Related papers: Application of the variational $R$-matrix method t…
We design variational pulse sequences tailored for neutral atom quantum simulators and show that we can engineer layers of single-qubit and multi-qubit gates. As an application, we discuss how the proposed method can be used to perform…
Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle…
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the…
We calculate the tunneling process of a Dirac particle across two square barriers separated a distance $d$, as well as the scattering by a double cusp barrier where the centers of the cusps are separated a distance larger than their…
In this paper an exponential multiplicative formula for the R-matrix is provided for the twisted affine quantum algebras.
We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding…
The variational quantum Monte Carlo (VQMC) method received significant attention in the recent past because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems. Close parallels exist between VQMC and…
The complex-time method for quantum tunneling is studied. In one-dimensional quantum mechanics, we construct a reduction formula for a Green function in the number of turning points based on the WKB approximation. This formula yields a…
Superconducting qubits already demonstrated potential in emulating coherent back scattering or weak localization (WL) and tunnelling phenomena however, in a real multipath system they have not been verified yet.Here we show how a…
Recurrent quantum models (RQMs) realize sequential quantum processes through repeated application of a unitary operation on a memory system coupled with a series of output registers. However, such models often rely on unnecessarily large…
We consider the optimization problem of minimizing an objective functional, which admits a variational form and is defined over probability distributions on the constrained domain, which poses challenges to both theoretical analysis and…
We present a global optimization routine for the variational quantum algorithms, which utilizes the dynamic tunneling flow. Originally designed to leverage information gathered by a gradient-based optimizer around local minima, we adapt the…
Despite the practicality of quantile regression (QR), simultaneous estimation of multiple QR curves continues to be challenging. We address this problem by proposing a Bayesian nonparametric framework that generalizes the quantile pyramid…
Quantum tunneling from a thin wire or a thin film through a static potential barrier in a zero magnetic field is studied. The wire or the film should satisfy a condition of transverse quantization of levels and be inhomogeneous. Depending…
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in…
We present a variational Monte Carlo (VMC) method that works equally well for the ground and the excited states of a quantum system. The method is based on the minimization of the variance of energy, as opposed to the energy itself in…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
We propose a variational alternative to the Trotter-Suzuki decomposition that provides greater control over errors while preserving the unitary structure of time evolution. The variational parameters in our ansatz are derived from a global…
The R-matrix method is a fully-quantum time-independent scattering method, used to simulate nuclear, electron-atom, electron-ion, electron-molecule scattering and more. Here, a novel R-matrix method, RmatReact, is presented as applied to…
One-dimensional scattering problem admitting a complex, PT-symmetric short-range potential V(x) is considered. Using a Runge-Kutta-discretized version of Schroedinger equation we derive the formulae for the reflection and transmission…