Quantum Logical Neural Networks

Entropy

Despite its undeniable success, classical machine learning remains a resource-intensive process. Practical computational efforts for training state-of-the-art models can now only be handled by high speed computer hardware. As this trend is expected to continue, it should come as no surprise that an increasing number of machine learning researchers are investigating the possible advantages of quantum computing. The scientific literature on Quantum Machine Learning is now enormous, and a review of its current state that can be comprehended without a physics background is necessary. The objective of this study is to present a review of Quantum Machine Learning from the perspective of conventional techniques. Departing from giving a research path from fundamental quantum theory through Quantum Machine Learning algorithms from a computer scientist’s perspective, we discuss a set of basic algorithms for Quantum Machine Learning, which are the fundamental components for Quantum Machine Lea...

2017

The aim of the project is to study two of the most widely used machine learning strategies, namely KNearest Neighbours algorithm and Perceptron Learning algorithm, in a quantum setting, and study the speedups that the quantum modules allow over the classical counterparts. The study is primarily based on the following 3 papers: 1. Quantum Perceptron Models, by N. Wiebe, A. Kapoor and K. M. Svore. 2. Quantum Algorithm for K-Nearest Neighbors Classification Based on the Metric of Hamming Distance, by Y. Ruan, X. Xue, H. Liu, J. Tan, and X. Li. 3. Quantum Algorithms for Nearest-Neighbor Methods for Supervised and Unsupervised Learning, by N. Wiebe, A. Kapoor and K. M. Svore.

Archives of Computational Methods in Engineering, 2018

Quantum neural network is a useful tool which has seen more development over the years mainly after twentieth century. Like artificial neural network (ANN), a novel, useful and applicable concept has been proposed recently which is known as quantum neural network (QNN). QNN has been developed combining the basics of ANN with quantum computation paradigm which is superior than the traditional ANN. QNN is being used in computer games, function approximation, handling big data etc. Algorithms of QNN are also used in modelling social networks, associative memory devices, and automated control systems etc. Different models of QNN has been proposed by different researchers throughout the world but systematic study of these models have not been done till date. Moreover, application of QNN may also be seen in some of the related research papers. As such, this paper includes different models which have been developed and further the implement of the same in various applications. In order to understand the powerfulness of QNN, few results and reasons are incorporated to show that these new models are more useful and efficient than traditional ANN.

Information Sciences

It is shown by classical simulation and experimentation that quantum artificial neural networks (QUANNs) are more efficient and in some cases more powerful than classical artificial neural networks (CLANNs) for a variety of experimental tasks. This effect is particularly noticeable with larger and more complex domains. The gain in efficiency is achieved with no generalisation loss in most cases. QUANNs are also more powerful than CLANNs, again for some of the tasks examined, in terms of what the network can learn. What is more, it appears that not all components of a QUANN architecture need to to be quantum for these advantages to surface. It is demonstrated that a fully quantum neural network has no advantage over a partly quantum network and may in fact produce worse results. Overall, this work provides a first insight into the expected behaviour of individual components of QUANNs, if and when quantum hardware is ever built, and raises questions about the interface between quantum...

arXiv: Quantum Physics, 2018

This text aims to present and explain quantum machine learning algorithms to a data scientist in an accessible and consistent way. The algorithms and equations presented are not written in rigorous mathematical fashion, instead, the pressure is put on examples and step by step explanation of difficult topics. This contribution gives an overview of selected quantum machine learning algorithms, however there is also a method of scores extraction for quantum PCA algorithm proposed as well as a new cost function in feed-forward quantum neural networks is introduced. The text is divided into four parts: the first part explains the basic quantum theory, then quantum computation and quantum computer architecture are explained in section two. The third part presents quantum algorithms which will be used as subroutines in quantum machine learning algorithms. Finally, the fourth section describes quantum machine learning algorithms with the use of knowledge accumulated in previous parts.

Journal of Quantum Information Science

In this paper, classical and continuous variable (CV) quantum neural network hybrid multi-classifiers are presented using the MNIST dataset. The combination of cutoff dimension and probability measurement method in the CV model allows a quantum circuit to produce output vectors of size n m where n =cutoff dimension and m =the number of qumodes. They are then translated as one-hot encoded labels, padded with n m − 10 zeros. The total of eight different classifiers are built using 2, 3,. .. , 8− qumodes, based on the binary classifier architecture proposed in "Continuous variable quantum neural networks" [14]. The displacement gate and the Kerr gate in the CV model allow for the bias addition and non-linear activation components of classical neural networks of the form L(x) = φ (W x + b) to be directly implemented in quantum as L(|x) = |φ (W x + b). The classifiers are composed of a classical feed-forward neural network, a quantum data encoding circuit, and a CV quantum neural network circuit. On a truncated MNIST dataset of 600 samples, a 4-qumode hybrid classifier achieves 100% training accuracy.

2018

Abstract:Recently, with the rapid development of technology, there are a lot of applications require to achieve low-cost learning. However the computational power of classical artificial neural networks, they are not capable to provide low-cost learning. In contrast, quantum neural networks may be representing a good computational alternate to classical neural network approaches, based on the computational power of quantum bit (qubit) over the classical bit. In this paper we present a new computational approach to the quantum perceptron neural network can achieve learning in low-cost computation. The proposed approach has only one neuron can construct self-adaptive activation operators capable to accomplish the learning process in a limited number of iterations and, thereby, reduce the overall computational cost. The proposed approach is capable to construct its own set of activation operators to be applied widely in both quantum and classical applications to overcome the linearity ...

Quantum Machine Intelligence, 2020

Recent results have demonstrated the successful applications of quantum-classical hybrid methods to train quantum circuits for a variety of machine learning tasks. A natural question to ask is consequentially whether we can also train such quantum circuits to discriminate quantum data, i.e., perform classification on data stored in form of quantum states. Although quantum mechanics fundamentally forbids deterministic discrimination of non-orthogonal states, we show in this work that it is possible to train a quantum circuit to discriminate such data with a trade-off between minimizing error rates and inconclusiveness rates of the classification tasks. Our approach achieves at the same time a performance which is close to the theoretically optimal values and a generalization ability to previously unseen quantum data. This generalization power hence distinguishes our work from previous circuit optimization results and furthermore provides an example of a quantum machine learning task ...

Level-generalization' 88 3.6.2 Insertion principle 3.6.3 The Divide and Conquer Principle 3.6.4 The Gate-collapsing principle 3.7 Examples of circuits obtained automatically for NMR technology using methods from sections 3.5 and 3.6 3.8 Chapter Conclusion 4 Genetic Algorithm for Logic Synthesis 4.1 Introduction 4.2 Genetic algorithm 4.2.1 Encoding/Representation 4.2.2 Initialization steps of GA 4.3 Evaluation of Synthesis Errors Ill 4.3.1 Element Error Evaluation method (EE) 4.3.2 Measurement Evaluation method (ME) 4.3.3 Comparison of EE and ME CONTENTS vi 4.4 Fitness functions of the GA 4.4.1 Simple Fitness Functions 4.4.2 Cost Based Fitness Functions 4.5 The Selection Process 4.6 Crossover and Mutation 4.6.1 Mutation 4.6.2 Additional GA tuning strategies 4.7 Chapter Conclusion 5 Evolutionary Search for Logic synthesis 5.1 Evolutionary Search 5.2 Experimental setup of GA 5.2.1 Input Sets of Quantum Primitives 5.3 Discussion of the Results of the Evolutionary Quantum Logic Synthesis using ME evaluation 5.3.1 Toffoli Gate 5.3.2 Synthesis of Fredkin Gate 5.3.3 Synthesis of Majority Gate 5.4 Discussion of the Results of the Evolutionary Quantum Logic Synthesis using EE evaluation CONTENTS vii 5.4.1 Toffoli Gate 5.4.2 Predkin Gate 176 5.4.3 Entanglement Circuit 5.5 Discussion of the results of the Evolutionary Synthesis .... 180 5.5.1 Results Comparison 180 5.5.2 Encountered problems during the Evolutionary QLS. . 5.6 Conclusion of the Evolutionary QLS 6 Structure Based Search for Universal Quantum Circuits 6.1 Introduction 6.2 The EX algorithm 6.3 Heuristic Search for Lowest Cost Function Class using the EX algorithm 6.3.1 New Quantum Logic Family 6.4 Discussion and Conclusion to the Structure Based Exhaustive search 7 Learning Quantum Behaviors 206 7.1 Quantum Behaviors 7.2 The concept of learning robotic behaviors from examples.. .. CONTENTS viu 7.2.1 Symbolic Quantum Synthesis of Single Output Quantum Circuits 7.3 Experiments and Results for learning Quantum Behaviors. . 7.3.1 Symbolic synthesis-Single output functions 7.4 Discussion on learning Quantum Benchmarks 7.5 Measurement Synthesis 7.5.1 Conclusions on the Measurement Dependent Quantum Logic

Companion of the 2023 International Conference on Management of Data

In the last few years, the field of quantum computing has experienced remarkable progress. The prototypes of quantum computers already exist and have been made available to users through cloud services (e.g., IBM Q experience, Google quantum AI, or Xanadu quantum cloud). While fault-tolerant and large-scale quantum computers are not available yet (and may not be for a long time, if ever), the potential of this new technology is undeniable. Quantum algorithms have the proven ability to either outperform classical approaches for several tasks, or are impossible to be efficiently simulated by classical means under reasonable complexity-theoretic assumptions. Even imperfect current-day technology is speculated to exhibit computational advantages over classical systems. Recent research is using quantum computers to solve machine learning tasks. Meanwhile, the database community has already successfully applied various machine learning algorithms for data management tasks, so combining the fields seems to be a promising endeavour. However, quantum machine learning is a new research field for most database researchers. In this tutorial, we provide a fundamental introduction to quantum computing and quantum machine learning and show the potential benefits and applications for database research. In addition, we demonstrate how to apply quantum machine learning to the join order optimization problem in databases. CCS CONCEPTS • Computer systems organization → Quantum computing; • Computing methodologies → Machine learning; • Information systems → Data management systems.