically the second-order one-dimensional hyperbolic telegraph equation provided with some initial and Dirichlet boundary conditions. The framework of the…
We establish quantum dynamical lower bounds for a number of discrete one-dimensional Schr\"odinger operators. These dynamical bounds are derived from power-law upper bounds on the norms of transfer matrices. We develop further the approach…
We develop some new analytic bounds on transmission probabilities (and the related reflection probabilities and Bogoliubov coefficients) for generic one-dimensional scattering problems. To do so we rewrite the Schrodinger equation for some…
We study the evolution of the most general initial Gaussian packet with nonzero correlation coefficient between the coordinate and momentum operators in the presence of a repulsive delta potential barrier, using the known exact propagator…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…
We propose simple protocols for performing quantum noise spectroscopy based on the method of transfer tensor maps (TTM), [Phys. Rev. Lett. 112, 110401 (2014)]. The TTM approach is a systematic way to deduce the memory kernel of a…
Transfer learning has become an essential technique to exploit information from the source domain to boost performance of the target task. Despite the prevalence in high-dimensional data, heterogeneity and heavy tails are insufficiently…
This paper addresses the numerical implementation of the transparent boundary condition (TBC) and its various approximations for the free Schr\"odinger equation on a rectangular computational domain. In particular, we consider the exact TBC…
Measurement-induced phase transitions (MIPTs) are known to be described by non-unitary conformal field theories (CFTs) whose precise nature remains unknown. Most physical quantities of interest, such as the entanglement features of quantum…
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…
As a model for the semiclassical analysis of quantum-mechanical systems with both potentials and boundary conditions, we construct the WKB propagator for a linear potential sloping away from an impenetrable boundary. First, we find all…
We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schr\"odinger operators which is based on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply…
Quantum scattering by a one-dimensional odd potential proportional to the square of the distance to the origin is considered. The Schr\"odinger equation is solved exactly and explicit algebraic expressions of the wavefunction are given. A…
Using a method of local transmission matrix, we generalize the well-known WKB formula for a barrier penetrability to multi-channel systems. We compare the WKB penetrability with a solution of the coupled-channels equations, and show that…
We introduce the third independent exactly solvable hypergeometric potential, after the Eckart and the P\"oschl-Teller potentials, which is proportional to an energy-independent parameter and has a shape that is independent of this…