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We present a noise deconvolution technique for obtaining noiseless expectation values of noisy observables at the output of multiqubit quantum channels. For any number of qubits or in the presence of correlations, our protocol applies to…

Machine learning employs dynamical algorithms that mimic the human capacity to learn, where the reinforcement learning ones are among the most similar to humans in this respect. On the other hand, adaptability is an essential aspect to…

In comparative studies, such as in causal inference and clinical trials, balancing important covariates is often one of the most important concerns for both efficient and credible comparison. However, chance imbalance still exists in many…

Conducting pairwise comparisons is a widely used approach in curating human perceptual preference data. Typically raters are instructed to make their choices according to a specific set of rules that address certain dimensions of image…

Understanding the noise affecting a quantum device is of fundamental importance for scaling quantum technologies. A particularly important class of noise models is that of Pauli channels, as randomized compiling techniques can effectively…

Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large…

Before we attempt to learn a function between two (sets of) observables of a physical process, we must first decide what the inputs and what the outputs of the desired function are going to be. Here we demonstrate two distinct, data-driven…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

Materials and machines are often designed with particular goals in mind, so that they exhibit desired responses to given forces or constraints. Here we explore an alternative approach, namely physical coupled learning. In this paradigm, the…

The analysis of a continuous measurement record $z(t)$ poses a fundamental challenge in quantum measurement theory. Different approaches have been used in the past as records can, e.g., exhibit predominantly Gaussian noise, telegraph noise,…

We present a method for training a neural network to perform image denoising without access to clean training examples or access to paired noisy training examples. Our method requires only a single noisy realization of each training example…

Suppose an experiment is conducted on pairs of objects with outcome responses a continuous variable measuring the interactions among the pairs. Furthermore, assume the response variable is hard to measure numerically but easy to be coded…

When learning from positive and unlabelled data, it is a strong assumption that the positive observations are randomly sampled from the distribution of $X$ conditional on $Y = 1$, where X stands for the feature and Y the label. Most…

Humans can often predict physical outcomes after only a few observations, a capability known as physical intuition. The mechanisms underlying this efficient learning remain elusive. Here, we introduce a variational learning framework in…

We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function and then study numerically the impact of time-correlated noise on the time evolution of a 1 + 1 dimensional generalized Langevin…

This paper presents the first general (supervised) statistical learning framework for point processes in general spaces. Our approach is based on the combination of two new concepts, which we define in the paper: i) bivariate innovations,…

The topic of nonparametric estimation of smooth boundaries is extensively studied in the conventional setting where pairs of single covariate and response variable are observed. However, this traditional setting often suffers from the cost…

The state of a system in classical mechanics can be uniquely reconstructed if we know the positions and the momenta of all its parts. In 1958 Pauli has conjectured that the same holds for quantum mechanical systems. The conjecture turned…

Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a…

We present an error analysis of various tomographic protocols based on the linear inversion for the reconstruction of an unknown two-qubit state. We solve the problem of finding a tomographic protocol which is the most robust against errors…