Related papers: Mirror subspace diagonalization: A quantum Krylov …
Pipelined Krylov subspace methods avoid communication latency by reducing the number of global synchronization bottlenecks and by hiding global communication behind useful computational work. In exact arithmetic pipelined Krylov subspace…
We present new policy mirror descent (PMD) methods for solving reinforcement learning (RL) problems with either strongly convex or general convex regularizers. By exploring the structural properties of these overall highly nonconvex…
The dual tasks of quantum Hamiltonian learning and quantum Gibbs sampling are relevant to many important problems in physics and chemistry. In the low temperature regime, algorithms for these tasks often suffer from intractabilities, for…
To address the time-scale limitations in molecular dynamics (MD) simulations, numerous enhanced sampling methods have been developed to expedite the exploration of complex free energy landscapes. A commonly employed approach accelerates the…
Massive MIMO systems are seen by many researchers as a paramount technology toward next generation networks. This technology consists of hundreds of antennas that are capable of sending and receiving simultaneously a huge amount of data.…
In this work, we propose a reduced basis method for efficient solution of parametric linear systems. The coefficient matrix is assumed to be a linear matrix-valued function that is symmetric and positive definite for admissible values of…
Standard Markov chain Monte Carlo methods struggle to explore distributions that are concentrated in the neighbourhood of low-dimensional structures. These pathologies naturally occur in a number of situations. For example, they are common…
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propose the use of the extended Krylov subspace method for this…
Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…
In this paper, a symplectic model reduction technique, proper symplectic decomposition (PSD) with symplectic Galerkin projection, is proposed to save the computational cost for the simplification of large-scale Hamiltonian systems while…
Simulating quantum systems is one of the most promising tasks where quantum computing can potentially outperform classical computing. However, the robustness needed for reliable simulations of medium to large systems is beyond the reach of…
We study a Q learning algorithm for continuous time stochastic control problems. The proposed algorithm uses the sampled state process by discretizing the state and control action spaces under piece-wise constant control processes. We show…
We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource…
In classical frameworks as the Euclidean space, positive definite kernels as well as their analytic properties are explicitly available and can be incorporated directly in kernel-based learning algorithms. This is different if the…
Computing eigenvalues is a computationally intensive task central to numerous applications in the natural sciences. Toward this end, we investigate the quantum block Krylov subspace projector (QBKSP) algorithm - a multireference quantum…
In many operations management problems, we need to make decisions sequentially to minimize the cost while satisfying certain constraints. One modeling approach to study such problems is constrained Markov decision process (CMDP). When…
We propose a novel Krylov subspace method for estimating the finite impulse response (FIR) of a one-dimensional linear time-invariant systems. The method approximates the system's FIR using a kernel-based formulation combined with…
We develop a novel convergence analysis of the classical deterministic block Krylov methods for the approximation of $h$-dimensional dominant subspaces and low-rank approximations of matrices $ A\in\mathbb K^{m\times n}$ (where $\mathbb…
Sample-based quantum diagonalization (SQD) is a hybrid quantum-classical algorithm for estimating ground-state energies in electronic-structure calculations. It uses a quantum processor as a sampler to construct a variational subspace, with…
In this paper, we build and explore supervised learning models of ferromagnetic system behavior, using Monte-Carlo sampling of the spin configuration space generated by the 2D Ising model. Given the enormous size of the space of all…