Related papers: Multi-product Hamiltonian simulation with explicit…
Trotter and linear-combination-of-unitary (LCU) are two popular Hamiltonian simulation methods. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates…
The product formula, commonly known as Trotter decomposition, is a central tool for digital quantum simulation, whose performance depends critically on how the Hamiltonian is partitioned into tractable blocks. Standard decompositions…
Motivated by a real failure dataset in a two-dimensional context, this paper presents an extension of the Markov modulated Poisson process (MMPP) to two dimensions. The one-dimensional MMPP has been proposed for the modeling of dependent…
Model predictive control (MPC) is a powerful control method that handles dynamical systems with constraints. However, solving MPC iteratively in real time, i.e., implicit MPC, remains a computational challenge. To address this, common…
Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, but their efficient approximation capability remains unclear. We characterize this boundary from both negative and positive…
We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling…
This paper proposes a prescribed performance function aware hybrid gain finite time sliding mode control framework for a class of nonlinear systems subject to matched disturbances. The hybrid gain structure ensures bounded control effort…
We consider conditional tests for non-negative discrete exponential families. We develop two Markov Chain Monte Carlo (MCMC) algorithms which allow us to sample from the conditional space and to perform approximated tests. The first…
Coulomb collisions in particle simulations for weakly coupled plasmas are modeled by the Landau-Fokker-Planck equation, which is typically solved by Monte-Carlo (MC) methods. One of the main disadvantages of MC is the timestep accuracy…
Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a…
An algorithm for separating the high- and low-frequency molecular dynamics modes in Hybrid Monte Carlo simulations of gauge theories with dynamical fermions is presented. The separation is based on splitting the pseudo-fermion action into…
We propose a framework to design concurrently a frustration-free quantum many-body Hamiltonian and its numerically exact ground states on a sufficiently large finite-size cluster in one and two dimensions using an elementary matrix product…
We explore two complementary modifications of the hybridization-expansion continuous-time Monte Carlo method, aiming at large multi-orbital quantum impurity problems. One idea is to compute the imaginary-time propagation using a matrix…
Automatic differentiation (autodiff) has revolutionized machine learning. It allows to express complex computations by composing elementary ones in creative ways and removes the burden of computing their derivatives by hand. More recently,…
Prior to the recent development of symplectic integrators, the time-stepping operator $\e^{h(A+B)}$ was routinely decomposed into a sum of products of $\e^{h A}$ and $\e^{hB}$ in the study of hyperbolic partial differential equations. In…
Explicit model-predictive control (MPC) is a widely used control design method that employs optimization tools to find control policies offline; commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP in the case of…
We explore a reinforcement learning strategy to automate and accelerate h/p-multigrid methods in high-order solvers. Multigrid methods are very efficient but require fine-tuning of numerical parameters, such as the number of smoothing…
In the present work, a highly efficient Moving Morphable Component (MMC) based approach for multi-resolution topology optimization is proposed. In this approach, high-resolution optimization results can be obtained with much less number of…
Product formulae are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial…
Hamiltonian simulation is one of the most promising applications of quantum computers, and the product formula is one of the most important methods for this purpose. Previous related work has mainly focused on the worst$-$case or…