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Gaussian channels with memory and with noiseless feedback have been widely studied in the information theory literature. However, a coding scheme to achieve the feedback capacity is not available. In this paper, a coding scheme is proposed…
It was recently shown that the use of feedback control can improve the performance of a flashing ratchet. We investigate the effect of a time delay in the implementation of feedback control in a closed-loop collective flashing ratchet,…
This paper presents extensions of finite-time stability results to some prototypical adaptive control and estimation frameworks. First, we present a novel scheme of online parameter estimation that guarantees convergence of the estimation…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…
Time estimation is a fundamental task that underpins precision measurement, global navigation systems, financial markets, and the organisation of everyday life. Many biological processes also depend on time estimation by nanoscale clocks,…
Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give…
The thermodynamic uncertainty relation posits that higher thermodynamic costs are essential for a system to function with greater precision. Recent discussions have expanded thermodynamic uncertainty relations beyond classical…
The traditional approach to feedback control is to apply forces to a system by modifying the Hamiltonian. Here we show that quantum systems can be controlled without any Hamiltonian feedback, purely by exploiting the random quantum…
Quantum feedback control protocols can improve the operation of quantum devices. Here we examine the performance of a purification protocol when there are imperfections in the controls. The ideal feedback protocol produces an $x$ eigenstate…
Analog quantum simulation offers a hardware-specific approach to studying quantum dynamics, but mapping a model Hamiltonian onto the available device parameters requires matching the hardware dynamics. We introduce a paradigm for quantum…
Error correction is generally demanded in large-scale quantum information processing and quantum computation. We provide here a universal and realtime control strategy to dynamically correct the arbitrary type of errors in the system…
A technique is introduced for estimating unknown parameters when time series of only one variable from a multivariate nonlinear dynamical system is given. The technique employs a combination of two different control methods, a linear…
We revisit the problem of stochastic online learning with feedback graphs, with the goal of devising algorithms that are optimal, up to constants, both asymptotically and in finite time. We show that, surprisingly, the notion of optimal…
We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this…
For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case, such as: given a fixed interaction between the system…
Optimal control problems of tracking type for a class of linear systems with uncertain parameters in the dynamics are investigated. An affine tracking feedback control input is obtained by considering the minimization of an energy-like…
A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form $\theta G$. For such "phase shift Hamiltonians" it has been shown that…
The identification of environmental changes is crucial in many fields. The present research is aimed at investigating the optimal performance for detecting change points in a quantum system when its Hamiltonian suddenly changes at a…
This paper traces the strong relations between experimental design and control, such as the use of optimal inputs to obtain precise parameter estimation in dynamical systems and the introduction of suitably designed perturbations in…