相关论文: Computing the Kalman form

Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…

By the Gottesman-Knill Theorem, the outcome probabilities of Clifford circuits can be computed efficiently. We present an alternative proof of this result for quopit Clifford circuits (i.e., Clifford circuits on collections of $p$-level…

A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…

A numerical algorithm to obtain the consistent conditions satisfied by singular arcs for singular linear-quadratic optimal control problems is presented. The algorithm is based on the presymplectic constraint algorithm (PCA) by Gotay-Nester…

Large-scale distributed systems such as sensor networks, often need to achieve filtering and consensus on an estimated parameter from high-dimensional measurements. Running a Kalman filter on every node in such a network is computationally…

Here we revisit the classic problem of linear quadratic estimation, i.e. estimating the trajectory of a linear dynamical system from noisy measurements. The celebrated Kalman filter gives an optimal estimator when the measurement noise is…

Clustering algorithms have regained momentum with recent popularity of data mining and knowledge discovery approaches. To obtain good clustering in reasonable amount of time, various meta-heuristic approaches and their hybridization,…

As electronic structure simulations continue to grow in size, the system-size scaling of computational costs increases in importance relative to cost prefactors. Presently, linear-scaling costs for three-dimensional systems are only…

In order to compute Hermitian forms on representations of real reductive groups, in the unequal rank case, it is necessary to compute twisted Kazhdan-Lusztig-Vogan polynomials. These were defined by Lusztig and Vogan (Quasisplit Hecke…

In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.

We describe an algorithm to solve Bellman optimization that replaces a sum over paths determining the optimal cost-to-go by an analytic method localized in state space. Our approach follows from the established relation between stochastic…

We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…

Quantum advantage in computation refers to the existence of computational tasks that can be performed efficiently on a quantum computer but cannot be efficiently simulated on any classical computer. Identifying the precise boundary of…

Herein, we present a polylogarithmic decomposition method to load the matrix from the linearized 1-dimensional Burgers' equation onto a quantum computer. First, we use the Carleman linearization method to map the nonlinear Burgers' equation…

We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…

We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterize the feasibility of…

In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting $L_1$-regularizer term. We first formulate such problems as minimization of the sum of linear or nonlinear quadratic error…

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…

The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…

We study the task of learning state representations from potentially high-dimensional observations, with the goal of controlling an unknown partially observable system. We pursue a cost-driven approach, where a dynamic model in some latent…