相关论文: Designing LU-QR hybrid solvers for performance and…

Modular architectures are a promising approach to scaling quantum computers to fault tolerance. Small, low-noise quantum processors connected through relatively noisy quantum links are capable of fault-tolerant operation as long as the…

Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite element methods. Mortar methods enable a variationally consistent imposition of coupling…

Clustering algorithms are at the basis of several technological applications, and are fueling the development of rapidly evolving fields such as machine learning. In the recent past, however, it has become apparent that they face challenges…

We introduce a new framework for the exact point-wise $\ell_p$ robustness verification problem that exploits the layer-wise geometric structure of deep feed-forward networks with rectified linear activations (ReLU networks). The activation…

Traditional time discretization methods use a single timestep for the entire system of interest and can perform poorly when the dynamics of the system exhibits a wide range of time scales. Multirate infinitesimal step (MIS) methods (Knoth…

This paper revisits and extends the convergence and robustness properties of value and policy iteration algorithms for discrete-time linear quadratic regulator problems. In the model-based case, we extend current results concerning the…

The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…

The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…

In order to exploit quantum advantages, quantum algorithms are indispensable for operating machine learning with quantum computers. We here propose an intriguing hybrid approach of quantum information processing for quantum linear…

Sparse linear system solvers are computationally expensive kernels that lie at the heart of numerous applications. This paper proposes a flexible preconditioning framework to substantially reduce the time and energy requirements of this…

Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…

A wide range of applications necessitates solving large-scale ill-posed problems contaminated by noise. Krylov subspace regularization methods are particularly advantageous in this context, as they rely solely on matrix-vector…

Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…

Quantum Phase Estimation (QPE) is a cardinal algorithm in quantum computing that plays a crucial role in various applications, including cryptography, molecular simulation, and solving systems of linear equations. However, the standard…

We present efficient realization of Householder Transform (HT) based QR factorization through algorithm-architecture co-design where we achieve performance improvement of 3-90x in-terms of Gflops/watt over state-of-the-art multicore,…

The paper describes the robust algorithm for linear time-invariant plants under parametric uncertainties, external disturbances and high-frequency noises in measurements. The proposed algorithm allows one to reduce the noise impact on the…

We survey the numerical stability of some fast algorithms for solving systems of linear equations and linear least squares problems with a low displacement-rank structure. For example, the matrices involved may be Toeplitz or Hankel. We…

Trajectory optimization is a popular strategy for planning trajectories for robotic systems. However, many robotic tasks require changing contact conditions, which is difficult due to the hybrid nature of the dynamics. The optimal sequence…

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…

The efficient and accurate QR decomposition for matrices with hierarchical low-rank structures, such as HODLR and hierarchical matrices, has been challenging. Existing structure-exploiting algorithms are prone to numerical instability as…