A Unitary Weights Based One-Iteration Quantum Perceptron Algorithm for Non-Ideal Training Sets

In order to solve the problem of non-ideal training sets (i.e., the less-complete or over-complete sets) and implement one-iteration learning, a novel efficient quantum perceptron algorithm based on unitary weights is proposed, where the singular value decomposition of the total weight matrix from the training set is calculated to make the weight matrix to be unitary. The example validation of quantum gates {H, S, T, CNOT, Toffoli, Fredkin} shows that our algorithm can accurately implement arbitrary quantum gates within one iteration. The performance comparison between our algorithm and other quantum perceptron algorithms demonstrates the advantages of our algorithm in terms of applicability, accuracy, and availability. For further validating the applicability of our algorithm, a quantum composite gate which consists of several basic quantum gates is also illustrated.Comment: 12 pages, 5 figure

Hierarchical quantum classifiers

Quantum circuits with hierarchical structure have been used to perform binary classification of classical data encoded in a quantum state. We demonstrate that more expressive circuits in the same family achieve better accuracy and can be used to classify highly entangled quantum states, for which there is no known efficient classical method. We compare performance for several different parameterizations on two classical machine learning datasets, Iris and MNIST, and on a synthetic dataset of quantum states. Finally, we demonstrate that performance is robust to noise and deploy an Iris dataset classifier on the ibmqx4 quantum computer

Simulations of a quantum perceptron on IBM-Qiskit

The principal aim of this thesis is to try to simulate the functioning of a quantum perceptron, that is an artificial neural network which task is to catalogue different input patterns. The model implemented has been tested through the realization of a learning procedure. This consists in teaching to the network to correctly recognize a pattern, in order to finally obtain a machine that is able to recognize an image. This procedure is fundamental in neural networks since it permits to the system, once it has been performed, to correctly recognize also patterns not encountered during learning. To this aim, this thesis will at first go through the explanation of some perceptron models in the first two chapters, and gives also in the Appendix some fundamental notions of quantum mechanics and quantum computing necessary for this treatment. In fact, the first chapter tries to explain how classical artificial neural networks have been thought and developed until now, in order to arrive to the theory of implementation of a perceptron and give some examples. Then, in the second chapter one of this models is taken and a perceptron of the same logic is implemented on a quantum circuit. This model of a quantum perceptron is then used in the third chapter and realized through a software development kit called Qiskit, provided by IBM Research. Here the steps followed for the implementation of the learning procedure will be explained and the results obtained will be analyzed. The process in which the machine is trained in this discussion is realized with a classical algorithm, and the quantum circuits have been run on a classical simulator, which behaves as an ideal quantum computer

A Novel Autonomous Perceptron Model for Pattern Classification Applications

Pattern classification represents a challenging problem in machine learning and data science research domains, especially when there is a limited availability of training samples. In recent years, artificial neural network (ANN) algorithms have demonstrated astonishing performance when compared to traditional generative and discriminative classification algorithms. However, due to the complexity of classical ANN architectures, ANNs are sometimes incapable of providing efficient solutions when addressing complex distribution problems. Motivated by the mathematical definition of a quantum bit (qubit), we propose a novel autonomous perceptron model (APM) that can solve the problem of the architecture complexity of traditional ANNs. APM is a nonlinear classification model that has a simple and fixed architecture inspired by the computational superposition power of the qubit. The proposed perceptron is able to construct the activation operators autonomously after a limited number of iterations. Several experiments using various datasets are conducted, where all the empirical results show the superiority of the proposed model as a classifier in terms of accuracy and computational time when it is compared with baseline classification models

Modern applications of machine learning in quantum sciences

In these Lecture Notes, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning

Towards Scalable Characterization of Noisy, Intermediate-Scale Quantum Information Processors

In recent years, quantum information processors (QIPs) have grown from one or two qubits to tens of qubits. As a result, characterizing QIPs – measuring how well they work, and how they fail – has become much more challenging. The obstacles to characterizing today’s QIPs will grow even more difficult as QIPs grow from tens of qubits to hundreds, and enter what has been called the “noisy, intermediate-scale quantum” (NISQ) era. This thesis develops methods based on advanced statistics and machine learning algorithms to address the difficulties of “quantum character- ization, validation, and verification” (QCVV) of NISQ processors. In the first part of this thesis, I use statistical model selection to develop techniques for choosing between several models for a QIPs behavior. In the second part, I deploy machine learning algorithms to develop a new QCVV technique and to do experiment design. These investigations help lay a foundation for extending QCVV to characterize the next generation of NISQ processors

Modern applications of machine learning in quantum sciences

In these Lecture Notes, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning.Comment: 268 pages, 87 figures. Comments and feedback are very welcome. Figures and tex files are available at https://github.com/Shmoo137/Lecture-Note