Related papers: Boltzmann machine learning with a variational quan…
In the context of quantum information, highly nonlinear regimes, such as those supporting solitons, are marginally investigated. We miss general methods for quantum solitons, although they can act as entanglement generators or as…
Restricted Boltzmann machines are used for probabilistic learning and are capable of capturing complex dependencies in data. They are employed for diverse purposes such as dimensionality reduction, feature learning and can be used for…
As one of the main governing equations in kinetic theory, the Boltzmann equation is widely utilized in aerospace, microscopic flow, etc. Its high-resolution simulation is crucial in these related areas. However, due to the high…
Variational Quantum Algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In variational quantum algorithm, wavefunction represented by a parametrized…
Inference is the task of drawing conclusions about unobserved variables given observations of related variables. Applications range from identifying diseases from symptoms to classifying economic regimes from price movements. Unfortunately,…
This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping…
We train a set of Restricted Boltzmann Machines (RBMs) on one- and two-dimensional Ising spin configurations at various values of temperature, generated using Monte Carlo simulations. We validate the training procedure by monitoring several…
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…
Simulating properties of quantum materials is one of the most promising applications of quantum computation, both near- and long-term. While real-time dynamics can be straightforwardly implemented, the finite temperature ensemble involves…
We devise a lattice Boltzmann method (LBM) for a matrix-valued quantum Boltzmann equation, with the classical Maxwell distribution replaced by Fermi-Dirac functions. To accommodate the spin density matrix, the distribution functions become…
Boltzmann generators (BGs) are now recognized as forefront generative models for sampling equilibrium states of many-body systems in the canonical ensemble, as well as for calculating the corresponding Helmholtz free energy. Furthermore,…
Restricted Boltzmann machines (RBMs) are endowed with the universal power of modeling (binary) joint distributions. Meanwhile, as a result of their confining network structure, training RBMs confronts less difficulties (compared with more…
Quantum neural networks (QNNs) are a framework for creating quantum algorithms that promises to combine the speedups of quantum computation with the widespread successes of machine learning. A major challenge in QNN development is a…
We explore alternative experimental setups for the iterative sampling (flow) from Restricted Boltzmann Machines (RBM) mapped on the temperature space of square lattice Ising models by a neural network thermometer. This framework has been…
While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…
Calibration is a common experimental physics problem, whose goal is to infer the value and uncertainty of an unobservable quantity Z given a measured quantity X. Additionally, one would like to quantify the extent to which X and Z are…
Compared to point estimates calculated by standard neural networks, Bayesian neural networks (BNN) provide probability distributions over the output predictions and model parameters, i.e., the weights. Training the weight distribution of a…
The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the systems behavior. In addition, empirical data typically…
Boiling is a complex phenomenon where different non-linear physical interactions take place and for which the quantitative modeling of the mechanism involved is not fully developed yet. In the last years, many works have been published…
The problem of identifying the phase of a given system for a certain value of the temperature can be reformulated as a classification problem in Machine Learning. Taking as a prototype the Ising model and using the Support Vector Machine as…