Related papers: Optimizing stochastic trajectories in exact quantu…
By exploiting the complexity intrinsic to quantum dynamics, quantum technologies promise a whole host of computational advantages. One such advantage lies in the field of stochastic modelling, where it has been shown that quantum stochastic…
In power system steady-state estimation (PSSE), one needs to consider (1) the need for robust statistics, (2) the nonconvex transmission constraints, (3) the fast-varying nature of the inputs, and the corresponding need to track optimal…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
Stochastic thermodynamics is the field of study relating fluctuations in stochastic systems to thermodynamic quantities. The total entropy production (EP), is central to the thermodynamic classification of systems. Non-equilibrium systems…
We present a framework for simulating the open dynamics of spin-boson systems by combining variational non-Gaussian states with a quantum trajectories approach. We apply this method to a generic spin-boson Hamiltonian that has both…
A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the…
This article develops a stochastic differential equation (SDE) for modeling the temporal evolution of queue length dynamics at signalized intersections. Inspired by the observed quasiperiodic and self-similar characteristics of the queue…
It is well known that some quantum and statistical fluctuations of a quantum field may be recovered by adding suitable stochastic sources to the mean field equations derived from the Schwinger-Keldysh (Closed-time-path) effective action. In…
We present a theoretical analysis of some popular adaptive Stochastic Gradient Descent (SGD) methods in the small learning rate regime. Using the stochastic modified equations framework introduced by Li et al., we derive effective…
In this article, we introduce a kind of numerical schemes, based on Pad$\acute{e}$ approximation, for two stochastic Hamiltonian systems which are treated separately. For the linear stochastic Hamiltonian systems, it is shown that the…
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…
We present an optimal control-based strategy to enhance the estimation of impulse-like disturbances in continuously monitored linear classical and quantum systems by exploiting non-equilibrium states. Using optimal estimation techniques for…
Stochastic resonance is a phenomenon in which noise enhances the response of a system to an input signal. The brain is an example of a system that has to detect and transmit signals in a noisy environment, suggesting that it is a good…
We introduce a classical stochastic field method that accounts for the quantum fluctuations responsible for spontaneous initiation of various atom optics processes. We assume a delta-correlated Gaussian noise in all initially empty modes of…
We propose a sampling-based trajectory optimization methodology for constrained problems. We extend recent works on stochastic search to deal with box control constraints,as well as nonlinear state constraints for discrete dynamical…
Spin-squeezed states constitute a valuable entanglement resource capable of surpassing the standard quantum limit (SQL). However, spin-squeezed states only enable sub-SQL uncertainty within a narrow parametric window near some specific…
Stochastic gradient descent (SGD) is a frequently used optimization technique in classical machine learning and Variational Quantum Eigensolver (VQE). For the implementation of VQE on quantum hardware, the results are always affected by…
Assuming that the effect of the residual interaction beyond mean-field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of Markovian quantum jump are presented. A simplified…
The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum…