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Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…
Hamiltonian simulation is a central task in quantum computing, with wide-ranging applications in quantum chemistry, condensed matter physics, and combinatorial optimization. A fundamental challenge lies in approximating the unitary…
First order methods, which solely rely on gradient information, are commonly used in diverse machine learning (ML) and data analysis (DA) applications. This is attributed to the simplicity of their implementations, as well as low…
In this paper we investigate the parallelization of two modular algorithms. In fact, we consider the modular computation of Gr\"obner bases (resp. standard bases) and the modular computation of the associated primes of a zero-dimensional…
We give classical and quantum algorithms for approximately solving second-order cone programs (SOCPs) based on the multiplicative weights (MW) update method. Our approach follows the MW framework previously applied to semidefinite programs…
Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has…
Hamiltonian simulation is a fundamental algorithm in quantum computing that has attracted considerable interest owing to its potential to efficiently solve the governing equations of large-scale classical systems. Exponential speedup…
We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster…
Langevin simulation provides an effective way to study collisional effects in beams by reducing the six-dimensional Fokker-Planck equation to a group of stochastic ordinary differential equations. These resulting equations usually have…
A stochastic iterative algorithm approximating second-order information using von Neumann series is discussed. We present convergence guarantees for strongly-convex and smooth functions. Our analysis is much simpler in contrast to a similar…
One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the…
We present the constructon and detailed analysis of highly-optimized self-refocusing pulse shapes for several rotation angles. We characterize the constructed pulses by the coefficients appearing in the Magnus expansion up to second order.…
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…
By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the…
Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in…
Historically speaking, it is hard to balance the global and local efficiency of second-order optimization algorithms. For instance, the classical Newton's method possesses excellent local convergence but lacks global guarantees, often…
The Stochastic Primal-Dual Hybrid Gradient (SPDHG) was proposed by Chambolle et al. (2018) and is an efficient algorithm to solve some nonsmooth large-scale optimization problems. In this paper we prove its almost sure convergence for…
We develop new numerical schemes for Vlasov--Poisson equations with high-order accuracy. Our methods are based on a spatially monotonicity-preserving (MP) scheme and are modified suitably so that positivity of the distribution function is…