Related papers: Inference, interference and invariance: How the Qu…
Quantum entanglement is the quintessence of quantum information processing mostly limited to the microscopic regime governed by Heisenberg uncertainty principle. For practical applications, however, macroscopic entanglement gives great…
Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
This paper presents a quantum-based Fourier-regression approach for machine learning hyperparameter optimization applied to a benchmark of models trained on a dataset related to a forecast problem in the airline industry. Our approach…
As in classical reversible computing, Quantum Arithmetic is typically seen as a set of tools that process binary data encoded into a quantum register to set the value of another quantum register. This article presents another approach to…
Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and…
We present one- and two-photon diffraction and interference experiments involving parametric down-converted photon pairs. By controlling the divergence of the pump beam in parametric down-conversion, the diffraction-interference pattern…
One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the…
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle.…
Kearns' statistical query (SQ) oracle (STOC'93) lends a unifying perspective for most classical machine learning algorithms. This ceases to be true in quantum learning, where many settings do not admit, neither an SQ analog nor a quantum…
By means of a simple example it is demonstrated that the task of finding and identifying certain patterns in an otherwise (macroscopically) unstructured picture (data set) can be accomplished efficiently by a quantum computer. Employing the…
Reinforcement learning algorithms have been widely used for decision-making tasks in various domains. However, the performance of these algorithms can be impacted by high variance and instability, particularly in environments with noise or…
Ensemble methods in machine learning aim to improve prediction accuracy by combining multiple models. This is achieved by ensuring diversity among predictors to capture different data aspects. Homogeneous ensembles use identical models,…
We give a quantum algorithm for solving a shifted multiplicative character problem over Z/nZ and finite fields. We show that the algorithm can be interpreted as a matrix factorization or as solving a deconvolution problem and give…
Class imbalance in training datasets can lead to bias and poor generalization in machine learning models. While pre-processing of training datasets can efficiently address both these issues in centralized learning environments, it is…
We consider algebras underlying Hilbert spaces used by quantum information algorithms. We show how one can arrive at equations on such algebras which define n-dimensional Hilbert space subspaces which in turn can simulate quantum systems on…
The double slit experiment provides a clear demarcation between classical and quantum theory, while multi-slit experiments demarcate quantum and higher-order interference theories. In this work we show that these experiments pertain to a…
Characterizing quantum systems through experimental data is critical to applications as diverse as metrology and quantum computing. Analyzing this experimental data in a robust and reproducible manner is made challenging, however, by the…
In higher-order quantum computing (HOQC), one typically considers the universal transformation of unknown quantum operations, treated as blackboxes. It is also implicitly assumed that the resulting operation must act on arbitrary, and thus…