Related papers: Storage Capacity Evaluation of the Quantum Percept…
Within a Kuhn-Tucker cavity method introduced in a former paper, we study optimal stability learning for situations, where in the replica formalism the replica symmetry may be broken, namely (i) the case of a simple perceptron above the…
Quantum reservoir computing has emerged as a promising paradigm within the field of quantum machine learning, harnessing the inherent properties of quantum systems to optimise and enhance information processing capabilities. Here, we…
The use of advanced quantum neuron models for pattern recognition applications requires fault tolerance. Therefore, it is not yet possible to test such models on a large scale in currently available quantum processors. As an alternative, we…
The capacity of a classical-quantum channel (or in other words the classical capacity of a quantum channel) is considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a…
Quantum reservoir computing (QRC) leverages the natural dynamics of quantum systems to process time-series data efficiently, offering a promising approach for near-term quantum devices. Unlike classical reservoir computing, the efficacy of…
Perceptrons with graded input-output relations and a limited output precision are studied within the Gardner-Derrida canonical ensemble approach. Soft non- negative error measures are introduced allowing for extended retrieval properties.…
We present a pedagogical, hands-on tutorial on \emph{replica tensor-network} techniques for random quantum circuits. At its core, the method recasts circuit-averaged observables acting on multiple copies of the system as the contraction of…
In the field of quantum reservoir computing (QRC), many different computational models and architectures have been proposed. From these models, we identify feedback-based models -- which use a feedback mechanism to re-embed classical…
Perceptron model is a fundamental linear classifier in machine learning and also the building block of artificial neural networks. Recently, Wiebe et al. (arXiv:1602.04799) proposed that the training of a perceptron can be quadratically…
Feedback-based control is the de-facto standard when it comes to controlling classical stochastic systems and processes. However, standard feedback-based control methods are challenged by quantum systems due to measurement induced…
We analysed the generalisation performance of a binary perceptron with quantum fluctuations using the replica method. An exponential number of local minima dominate the energy landscape of the binary perceptron. Local search algorithms…
For the past two decades, researchers have attempted to create a Quantum Neural Network (QNN) by combining the merits of quantum computing and neural computing. In order to exploit the advantages of the two prolific fields, the QNN must…
Reservoir computing (RC) is an effective method for predicting chaotic systems by using a high-dimensional dynamic reservoir with fixed internal weights, while keeping the learning phase linear, which simplifies training and reduces…
In this paper we consider the classical spherical perceptron problem. This problem and its variants have been studied in a great detail in a broad literature ranging from statistical physics and neural networks to computer science and pure…
Characterizing a system often demands learning its response function to an applied field. Such knowledge is rooted on the experimental evaluation of punctual fiducial response and interpolation to access prediction at arbitrary values.…
In this paper, we address the problem of how many randomly labeled patterns can be correctly classified by a single-layer perceptron when the patterns are correlated with each other. In order to solve this problem, two analytical schemes…
Classical feedback is defined here as the knowledge by the transmitter of the quantum state of the qubit received by the receiver. Such classical feedback doubles capacities of certain memoryless quantum channels without preexisting…
Quantum reservoir computing uses the dynamics of quantum systems to process temporal data, making it particularly well-suited for machine learning with noisy intermediate-scale quantum devices. Recent developments have introduced…
A central challenge in machine learning is to distinguish genuine structure from chance correlations in high-dimensional data. In this work, we address this issue for the perceptron, a foundational model of neural computation. Specifically,…
A recent method to certify the classical capacity of quantum communication channels is applied for general damping channels in finite dimension. The method compares the mutual information obtained by coding on the computational and a…