相关论文: Global Error Control in the Runge-Kutta Solution o…
Ensemble methods in machine learning aim to improve prediction accuracy by combining multiple models. This is achieved by ensuring diversity among predictors to capture different data aspects. Homogeneous ensembles use identical models,…
We develop a protocol for continuous operation of a quantum error correcting code for protection of coherent evolution due to an encoded Hamiltonian against environmental errors, using the three qubit bit flip code and bit flip errors as a…
In this work we consider a mixed precision approach to accelerate the implemetation of multi-stage methods. We show that Runge-Kutta methods can be designed so that certain costly intermediate computations can be performed as a…
The reliability and precision of numerically solving stochastic non-Markovian equations by standard numerical codes, more specifically, with the fourth-order Runge-Kutta routine for solving differential equations, is gauged by comparing the…
With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between…
In quantum engineering, faults may occur in a quantum control system, which will cause the quantum control system unstable or deteriorate other relevant performance of the system. This note presents an estimator-based fault-tolerant control…
Accurate tracking of planned trajectories in the presence of perturbations is an important problem in control and robotics. Symmetry is a fundamental mathematical feature of many dynamical systems and exploiting this property offers the…
This paper develops a general methodology for a posteriori error estimation in time-dependent multiphysics numerical simulations. The methodology builds upon the generalized-structure additive Runge--Kutta (GARK) approach to time…
Accurate methods of assessing the performance of quantum gates are extremely important. Quantum process tomography and randomized benchmarking are the current favored methods. Quantum process tomography gives detailed information, but…
Finite precision computations using digital computers involve the following inherent errors: (1) Round-off error of finite precision computations (2) Binary computer arithmetic precludes exact number representation of traditional decimal…
This paper presents a one-shot learning approach with performance and robustness guarantees for the linear quadratic regulator (LQR) control of stochastic linear systems. Even though data-based LQR control has been widely considered,…
Based on reasonable testing model problems, we study the preservation by symplectic Runge-Kutta method (SRK) and symplectic partitioned Runge-Kutta method (SPRK) of structures for fixed points of linear Hamiltonian systems. The…
Recent advancements in quantum technologies have highlighted the importance of mitigating system imperfections, including parameter uncertainties and decoherence effects, to improve the performance of experimental platforms. However, most…
We present a blueprint for building a fault-tolerant universal quantum computer with Rydberg atoms. Our scheme, which is based on the surface code, uses individually-addressable optically-trapped atoms as qubits and exploits…
Quantum information is very fragile to environmentally and operationally induced imperfections. Therefore, the construction of practical quantum computers requires quantum error-correction techniques to protect quantum information. In…
We generalize the idea of relaxation time stepping methods in order to preserve multiple nonlinear conserved quantities of a dynamical system by projecting along directions defined by multiple time stepping algorithms. Similar to the…
We study symplectic numerical integration of mechanical systems with a Hamiltonian specified in non-canonical coordinates and its application to guiding-center motion of charged plasma particles in magnetic confinement devices. The…
The design of time-independent local Hamiltonians that realise quantum algorithms is derived from the study of perfect state transfer. The novel features of this evolution are the perfect realisation of the computation, and the ability to…
A standard approach to solve ordinary differential equations, when they describe dynamical systems, is to adopt a Runge-Kutta or related scheme. Such schemes, however, are not applicable to the large class of equations which do not…
This paper is concerned with linear-quadratic-Gaussian (LQG) control for a field-mediated feedback connection of a plant and a coherent (measurement-free) controller. Both the plant and the controller are multimode open quantum harmonic…