Related papers: A gradient system on the quantum information space…
In the paper of Uwano [Czech. J. of Phys., vol.56, pp.1311-1316 (2006)], a gradient system is found on the space of density matrices endowed with the quantum SLD Fisher metric (to be referred to as the quantum information space) that…
Optimization in large language models (LLMs) unfolds over high-dimensional parameter spaces with non-Euclidean structure. Information geometry frames this landscape using the Fisher information metric, enabling more principled learning via…
A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…
In the NISQ (Noisy intermediate-scale quantum) area, Quantum computers can be utilized for deep learning by treating variational quantum circuits as neural network models. This can be achieved by first encoding the input data onto quantum…
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose,…
In this paper, two families of trajectories on the quantum state space (QSS) originating from a synaptic-neuron model and from quantum information geometry meet together. The extended averaged Hebbian learning equation (EAHLE) on the QSS…
We introduce the attention-indexed model (AIM), a theoretical framework for analyzing learning in deep attention layers. Inspired by multi-index models, AIM captures how token-level outputs emerge from layered bilinear interactions over…
In a variety of physically relevant settings for learning from quantum data, designing protocols that can computationally efficiently extract information remains largely an art, and there are important cases where we believe this to be…
Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given…
Machine learning is a powerful method of extracting meaning from data; unfortunately, current digital hardware is extremely energy-intensive. There is interest in an alternative analog computing implementation that could match the…
The parameters of the quantum circuit in a variational quantum algorithm induce a landscape that contains the relevant information regarding its optimization hardness. In this work we investigate such landscapes through the lens of…
The expectation that quantum computation might bring performance advantages in machine learning algorithms motivates the work on the quantum versions of artificial neural networks. In this study, we analyze the learning dynamics of a…
Within the algebraic framework of Hopf algebras, random walks and associated diffusion equations (master equations) are constructed and studied for two basic operator algebras of Quantum Mechanics i.e the Heisenberg-Weyl algebra (hw) and…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…
Machine learning has been presented as one of the key applications for near-term quantum technologies, given its high commercial value and wide range of applicability. In this work, we introduce the \textit{quantum-assisted Helmholtz…
Gradient estimation is a central challenge in training parameterized quantum circuits (PQCs) for hybrid quantum-classical optimization and learning problems. This difficulty arises from several factors, including the exponential…
An Ising machine is any hardware specifically designed for finding the ground state of the Ising model. Relevant examples are coherent Ising machines and quantum annealers. In this paper, we propose a new machine learning model that is…
Hybrid quantum neural networks are increasingly explored for classification, yet it remains unclear how their performance and quantum behavior scale with circuit depth and qubit count. We present a controlled scaling study of hybrid…
Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters,…