Related papers: Recursive Generation of The Semi-Classical Expansi…
The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation…
For a subquadratic symbol $H$ on $\R^d\times\R^d = T^*(\R^d)$, the quantum propagator of the time dependent Schr\"odinger equation $i\hbar\frac{\partial\psi}{\partial t} = \hat H\psi$ is a Semiclassical Fourier-Integral Operator when $\hat…
Nonlinear time-dependent partial differential equations are essential in modeling complex phenomena across diverse fields, yet they pose significant challenges due to their computational complexity, especially in higher dimensions. This…
Quantum computation is an emerging technology that promises to be a powerful tool in many areas. Though some years likely still remain until significant quantum advantage is demonstrated, the development of the technology has led to a range…
We present a detailed theory of spectacular semiclassical catastrophes happening during the time evolution of a kicked quantum rotor (Phys.Rev. Lett. {\bf 87}, 163601 (2001)). Both two- and three-dimensional rotational systems are analyzed.…
The quantum mechanical expression relating two commuting operators is reformulated such that the power method (also called method of moments) for iteratively calculating eigenvalues and eigenvectors becomes applicable. The new iterative…
The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
Random pulse sequences are a powerful method for qubit noise spectroscopy, enabling efficient reconstruction of sparse noise spectra. Here, we advance this method in two complementary directions. First, we extend the method using a…
We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation…
Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing…
In arXiv:2204.03190, we proposed a universal method to reduce one-loop integrals with both tensor structure and higher-power propagators. But the method is quite redundant as it does not utilize the results of lower rank cases when…
Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has…
Unbound wave packets propagating to macroscopic space and time coordinates become proportional to their (Fourier transform) momentum distribution at earlier times whereby the asymptotic coordinates and the initial momenta are connected…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
We present a simple stochastic algorithm for generating multiplicative processes with multiscaling both in space and in time. With this algorithm we are able to reproduce a synthetic signal with the same space and time correlation as the…
A primary goal of computer experiments is to reconstruct the function given by the computer code via scattered evaluations. Traditional isotropic Gaussian process models suffer from the curse of dimensionality, when the input dimension is…
We present a new scheme for the general computation of cosmic propagators that allow to interpolate between standard perturbative results at low-k and their expected large-k resummed behavior. This scheme is applicable to any multi-point…
We discuss the implementation of arbitrary precision composite pulses developed using the methods of Brown et al. [Phys. Rev. A 70 (2004) 052318]. We give explicit results for pulse sequences designed to tackle both the simple case of pulse…
Classical molecular dynamics simulation is performed mostly using the established velocity Verlet integrator or other symplectic propagation schemes. In this work, an alternative formulation of numerical propagators for classical molecular…