Related papers: A gradient system on the quantum information space…

Gradient-based meta-learning methods leverage gradient descent to learn the commonalities among various tasks. While previous such methods have been successful in meta-learning tasks, they resort to simple gradient descent during…

A `register' in quantum information processing -- is composition of k quantum systems, `qudits'. The dimensions of Hilbert spaces for one qudit and whole quantum register are d and d^k respectively, but we should have possibility to prepare…

We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…

The paper presents a generalization bound for quantum neural networks based on a dynamical Lie algebra. Using covering numbers derived from a dynamical Lie algebra, the Rademacher complexity is derived to calculate the generalization bound.…

Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to…

Two-level systems are one of the most important quantum systems and they form the basis of quantum computers. We briefly look at the traditional approach to two-level systems with an external driving field as well as those subjected to…

There are two classes of quantum integrable systems on a manifold with quadratic integrals, the Liouville and the Lie integrable systems as it happens in the classical case. The quantum Liouville quadratic integrable systems are defined on…

We introduce a unified framework -- Quantum Neural Ordinary and Partial Differential Equations (QNODEs and QNPDEs) -- which extends the continuous-time formalism of classical neural ordinary and partial differential equations into quantum…

This thesis explores adaptive inference as a tool to characterize quantum systems using experimental data, with applications in sensing, calibration, control, and metrology. I propose and test algorithms for learning Hamiltonian and Kraus…

Edge machine learning involves the deployment of learning algorithms at the wireless network edge so as to leverage massive mobile data for enabling intelligent applications. The mainstream edge learning approach, federated learning, has…

Intrusion Detection Systems (IDSs) must maintain high detection sensitivity while operating under strict false-positive constraints, a challenge intensified by class imbalance and heterogeneous IoT traffic. This work investigates whether…

This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…

We study the natural gradient method for learning in deep Bayesian networks, including neural networks. There are two natural geometries associated with such learning systems consisting of visible and hidden units. One geometry is related…

This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation…

We propose a mathematical framework that we call quantum, higher-order Fourier analysis. This generalizes the classical theory of higher-order Fourier analysis, which led to many advances in number theory and combinatorics. We define a…

We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…

The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…

Quantum machine learning (QML) has emerged as an innovative framework with the potential to uncover complex patterns by leveraging quantum systems ability to simulate and exploit high-dimensional latent spaces, particularly in learning…

In order to exploit quantum advantages, quantum algorithms are indispensable for operating machine learning with quantum computers. We here propose an intriguing hybrid approach of quantum information processing for quantum linear…

We consider machine learning applications that train a model by leveraging data distributed over a trusted network, where communication constraints can create a performance bottleneck. A number of recent approaches propose to overcome this…