Related papers: High-order geometric integrators for the local cub…
We present a quadrotor dynamics Gaussian Process (GP) with gradient information that achieves real-time inference via state-space partitioning and approximation, and that includes aerodynamic effects using data from mid-fidelity potential…
There is a growing interest in the conservation of invariants when numerically solving a system of ordinary differential equations. Methods that exactly preserve these quantities in time are known as geometric integrators. In this paper we…
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…
Dynamical quantum simulation may be one of the first applications to see quantum advantage. However, the circuit depth of standard Trotterization methods can rapidly exceed the coherence time of noisy quantum computers. This has led to…
A mixed semiclassical initial value representation expression for spectroscopic calculations is derived. The formulation takes advantage of the time-averaging filtering and the hierarchical properties of different trajectory based…
Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single…
Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
Variational hybrid quantum-classical algorithms are some of the most promising workloads for near-term quantum computers without error correction. The aim of these variational algorithms is to guide the quantum system to a target state that…
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the…
During the noisy intermediate-scale quantum (NISQ) era, quantum computational approaches refined to overcome the challenge of limited quantum resources are highly valuable. However, the accuracy of the molecular properties predicted by most…
By exploiting the invariance of the molecular Hamiltonian by a unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in the Variational Quantum Eigensolver (VQE) algorithm by…
The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…
This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to…
We study the computation of Gaussian orthant probabilities, i.e. the probability that a Gaussian falls inside a quadrant. The Geweke-Hajivassiliou-Keane (GHK) algorithm [Genz, 1992; Geweke, 1991; Hajivassiliou et al., 1996; Keane, 1993], is…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
This work discusses the model reduction problem for large-scale multi-symplectic PDEs with cubic invariants. For this, we present a linearly implicit global energy-preserving method to construct reduced-order models. This allows to…
This paper is concerned with geometric exponential energy-preserving integrators for solving charged-particle dynamics in a magnetic field from normal to strong regimes. We firstly formulate the scheme of the methods for the system in a…
Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to…
Determining low-energy eigenstates in electronic many-body quantum systems is a key challenge in computational chemistry and condensed-matter physics. Hybrid quantum-classical approaches, such as the Variational Quantum Eigensolver and…