Related papers: Wei-Norman equations for a unitary evolution
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an…
Nonadiabatic unitary evolution with tailored time-dependent Hamiltonians can prepare systems of cold atomic gases with various desired properties. For a system of two one-dimensional quasicondensates coupled with a time-varying tunneling…
From weather to neural networks, modeling is not only useful for understanding various phenomena, but also has a wide range of potential applications. Although nonlinear differential equations are extremely useful tools in modeling, their…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
This note contains a short and simple proof of Wormald's differential equation method (that yields slightly improved approximation guarantees and error probabilities). This powerful method uses differential equations to approximate the…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
Having a broad range of methods available for implementing unitary operations is crucial for quantum information tasks. We study a dissipative process commonly used to describe dissipatively coupled systems and show that the process can…
We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterize the feasibility of…
As it is known various dynamical processes can be modeled through the systems of time-fractional order pseudo-differential equations. In the modeling process one frequently faces with determining the adequate orders of time-fractional…
Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…
A normal ordered exponential parametrization is used to obtain equations for thermal one-and two-particle reduced density matrices, as well as free energies, partition functions and entropy for both Fermionic (electronic) and Bosonic…
Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…
The data-driven techniques have been developed to deal with the output regulation problem of unknown linear systems by various approaches. In this paper, we first extend an existing algorithm from single-input single-output linear systems…
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
An approach to stochastic evolution equations based on a simple generalization of known embedding theorems is presented. It allows for the inclusion of problems which have nonlinear non monotone operators. This is used to discuss the…
We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or nonstationary quantum states. In particular we discuss the stationary states of quantum systems with singular velocity fields. We introduce a…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation…
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…