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We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
Direct Preference Optimization (DPO) has been successfully used to align large language models (LLMs) according to human preferences, and more recently it has also been applied to improving the quality of text-to-image diffusion models.…
Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…
This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. The proposed methods are based on a specific subset of explicit one-step…
We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…
The Moody-Shapere-Wilczek's adiabatic effective Hamiltonian and Lagrangian method is developed further into the matrix effective Hamiltonian (MEH) and Lagrangian (MEL) approach to a parameter-dependent quantum system. The matrix-operator…
We present NEO, a fast and purely reactive motion controller for manipulators which can avoid static and dynamic obstacles while moving to the desired end-effector pose. Additionally, our controller maximises the manipulability of the robot…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In this context, the iterates are vectors generated from a…
Model Predictive Control (MPC) is widely used to achieve performance objectives, while enforcing operational and safety constraints. Despite its high performance, MPC often demands significant computational resources, making it challenging…
We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate…
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…
Solving partial differential equations (PDEs) efficiently is essential for analyzing complex physical systems. Recent advancements in leveraging deep learning for solving PDE have shown significant promise. However, machine learning…
Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay…
We introduce a matrix product operator (MPO) encoding of the Magnus expansion and the Dyson series for one-dimensional quantum lattice models with time-dependent Hamiltonians. The MPO construction can be made accurate up to arbitrary order…
Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally…
In this paper, we discuss the solution of certain matrix-valued partial differential equations. Such PDEs arise, for example, when constructing a Riemannian contraction metric for a dynamical system given by an autonomous ODE. We develop…
Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…
Recent studies suggest that gradient-based methods applied to relaxed box-constrained Quadratic Unconstrained Binary Optimization (QUBO) formulations can outperform classical heuristics in some large-scale regimes, often relying on heavy…
Quantum optimization methods use a continuous degree-of-freedom of quantum states to heuristically solve combinatorial problems, such as the MAX-CUT problem, which can be attributed to various NP-hard combinatorial problems. This paper…