Related papers: Exact Numerical Solution of the BCS Pairing Proble…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to…
Comprehending the dynamical behaviour of quantum systems driven by time-varying Hamiltonians is particularly difficult. Systems with as little as two energy levels are not yet fully understood as the usual methods including diagonalisation…
A great variety of fundamental optimization and counting problems arising in computer science, mathematics and physics can be reduced to one of the following computational tasks involving polynomials and set systems: given an $m$-variate…
We present an efficient method to solve the problem of the constrained least squares approximation of the rational B\'{e}zier curve by the B\'{e}zier curve. The presented algorithm uses the dual constrained Bernstein basis polynomials,…
We present a Bayesian scheme for the approximate diagonalisation of several square matrices which are not necessarily symmetric. A Gibbs sampler is derived to simulate samples of the common eigenvectors and the eigenvalues for these…
In this work we revisit the problem of solving multi-matrix systems through numerical large $N$ methods. The framework is a collective, loop space representation which provides a constrained optimization problem, addressed through…
The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems…
In this work, the problem of optimizing damper positions in vibrational systems is investigated. The objective is to determine the positions of external dampers in such a way that the influence of the input on the output is minimized. The…
We study and exactly solve the two-photon and k-photon Jaynes-Cummings models by using a novelty algebraic method. This algebraic method is based on the Pauli matrices realization and the tilting transformation of the $SU(2)$ group and let…
We propose a modification of the GPGCD algorithm, which has been presented in our previous research, for calculating approximate greatest common divisor (GCD) of more than 2 univariate polynomials with real coefficients and a given degree.…
We impose U spin symmetry ($SU(2)_{\rm Uspin}$) on the Hamiltonian for $B$ decays. As expected, we find the equality of amplitudes related by the exchange $d \leftrightarrow s$. We also find that the amplitudes for the $\Delta S=0$…
We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (enviroment). An exact solution of the Schrodinger equation with the paradigmatic spin-boson Hamiltonian is obtained.…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
We study Bosonic representation of spin Ising model with the application of simulating two level systems using continuous variable quantum processors. We decompose the time evolution of spin systems into a sequence of continuous variable…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…
We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. For various quantum algorithms, in particular in the context of quantum chemistry, it is crucial to have energy…
We present an ab initio stochastic method for calculating thermal properties of a trapped, 1D Bose-gas covering the whole range from weak to strong interactions. Discretization of the problem results in a Bose-Hubbard-like Hamiltonian,…
The simulation of quantum systems is one of the most promising applications of quantum computers. In this paper we present a quantum algorithm to perform digital quantum simulations of the BCS model on a quantum register with a star shaped…
This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the…