Related papers: On the linear dispersion--linear potential quantum…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
The synchronization properties of two self-sustained quantum oscillators are studied in the Wigner representation. Instead of considering the quantum limit of the quantum van-der-Pol master equation we derive the quantum master equation…
Variational Quantum Algorithms (VQAs) have emerged as promising methods for tackling complex problems on near-term quantum devices. Among these algorithms, the Variational Quantum Linear Solver (VQLS) addresses linear systems of the form…
High-rate quantum error correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of non-local, many-body entanglement. We provide a linear-optical architecture with these properties,…
A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation.We find exact solutions of an equation for potential stationary…
A new approach to multi-dimensional quantum scattering by the infinite order discrete variable representation is presented. Determining the expansion coefficients of the wave function at the asymptotic regions by the solution of the…
Integrable systems on quantum groups are investigated. The Heisenberg equations possessing the Lax form are solved in terms of the solution to the factorization problem on the corresponding quantum group.
We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states…
In this paper, we investigate the quantum dynamics of underlying two one-dimensional quadratic Li'enard type nonlinear oscillators which are classified under the category of maximal (eight parameter) Lie point symmetry group (J. Math.…
We present lifted linear relaxations of the OPF problem.
A polynomial algorithm is obtained for the NP-complete linear ordering problem.
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
Multiple scale techniques are well-known in classical mechanics to give perturbation series free from resonant terms. When applied to the quantum anharmonic oscillator, these techniques lead to interesting features concerning the solution…
In the present work the classical problem of harmonic oscillator in the hyperbolic space $H_2^2$: $z_0^2+z_1^2-z_2^2-z_3^2=R^2$ has been completely solved in framework of Hamilton-Jacobi equation. We have shown that the harmonic oscillator…
We consider the semilinear wave equation $V(x) u_{tt} -u_{xx}+q(x)u = \pm f(x,u)$ for three different classes (P1), (P2), (P3) of periodic potentials $V,q$. (P1) consists of periodically extended delta-distributions, (P2) of periodic step…
We consider a planar doublebox with four massive external momenta and two massive internal propagators. We derive the system of differential equations for the relevant master integrals, cast it in canonical form, write it as a $d\log$ form…
In the present paper we study the existence of solutions for some classes of singular systems involving the p(x) and q(x) Laplacian operators. The approach is based on bifurcation theory and subsupersolution method for systems of…
The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of…
The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is…
With the advent of quantum computers, researchers are exploring if quantum mechanics can be leveraged to solve important problems in ways that may provide advantages not possible with conventional or classical methods. A previous work by…