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A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first con- tribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i)…
The goal of this article is to introduce the Hamiltonian Monte Carlo (HMC) method -- a Hamiltonian dynamics-inspired algorithm for sampling from a Gibbs density $\pi(x) \propto e^{-f(x)}$. We focus on the "idealized" case, where one can…
The quasicontinuum (QC) method, originally proposed by Tadmor, Ortiz and Phillips in 1996, is a computational technique that can efficiently handle regular atomistic lattices by combining continuum and atomistic approaches. In the present…
We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with…
Accurately modeling robot dynamics is crucial to safe and efficient motion control. In this paper, we develop and apply an iterative learning semi-parametric model, with a neural network, to the task of autonomous racing with a Model…
We introduce random-LCHS, a circuit-efficient randomized-compilation framework for simulating linear non-unitary dynamics of the form $\partial_t u(t) = -A(t) u(t) + b(t)$ built on the linear combination of Hamiltonian simulation (LCHS). We…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
Mapping methods, including the Meyer-Miller-Stock-Thoss (MMST) mapping and spin-mapping, are commonly utilised to simulate nonadiabatic dynamics by propagating classical mapping variable trajectories. Recent work confirmed the Momentum…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
Several disciplines, such as econometrics, neuroscience, and computational psychology, study the dynamic interactions between variables over time. A Bayesian nonparametric model known as the Wishart process has been shown to be effective in…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
This paper introduces a novel nonlinear model predictive control (NMPC) framework that incorporates a lifting technique to enhance control performance for nonlinear systems. While the lifting technique has been widely employed in linear…
The universal mathematical form of machine-learning potentials (MLPs) shifts the core of development of interatomic potentials to collecting proper training data. Ideally, the training set should encompass diverse local atomic environments…
Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC…
We derive the theory of open quantum system dynamics intervened by a series of nonselective measurements. We analyze the cases of time independent and time dependent Hamiltonian dynamics in between the measurements and find the approximate…
We introduce a new approach to deriving approximate analytical solutions of a harmonic oscillator damped by purely nonlinear, or combinations of linear and nonlinear damping forces. Our approach is based on choosing a suitable trial…
We review a dynamical approach to non-equilibrium MD (D-NEMD). We show how, using a proper simulation setup, is possible to treat interesting cases in which the initial condition is a stationary non-equilibrium state produced by a suitable…
We use the effective Hamiltonian that we recently fitted against the first 306 experimentally observed vibronic transitions of NO2 [J. Chem. Phys. 119, 5923 (2003)] to investigate the time domain nonadiabatic dynamics of this molecule on…
It is a challenge to obtain an accurate model of the state-to-state dynamics of a complex biological system from molecular dynamics (MD) simulations. In recent years, Markov State Models have gained immense popularity for computing…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…