Related papers: Optimally Convergent Quantum Jump Expansion
Accurate derivatives are important for efficiently locally traversing and converging in quantum optimization landscapes. By deriving analytically exact control derivatives (gradient and Hessian) for unitary control tasks, we show here that…
We present the first higher-order approximation scheme for solutions of jump-diffusion stochastic differential equations with discontinuous drift. For this transformation-based jump-adapted quasi-Milstein scheme we prove $L^p$-convergence…
We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in $L^2([0,1))$ our…
We present a technique that enables the evaluation of perturbative expansions based on one-loop-renormalized vertices up to large expansion orders. Specifically, we show how to compute large-order corrections to the random phase…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
We study the use of approximate Lagrange multipliers and discrete actions in solving convex optimisation problems. We observe that descent, which can be ensured using a wide range of approaches (gradient, subgradient, Newton, etc.), is…
In this paper, we study stochastic optimization of areas under precision-recall curves (AUPRC), which is widely used for combating imbalanced classification tasks. Although a few methods have been proposed for maximizing AUPRC, stochastic…
We consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address…
Bayesian analysis for Markov jump processes is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding thus its applicability is limited to a small class of problems. In…
We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike…
In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has…
In this paper, we establish an abstract framework for the approximation of the invariant probability measure for a Markov semigroup. Following Pag{\`e}s and Panloup [40] we use an Euler scheme with decreasing step (unadjusted Langevin…
An important class of physical systems that are of interest in practice are input-output open quantum systems that can be described by quantum stochastic differential equations and defined on an infinite-dimensional underlying Hilbert…
This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…
Digital quantum simulation on quantum systems require algorithms that can be implemented using finite quantum resources. Recent studies have demonstrated digital quantum simulation of open quantum systems on Noisy Intermediate-Scale Quantum…
Physical quantum systems are generically coupled to an environment, resulting in open system dynamics. A typical approach to simulating this dynamics is to propagate the density matrix of the system via the Lindblad master equation. This…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…
We study the convergence of the derivative expansion for flow equations. The convergence strongly depends on the choice for the infrared regularisation. Based on the structure of the flow, we explain why optimised regulators lead to better…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…