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We propose a method for providing unbiased estimators of multiple observables with low statistical error by utilizing informationally (over)complete measurements and tensor networks. The technique consists of an observable-specific classical optimization of the measurement data based on tensor networks leading to low-variance estimations. Compared to other observable estimation protocols based on classical shadows and measurement frames, our approach offers several advantages: (i) it can be optimized to provide lower statistical error, resulting in a reduced measurement budget to achieve a specified estimation precision; (ii) it scales to a large number of qubits due to the tensor network structure; (iii) it can be applied to any measurement protocol with measurement operators that have an efficient representation in terms of tensor networks. We benchmark the method through various numerical examples, including spin and chemical systems in both infinite and finite statistics scenarios, and show how optimal estimation can be found even when we use tensor networks with low bond dimensions., Comment: 20 pages, 4 figures. Updated version with corrected typos and minor modifications

Characterization of noise in current near-term quantum devices is of paramount importance to fully use their computational power. However, direct quantum process tomography becomes unfeasible for systems composed of tens of qubits. A promising alternative method based on tensor networks was recently proposed [Nat. Commun. 14, 2858 (2023)]. In this paper, we adapt it for the characterization of noise channels on near-term quantum computers and investigate its performance thoroughly. In particular, we show how experimentally feasible tomographic samples are sufficient to accurately characterize realistic correlated noise models affecting individual layers of quantum circuits, and study its performance on systems composed of up to 20 qubits. Furthermore, we combine this noise characterization method with a recently proposed noise-aware tensor network error mitigation protocol for correcting outcomes in noisy circuits, resulting accurate estimations even on deep circuit instances. This positions the tensor-network-based noise characterization protocol as a valuable tool for practical error characterization and mitigation in the near-term quantum computing era., Comment: Updated version matching publication (minor modifications, added section on SPAM errors)

Quantum noise is currently limiting efficient quantum information processing and computation. In this work, we consider the tasks of reconstructing and classifying quantum states corrupted by the action of an unknown noisy channel using classical feedforward neural networks. By framing reconstruction as a regression problem, we show how such an approach can be used to recover with fidelities exceeding 99% the noiseless density matrices of quantum states of up to three qubits undergoing noisy evolution, and we test its performance with both single-qubit (bit-flip, phase-flip, depolarising, and amplitude damping) and two-qubit quantum channels (correlated amplitude damping). Moreover, we also consider the task of distinguishing between different quantum noisy channels, and show how a neural network-based classifier is able to solve such a classification problem with perfect accuracy.

This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief summary of quantum computing and an in-depth analysis of variational quantum algorithms. The discussion then shifts to quantum machine learning, where an introduction to the elements of machine learning and statistical learning theory is followed by a review of the most common quantum counterparts of machine learning models. Next, several novel contributions to the field based on previous work are presented, namely: a newly introduced model for a quantum perceptron with applications to recognition and classification tasks; a variational generalization of such a model to reduce the circuit footprint of the proposed architecture; an industrial use case of a quantum autoencoder followed by a quantum classifier used to analyze classical data from an industrial power plant; a study of the entanglement features of quantum neural network circuits; and finally, a noise deconvolution technique to remove a large class of noise when performing arbitrary measurements on qubit systems., Comment: Final thesis for the Ph.D in Physics at the University of Pavia, 220 pages

Variational quantum machine learning algorithms have become the focus of recent research on how to utilize near-term quantum devices for machine learning tasks. They are considered suitable for this as the circuits that are run can be tailored to the device, and a big part of the computation is delegated to the classical optimizer. It has also been hypothesized that they may be more robust to hardware noise than conventional algorithms due to their hybrid nature. However, the effect of training quantum machine learning models under the influence of hardware-induced noise has not yet been extensively studied. In this work, we address this question for a specific type of learning, namely variational reinforcement learning, by studying its performance in the presence of various noise sources: shot noise, coherent and incoherent errors. We analytically and empirically investigate how the presence of noise during training and evaluation of variational quantum reinforcement learning algorithms affect the performance of the agents and robustness of the learned policies. Furthermore, we provide a method to reduce the number of measurements required to train Q-learning agents, using the inherent structure of the algorithm., Comment: 30 pages, 17 figures

Quantum Neural Networks (QNN) are considered a candidate for achieving quantum advantage in the Noisy Intermediate Scale Quantum computer (NISQ) era. Several QNN architectures have been proposed and successfully tested on benchmark datasets for machine learning. However, quantitative studies of the QNN-generated entanglement have been investigated only for up to few qubits. Tensor network methods allow to emulate quantum circuits with a large number of qubits in a wide variety of scenarios. Here, we employ matrix product states to characterize recently studied QNN architectures with random parameters up to fifty qubits showing that their entanglement, measured in terms of entanglement entropy between qubits, tends to that of Haar distributed random states as the depth of the QNN is increased. We certify the randomness of the quantum states also by measuring the expressibility of the circuits, as well as using tools from random matrix theory. We show a universal behavior for the rate at which entanglement is created in any given QNN architecture, and consequently introduce a new measure to characterize the entanglement production in QNNs: the entangling speed. Our results characterise the entanglement properties of quantum neural networks, and provides new evidence of the rate at which these approximate random unitaries., Comment: 27 pages, 12 figures. Accepted in Quantum 2023-04-11. Code available at https://github.com/mballarin97/mps_qnn

Several proposals have been recently introduced to implement Quantum Machine Learning (QML) algorithms for the analysis of classical data sets employing variational learning means. There has been, however, a limited amount of work on the characterization and analysis of quantum data by means of these techniques, so far. This work focuses on one such ambitious goal, namely the potential implementation of quantum algorithms allowing to properly classify quantum states defined over a single register of $n$ qubits, based on their degree of entanglement. This is a notoriously hard task to be performed on classical hardware, due to the exponential scaling of the corresponding Hilbert space as $2^n$. We exploit the notion of "entanglement witness", i.e., an operator whose expectation values allow to identify certain specific states as entangled. More in detail, we made use of Quantum Neural Networks (QNNs) in order to successfully learn how to reproduce the action of an entanglement witness. This work may pave the way to an efficient combination of QML algorithms and quantum information protocols, possibly outperforming classical approaches to analyse quantum data. All these topics are discussed and properly demonstrated through a simulation of the related quantum circuit model., Comment: Accepted for publication at IEEE WCCI 2022

Quantum computing technologies are in the process of moving from academic research to real industrial applications, with the first hints of quantum advantage demonstrated in recent months. In these early practical uses of quantum computers it is relevant to develop algorithms that are useful for actual industrial processes. In this work we propose a quantum pipeline, comprising a quantum autoencoder followed by a quantum classifier, which are used to first compress and then label classical data coming from a separator, i.e., a machine used in one of Eni's Oil Treatment Plants. This work represents one of the first attempts to integrate quantum computing procedures in a real-case scenario of an industrial pipeline, in particular using actual data coming from physical machines, rather than pedagogical data from benchmark datasets., Comment: 12 pages, 9 figures. To appear on Quantum Machine Intelligence

We present a noise deconvolution technique to remove a wide class of noises when performing arbitrary measurements on qubit systems. In particular, we derive the inverse map of the most common single qubit noisy channels and exploit it at the data processing step to obtain noise-free estimates of observables evaluated on a qubit system subject to known noise. We illustrate a self-consistency check to ensure that the noise characterization is accurate providing simulation results for the deconvolution of a generic Pauli channel, as well as experimental evidence of the deconvolution of decoherence noise occurring on Rigetti quantum hardware., Comment: 17 pages, 3 figures. Updated version taking into account the referee's comments. Added references and minor changes

In this paper, we discuss the initial attempts at boosting understanding human language based on deep-learning models with quantum computing. We successfully train a quantum-enhanced Long Short-Term Memory network to perform the parts-of-speech tagging task via numerical simulations. Moreover, a quantum-enhanced Transformer is proposed to perform the sentiment analysis based on the existing dataset.

In the last few years, quantum computing and machine learning fostered rapid developments in their respective areas of application, introducing new perspectives on how information processing systems can be realized and programmed. The rapidly growing field of Quantum Machine Learning aims at bringing together these two ongoing revolutions. Here we first review a series of recent works describing the implementation of artificial neurons and feed-forward neural networks on quantum processors. We then present an original realization of efficient individual quantum nodes based on variational unsampling protocols. We investigate different learning strategies involving global and local layer-wise cost functions, and we assess their performances also in the presence of statistical measurement noise. While keeping full compatibility with the overall memory-efficient feed-forward architecture, our constructions effectively reduce the quantum circuit depth required to determine the activation probability of single neurons upon input of the relevant data-encoding quantum states. This suggests a viable approach towards the use of quantum neural networks for pattern classification on near-term quantum hardware., Comment: 10 pages, 8 figures. Pre-submission manuscript, see DOI for the final version

Neural networks are computing models that have been leading progress in Machine Learning (ML) and Artificial Intelligence (AI) applications. In parallel, the first small scale quantum computing devices have become available in recent years, paving the way for the development of a new paradigm in information processing. Here we give an overview of the most recent proposals aimed at bringing together these ongoing revolutions, and particularly at implementing the key functionalities of artificial neural networks on quantum architectures. We highlight the exciting perspectives in this context and discuss the potential role of near term quantum hardware in the quest for quantum machine learning advantage., Comment: Pre-submission manuscript, see DOI for the final version

Artificial neural networks have been proposed as potential algorithms that could benefit from being implemented and run on quantum computers. In particular, they hold promise to greatly enhance Artificial Intelligence tasks, such as image elaboration or pattern recognition. The elementary building block of a neural network is an artificial neuron, i.e. a computational unit performing simple mathematical operations on a set of data in the form of an input vector. Here we show how the design for the implementation of a previously introduced quantum artificial neuron [npj Quant. Inf. $\textbf{5}$, 26], which fully exploits the use of superposition states to encode binary valued input data, can be further generalized to accept continuous -- instead of discrete-valued input vectors, without increasing the number of qubits. This further step is crucial to allow for a direct application of an automatic differentiation learning procedure, which would not be compatible with binary-valued data encoding.

We present a model of Continuous Variable Quantum Perceptron (CVQP) whose architecture implements a classical perceptron. The necessary non-linearity is obtained via measuring the output qubit and using the measurement outcome as input to an activation function. The latter is chosen to be the so-called ReLu activation function by virtue of its practical feasibility and the advantages it provides in learning tasks. The encoding of classical data into realistic finitely squeezed states and the use of superposed (entangled) input states for specific binary problems are discussed., Comment: 16 pages, 2 figures