Related papers: On General Linearly Implicit Quantized State Syste…

The Logarithmic Linear Relaxation (LLR) algorithm is an efficient method for computing densities of states for systems with a continuous spectrum. A key feature of this method is exponential error reduction, which allows us to evaluate the…

For linear systems $Ax=b$ we develop iterative algorithms based on a sketch-and-project approach. By using judicious choices for the sketch, such as the history of residuals, we develop weighting strategies that enable short recursive…

A powerful method for solving non-linear first-order ordinary differential equations, which is based on geometrical understanding of the corresponding dynamics of the so called Lie systems, is developed. This method allows us not only to…

Hybrid dynamical systems pose significant challenges for effective planning and control, especially when additional constraints such as obstacle avoidance, state boundaries, and actuation limits are present. In this letter, we extend the…

Due to the strong correlations present in quantum systems, classical machine learning algorithms like stochastic gradient descent are often insufficient for the training of neural network quantum states (NQSs). These difficulties can be…

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…

The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix…

Cyber-physical systems involve a network of discrete controllers that control physical processes. Examples range from autonomous cars to implantable medical devices, which are highly safety critical. Hybrid Automata (HA) based formal…

Following the celebrated quantum algorithm for solving linear equations (so-called HHL algorithm), Childs, Kothari and Somma [SIAM Journal on Computing, {\bf 46}: 1920, (2017)] provided an approach to solve a linear system of equations with…

Measurement of entanglement remains an important problem for quantum information. We present the design and simulation of an experimental method for entanglement estimation for a general multiqubit state. The system can be in a pure or a…

In this paper, we propose a filtering algorithm for simultaneously estimating the mode, input and state of hidden mode switched linear stochastic systems with unknown inputs. Using a multiple-model approach with a bank of linear input and…

Hybrid quantum-classical algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In this paper, at first, we investigate a quantum dynamics algorithm for…

Considering some important classes of generalized coherent states known in literature, we demonstrated that all of them can be created via conventional fashion, i.e. the "lowering operator eigen-state" and the "displacement operator"…

Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…

Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle…

We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…

Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability properties from the differential inclusion. Their…

Black-box quantum state preparation is a fundamental primitive in quantum algorithms. Starting from Grover, a series of techniques have been devised to reduce the complexity. In this work, we propose to perform black-box state preparation…

This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…