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Quantum systems are exceedingly difficult to engineer because they are sensitive to various types of noises. In particular, time-dependent noises are frequently encountered in experiments but how to overcome them remains a challenging…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
We show that there exist non-relativistic scattering experiments which, if successful, freeze out, speed up or even reverse the free dynamics of any ensemble of quantum systems present in the scattering region. This time translation effect…
We present a machine-learning method for predicting sharp transitions in a Hamiltonian phase diagram by extrapolating the properties of quantum systems. The method is based on Gaussian Process regression with a combination of kernels chosen…
The superposition of data sets with internal parametric self-similarity is a longstanding and widespread technique for the analysis of many types of experimental data across the physical sciences. Typically, this superposition is performed…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
Data assimilation in models representing spatio-temporal phenomena poses a challenge, particularly if the spatial histogram of the variable appears with multiple modes. The traditional Kalman model is based on a Gaussian initial…
Evolutionary deep neural networks have emerged as a rapidly growing field of research. This paper studies numerical integrators for such and other classes of nonlinear parametrizations $ u(t) = \Phi(\theta(t)) $, where the evolving…
Transformer architectures have been widely adopted for time series forecasting, yet whether the representational mechanisms that make them powerful in NLP actually engage on time series data remains unexplored. The persistent…
The method of regularization with the Gaussian reproducing kernel is popular in the machine learning literature and successful in many practical applications. In this paper we consider the periodic version of the Gaussian kernel…
Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…
The Koopman operator, as a linear representation of a nonlinear dynamical system, has been attracting attention in many fields of science. Recently, Koopman operator theory has been combined with another concept that is popular in data…
Marginalization techniques are presented for the Bayesian filtering problem under the assumption of Gaussian priors and posteriors and a set of sequentially more constraining state space model assumptions. The techniques provide the…
An efficient method to coherently control the waveforms of gamma-photons has been proposed and experimentally realized. It is based on the resonant interaction of gamma-photons with an ensemble of nuclei with modulated frequency of the…
Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian…
A number of physically intuitive results for the calculation of multi-time correlations in phase-space representations of quantum mechanics are obtained. They relate time-dependent stochastic samples to multi-time observables, and rely on…
We study a novel class of open-loop control protocols constructed to perform arbitrary nontrivial single-qubit logic operations robust against time-dependent non-Markovian noise. Amplitude and phase modulation protocols are crafted…
In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions.…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
Koopman operator theory is a key tool in data assimilation of complex dynamical systems, with the potential to be applied to multimodal data. We formulate the problem of learning Koopman eigenfunctions from observations at arbitrary,…