Quantum Computing: A Shift from Bits to Qubits

Non-classical correlations such as entanglement and quantum discord are essential concepts in the context of quantum technologies nowadays. A plethora of both theoretical and experimental advances on this sort of correlation can be found in the literature. However, it is worth pointing out that new insights on their quantification, detection and application, to name a few, continue to be very welcome. In this chapter, we present a discussion on the quantification of correlations in quantum states. For doing so, we discuss how to quantify the so-called quantum discord in the light of a recently proposed measure inspired by the resource theory for coherence and operationally well-defined in the context of parameter estimation. On the other hand, we also comment on the problem of identifying genuine multipartite correlations in many-body systems. In this case, we discuss a proposal to quantify genuine total (classical plus quantum) correlations at different order \(2\le k\le N\).

Quantum computing is an upcoming technology which has the potential to revolutionize our lives with its unprecedented computating powers. A quantum computer works on the principles of Quantum Mechanics, a branch of Physics. Quantum mechanics is the universal theory of nature which governs the microworld and underlies all the physical phenomena. In this chapter, we outline how the basic quantum concepts like probability amplitudes, linear superposition principle, entanglement, etc can be harnessed to perform computations. We discuss the basic concepts of quantum mechanics, starting with Hilbert space methods and describe how quantum bits or qubits can be used.

This chapter introduces quantum mechanics in phase space. One of the guiding principles is the belief that the physical states of a system can be parametrized by finite dimensional smooth manifolds. Our motivating example is radar theory. Radar measurements take place on classical phase space and exhibit quantum features such as operator representations of the Heisenberg group. Classical physics is described by algebraic and geometrical structures in symplectic manifolds that serve as the arena of classical as well as quantum measurements. We treat the Kahler case as a special kind of symplectic manifold that paves the way to a presentation of quantum mechanics by deformation theory. Deformation quantization proceeds via the introduction of a star product, an associative but not commutative product between functions in phase space. The founders of this approach “suggest quantization be understood as a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables.” We show how the quantization of the spin 1/2 particle arises in deformation theory: it can be understood by a star product on the Bloch sphere autonomously, through the geometrical data. Hilbert space methods are introduced in this approach to make contact with conventional approaches.

The purpose of this paper is to introduce statistical states through signals used as the probes of physical systems. Phase space is the arena of both quantum and classical mechanics. This work reviews the origin of information in signal theory as a gateway to understanding quantum information theory. Concepts of operational physics and Lie group representation theory are applied to the study of phase space measurements. A statistical model of Hamiltonian dynamics in the Koopman representation is a Hilbert bundle over a symplectic manifold. Bochner’s theorem and its relationship with group characters pave the way to statistical observables in classical physics through an extension of the Fourier transform. The natural extension to non-commutative signal theory gives rise to representations of dynamical groups like in quantum mechanics. Two methods of quantization are discussed with emphasis on the appearance of statistical states: Souriau’s functions of positive type and the more general scheme of star product quantization. Quantum Signals are described by states arising from representations of the SU(2) group on the Poincare sphere that are introduced in the deformation theory approach by the star exponential.

The fundamental element of quantum computing is the quantum circuit. An efficient quantum circuit saves quantum hardware resources by reducing the number of gates without increasing the number of qubits. Quantum circuits with many qubits are very difficult to realize. Thus, the number of qubits is an important parameter in a quantum circuit design. Using reversible logic in quantum circuits has many advantages such as diminishing power consumption, reducing heat propagation and decreasing quantum cost, ancilla inputs, and garbage outputs that lead to increased performance of quantum computers. Quantum circuits for arithmetic operations such as addition, subtraction, and multiplication are required in the implementation of quantum circuits for many quantum algorithms in this area. In this article two novel designs for GF(2ⁿ) multiplier using Karatsuba algorithm have been proposed that have been proved to have an improvement in qubits, garbage outputs, and ancilla inputs when it comes to comparison with recent research that have been done concerning this field. Bennett’s garbage removal strategy with the SWAP gate is used to remove garbage output from existing works in order to establish a fair comparison to existing work.

This chapter will help in understanding the concepts of representing quantum states, superposition states, quantum gates, quantum entanglement, and various output visualizations, along with hands-on code using IBM’s Quantum Experience Qiskit, an open-source framework to write and execute quantum programs. Classical computers work on bits whereas quantum computers work on quantum bits or qubits. A state in a qubit can be represented as \(|\left. 0 \right\rangle ,\,\left| 1 \right\rangle\) or both in \(\left| 0 \right\rangle\) and \(\left| 1 \right\rangle\) at the same time, called a superposition state. The advantage of storing a qubit in a superposition state is one can perform computation on all values at the same time, which leads to quantum parallelism. Qubits can be represented using two-dimensional vectors and there are three computational bases called Z basis, X basis, and Y basis. The next part of the chapter will discuss the various quantum gates—single qubit and multi qubit quantum gates. Output of these gates when applied to various states such as \(\left| 0 \right\rangle ,\,\left| 1 \right\rangle ,\,\left| + \right\rangle ,\left| - \right\rangle ,\,\left| i \right\rangle ,\, - \left| i \right\rangle\) are discussed. The last part of this chapter will discuss the code to generate Bell states also called as quantum entanglement, the output of quantum entanglement using various visualizations supported by Qiskit such as qsphere, state_city, state_hinton, bloch sphere, etc. are explored.

Quantum computing has evolved from traditional classical computing due to the integration of multiple scientific domains. Quantum physics and quantum mechanics to name a few. Classical computers worked on a 1 and 0 logic, whereby the value would be either a voltage high or voltage low respectively. Quantum computers on the contrary use Qubits to represent the states, these state vectors have the capability to represent multiple states simultaneously and thus render scalability and exponential speed to quantum computing. Quantum computers harness the unique behaviour of quantum physics by applying concepts such as superposition, entanglement, and quantum interference. This chapter is authored to take us through the transition from classical to quantum computing. The chapter shall present a comparison of features that are exhibited by classical computers and how quantum principles enable quantum to compute, The chapter is aimed to provide an introduction to the various quantum gates which are to be deliberated in the subsequent chapters.

The transistors, which can represent either 0 or 1 (bits) at the same time, are computed in classical computing. Even though classical computers have become smaller and faster, they are still incapable of solving issues like factoring huge integers, messages are sent in coded form using large digit prime integers. Currently, hundreds of electrons are used to turn on or off a single transistor on a chip in classical computing. To achieve great performance, we must progress past the limitations of conventional computing using electrons as well as silicon and into the non-silicon era. One solution that is gaining some traction is quantum computing. Quantum computers typically built on quantum bits (qubits) and take advantage of quantum features like quantum superposition and quantum entanglement to overcome the miniaturization issues of classical computing. Quantum superposition simply states that a quantum unit can exist in 2 different places at once. According to this hypothesis, simultaneously qubits can represent a wide range of 1 and 0 combinations. Quantum computers are acquiring processing power at a twice exponential rate, according to this observation. To gain an exponential growth in power scaling, the qubits are replaced with bits. The best part is that there are numerous choices available, from quantum computing to miraculous materials such as nanotechnology, and customized processors. Regardless of which path we choose, the future of computers promises to be exciting.

CMOS innovation shows limited features when diminishing the size and region of a circuit. The burden of such a technology incorporates higher force utilization and also shows some temperature issues. Quantum-Dot Cell Automata is another innovation which is useful to defeat any of its weaknesses. The reversible rationale is innovation used to diminish the force misfortune in QCA. QCAs are utilized to plan recollections requiring a high working rate. In the following research, construction of reversible memory is proposed in QCA. It is designed by using a 3-layer innovation that altogether has an effect on the decreased size of the circuit. The reversible memory proposed here has 61% increase in cell number, with a 74% enhancement in the territory inhabitance, and 59% decrease in delay contrasted with any previous optimal designs.

Quantum neural networks are artificial neural networks that are designed using the principles of classical artificial neural networks and quantum information. Developing a quantum neural network requires knowledge of both classical neural networks and quantum computing techniques. TensorFlow Quantum is a library for developing quantum and hybrid neural network models. The MNIST handwritten digits dataset was used as a sample dataset for quantum neural network development. This chapter introduces the design and development process of a simple quantum neural network for image classification tasks using the TensorFlow quantum library. Also, it compared the classification performances of the quantum neural network and classical neural network on the MNIST handwritten digits classification. This chapter identified that the quantum neural network performed better than the classical neural network on digit classification. Also, the chapter discussed the advantages and limitations of quantum neural networks in image classification. The first section of the chapter introduced the quantum neural network models and the TensorFlow quantum library. Afterward, the data preparation steps such as data loading, downscaling, contradictory removal, and Tensorflow Quantum circuit conversions were discussed. Furthermore, the building process of quantum neural networks for image classification, such as quantum neural network designing, the model circuit to the Tensorflow Quantum model binding, and model training, was discussed in the third section of the chapter. Subsequently, the testing performance of the simple quantum neural network was discussed in section four of this chapter. Finally, the conclusions of the chapter were discussed in the fifth section.

In this chapter, the idea of the deployment of quantum key distribution (QKD) techniques within a more realistic insecure network has been discussed for achieving unconditional secure communication between two or more legitimate users in presence of eavesdroppers. The architecture of the network can play a crucial role in protocol design with trusted or un-trusted repeaters/relays in between these legitimate users. Point-to-point link (P2P) communication for long distance-based communication is not desirable as per the security concern. The present QKD techniques can achieve low-distance group communications where one trusted server can authenticate the users within the group. Stand-alone QKD communication architecture can be extended to create a wide network using the relays at regular intervals depending on the network topology. Efficient QKD protocols with proper network topologies have been discussed for achieving better security in different eavesdropping scenarios.

Machine learning is an exciting area where ever-growing problems such as anomaly detection using sensor data, natural language processing, image processing, etc., are solved using complex yet fascinating algorithms. Such algorithms learn the function that maps input to output from the training examples. The algorithms are evaluated with the validation data and then used to predict the output for an unknown dataset. For the past few years, scholars have been researching to improve such classical machine learning algorithms using quantum computing. Some of the latest research is the optimization of computationally expensive algorithms with quantum computing and transforming stochastic procedures into the semantics of quantum theory. The quest for the learning-based algorithm is aspiring: the discipline seeks to comprehend what learning is and studies how algorithms approximate learning. Quantum machine learning takes these aspirations further by looking at the subatomic level to aid learning. Machine learning-based algorithms minimize a constrained multivariate function. Different algorithms have different hyper-parameters that need to be tuned for the trained model to generalize well. Such optimization has high time and space complexity, which is central to learning theory. This contribution gives an organized overview of the evolving arena of quantum machine learning. It presents the methods as well as practical details. We start this chapter by introducing the major components of Quantum Computers, where we provide an overview of quantum computing with an in-depth explanation of the superposition of state, which will be crucial for all quantum algorithms. Next, we exploit a fascinating phenomenon called entanglement in quantum computations. Parallelism is the key to speeding up the training process of learning algorithms. One of the significant advantages of quantum computing is quantum parallelism which we will explore through Grover's search algorithm. Next, we go over the learning mechanism of a traditional machine learning algorithm, namely a Support Vector Machine (SVM) trained on classical computers. Furthermore, we exploit the Quantum SVM (QSVM) trained on quantum computers. Finally, we solve the famous malignant breast cancer classification problem using the quantum SVM algorithm. We study various simulations in Python language on the mentioned dataset to analyze their time complexity and performances on standard evaluation metrics, namely accuracy, precision, recall, and F1-score. Two simulations are conducted using classical machine learning algorithms using the Python library Scikit-learn. Finally, the last simulation is based on IBM's real quantum computer using its quantum machine learning library called Qiskit.

The Major Temporal Arcade (MTA) is the thickest vessel in the retina, which can be useful to analyze different pathologies related to the retina such as diabetic retinopathy. Consequently, its numerical modeling plays a vital role in systems that perform computer aided-diagnosis in Ophthalmology. In the present chapter, a novel method for the automatic modeling of the MTA is introduced. The method consists of the steps of automatic MTA segmentation and numerical modeling based on spline curves and the use of the Quantum genetic algorithm (QGA). In this step, the QGA is analyzed and implemented in order to determine the optimal control points on a set of previously segmented vessel pixels of the MTA in retinal fundus images. These control points are used to generate the best curve to fit the MTA through spline curves. In the experimental results, the proposed method was evaluated in terms of the Mean distance to the closest point and Hausdorff distance obtaining the average values of 9.91 and 53.32, respectively, using a test set of images. Finally, in terms of computational time, the proposed method achieved an average of 7.51 s per image, which makes it suitable for computer-aided diagnosis in ophthalmology.

Quantum entanglement (QE) is the phenomenon that when several particles interact, the properties of each particle will be integrated into the properties of the overall system, and the properties of each particle cannot be described independently from others. QE can be proved by violating Bell Inequality, that is, it can describe strong statistical correlation (i.e., quantum correlation). By introducing QE into machine learning, the adjusted framework would have advantages such as faster execution time of the learning algorithms and stronger capacity. Therefore, here we introduce our novel framework called Entangled Quantum Neural Network, EQNN. Using quantum entanglement to development on neuron networks can be described in three different ways: By replacing the hidden layer nodes of the Multi-Layer Perception (MLP) with a measurement process of entangled states (QECA, QCCA); by replacing the output layer of MLP with a quantum measurement operation (ECA); or by reconstructing the neurons in NN using regularizer to constrain state vectors to entangled states (QNN). With extensive experiments on the three most frequently used machine learning datasets from UCI, Abalone, Wine Quality (Red), and Wine Quality (White), we demonstrate that all QCCA, QECA, ECA, and QNN outperform the baseline algorithms. Under the same parameter settings, which are: learning rate is 0.001, mini-batch is 1, training epochs is 500 and initial weight is 0.01, the performance among themselves in descending order are QNN > ECA > QECA > QCCA.

Nowadays, quantum computing is a very promising technology. Quantum computers, rather than using merely 1 s or 0 s, execute calculations based on the probability of an object's condition before it is measured, allowing them to process exponentially more data than traditional computers. A bit is a single state, such as on or off, up or down, 1 or 0. Instead, operations in quantum computing utilise the quantum state of an item to produce a qubit. These are the undefined qualities of an object before they are discovered, such as an electron's spin or a photon's polarisation. Several firms are releasing tools for quantum computing practice. One of the tools we'll use to implement our quantum programming is IBM's experience. It also aids in the execution of our programs on real quantum devices. We'll look at the IBM Q experience, circuit composer and building circuits with quantum lab notebooks in this chapter. The dashboard containing the fundamental information is introduced in the IBM Q experience. The user interface for learning quantum circuits, qubits and the gates that are used to perform operations on each qubit is outlined in circuit composer. Creating quantum circuits using quantum lab notebooks shows how to build circuits with the Notebook with Qiskit that comes pre-installed on IBM Quantum Experience.

Quantum computing has become a new buzzword in recent years. Although quantum computing techniques have been available in the literature for the past 40 or more years, the desire for real-time implementation of such quantum computing techniques has become possible due to the ongoing superspeed development of quantum computers by multinational corporations. Albeit, only 40 qubits quantum computer has been developed to date. Still, the pathway of big corporations reveals that by the end of this decade, a full-fledged quantum computer will be available in the market for everyone. Quantum computing uses quantum key distribution for quantum communication. It is expected that quantum computing and quantum communication will completely change the workflow of many industries. Studies are also predicting that the market demand for the quantum computing industry will be in multi-trillion dollars as early as 2030. Besides, the perspective of researchers has been drastically changing due to the plethora of opportunities brought forth by quantum computing for data processing and data encryption tasks. The quantum computer is deep-rooted in uncertainty principle, and probability theories thereby prohibit the copying and replicating of quantum information. Consequently, the guarantee of unconditional security for transmitted data is ensured, otherwise impossible. Generally, transmitted data are hacked due to attackers’ generation of keys replica. We may note that despite quantum computing being in a nascent stage, it possesses the potential to change internet activities by speeding up many tasks. Many day-to-day activities of many industries like finance, healthcare, and security will unseal imperceptible abilities. Furthermore, many big corporations invest in developing quantum computers and open-source tools to enable the development of quantum programs running on quantum computers. Also, community-driven activities are accomplished to upgrade the skills of current software developers to make them ready with appropriate skills for the development of future quantum software, which will run on large bits quantum computers. In this direction, Microsoft Incorporation has not only developed a quantum development kit (QDK) but also provides cloud-based quantum computing as a service, namely Azure Quantum, for developing and testing new quantum programs for the community. The newly designed quantum programs can now be simulated locally or run on the real quantum computer through Azure Quantum. Consequently, this chapter introduces the what, when, and why’s of quantum computing. Also, this chapter presents all necessary tools (with detailed installation and execution steps) required by the quantum developer for the possible development of a quantum program.

Quantum computing is an advanced-level computing paradigm based on the fundamental principles on which nature operates, i.e. quantum mechanics and its ability to perform complex computations and high potential to set trends in the new era in computing technology. As quantum computing is slightly different from traditional computing, special types of software are needed for implementing Quantum Computing. There is a list of quantum software projects which are exclusively available on GitHub and/or maintained by the Quantum Open Source Foundation and there are proprietary tools offered by leading companies. With this in mind, we have compiled and curated detailed information & insights on some of the best quantum computing software tools which are widely used now-a-days. This chapter focuses on Microsoft Quantum Development Kit, IBM Quantum Tools, Amazon Braket, Google Quantum tools, and other popular open-source tools.

Quantum computing is a computing paradigm for addressing computer issues of classical systems by harnessing all the possibilities given by quantum physics concepts. In these computers, information is represented by quantum states and utilizes different quantum phenomena such as quantum superposition, entanglement, and interference provided by quantum physics. Quantum computations are based on the fundamental notion of reversible computing. Quantum algorithms are built based on quantum computational complexity. Various quantum algorithms have been developed so far, with the general conclusion that exploiting quantum physics effects results in a significant speedup over conventional algorithms. In this chapter, we have implemented some important quantum principles using different open-source software development kit for dealing with quantum computers with an aim to provide an understanding on how we can create and execute quantum programs on prototype quantum devices or simulate them on a local machine. The chapter deals in the implementation details of quantum principles along with providing other prime representations like Visual Circuit, State vector, Q-sphere, and Visual Probabilistic result.

Machine learning (ML) is the most promising subset of artificial intelligence. Quantum computing is prevalent for fast problem-solving approaches. The complex problems are classified and solved using huge multi-dimensional space. The various algorithms can interfere in multi-dimensional space and resolve the problems. Quantum Machine Learning provides the platform for various mining processes with to the point developments in quantum computing. Quantum computing & Machine learning both are very complex. Quantum Machine learning focuses on quick problem-solving synthesis with a quantum framework using different algorithms. Machine Learning functions by supervised, unsupervised, and semi-supervised learning mechanisms. ML uses label and unlabeled data to implement different classification, clustering, and decision trees for complex problems. Quantum computing comprises quantum counterparts for various computational complexity. Quantum Machine Learning provides a profound sympathetic approach for various subjects to derive new dimensioned results. There are several serious life-threatening diseases such as cancer, hepatotoxicity, cardiotoxicity, nephrotoxicity, etc. require prompt and precise detection at the early stages of progression. The need of the hour is to develop rapid, accurate, and more efficient strategies for various disease predictions which are also cost-effective and non-invasive in nature. Breast cancer is also such a disease that early screening is challenging owning to hereditary predisposition. Quantum computation techniques emerged with Machine learning as the promising approach in the past decade concerning the prediction of breast cancer. The quantum computes can be utilized for assisting cancer detection by employing quantum neural networks, quantum simulators, Super Vector Machine (SVM); Artificial Neural Networks (ANN), Dimensionality Reduction Algorithms etc. are used on the pre-processed dataset for the derived prediction of breast cancer. This book chapter will focus on current trends of Quantum Machine leaning for the prediction of breast cancers by solving complex computational problems using above stated algorithms. This chapter discusses the Molecular Classification of Breast Cancer as Luminal-A, Luminal-B, Normal-like, HER2 enriched, and Basal-like with Breast Cancer Diagnostic Techniques. It covers the study of Brest cancer prediction using Quantum Neural Network, Dimensionality Reduction Algorithms, and Support vector machines (SVM). It includes comparative discussions about different algorithms for breast cancer prediction.

Investigation of argon concentration in their fluid is made in this chapter. This assessment of argon fluid is realized through three layers of silicon-based quantum well structure. The principle of measurement of argon relies on the variation of electronic band-gap pertaining to the density of argon which ranges from 0 to 1.5 g/cm³. The physics of the work depends on both nature of the structure including material properties, whereas mathematics of the research relies on the configuration of the proposed structure which is derived through Kronig–Penny model. As far as numerical results are concerned, the electronic band-gaps are 0, 0.12, 0.29, 0.48, and 0.65 eV pertaining to the density (concentration) of argon, 0, 0.5, 1.0, 1.3, 1.5 g/cm³ respectively, that indicates electronic band-gap increases with the increasing of concentration. Further, the transmitted energy corresponding to the same concentration are 0, 0.12, 0.29, 0.48 and 0.65 eV respectively, which show that the transmitted energy and subsequently potential decreases linearly concerned to the concentration. Finally, the linear regression is used to estimate the relation between concentration and output potential, which is measured through the photo diode. More over the formula for this relation is concentration = −2.254 × potential + 3.366 with regression factor of 94.35. The outcomes of the chapter infer that one can determine the concentration of argon fluid by knowing the output potential.

With the increase of e-payments methods and the essential requirement to keep everything secret during online transactions, the demand of cryptography has increased a lot. In cryptography, factorization of huge integers or calculation of the exponents of a large prime number using hands or by normal computers is very hard but quantum computer can easily solve them within a lesser time. There is a need to move from classical cryptography to quantum cryptography to cope up with the advancement of technology and to maintain the demand of high level of information security. This chapter focuses on quantum cryptography, its need, and quantum key distribution that allows two parties to secretly share their information under the nose of an attacker with high computational power. This chapter also focusses on BB84, Ekert 91 protocol and the detection of eavesdropper in quantum key distribution based on photon polarization. Also, discuss the quantum masked authentication protocols in detail.

Even though Quantum Computers are still in their developmental phases, their technological implementation regarding their integration with classical computations is showing fascinating results around the world. Quantum Computers when compared with Classical Computational devices can be interpreted as a ‘candle and light bulb’, two different things accomplishing the same motive. Quantum Computers can provide us with tremendous processing power, which was unforeseen and has led us to question the ways in which they can transform existing technologies even raising concerns for current cryptic methods. Quantum systems have shown great potential in several fields one such is Quantum Machine Learning (QML) which even though a considerably novel field has benefitted from the integration of Quantum algorithms and Machine Learning algorithms, presenting exceptional results from various results. Scientists at Google were able to proclaim Quantum supremacy, this presented the Quantum computer's ability to perform extensively large computations in an extremely short time compared to a Super Computer, this could be beneficial for Machine learning algorithms to process huge amounts of data. Recent usage of a VPN for teleconferencing and a “work from home” scheme during the pandemic has caused a huge surge in network traffic forcing IT infrastructure providers to switch toward Software-Defined Network (SDN), Software Defined Network (SDN) is a prominent technology to provide betterment to the traditional network architecture. Machine Learning and Artificial Intelligence have been used extensively for various aspects of SDN, hence we attempted to explore QML and SDN interactions to assess their ability and the benefits we can achieve from this integration. This manuscript attempts to provide insights on the developments of QML over time and experimenting with SDN to provide a robust and efficient SDN system.

Question Answering (QA) has proved to be an arduous challenge in the area of natural language processing (NLP) and artificial intelligence (AI). Many attempts have been made to develop complete solutions for QA as well as improving significant sub-modules of the QA systems to improve the overall performance through the course of time. Questions are the most important piece of QA, because knowing the question is equivalent to knowing what counts as an answer (Harrah in Philos Sci 28:40–46, 1961, [1]). In this work, we have attempted to understand questions in a better way by using Quantum Machine Learning (QML). The properties of Quantum Computing (QC) have enabled classically intractable data processing. So, in this paper, we have performed question classification on questions from two classes of SelQA (Selection-based Question Answering) dataset using quantum-based classifier algorithms—quantum support vector machine (QSVM) and variational quantum classifier (VQC) from Qiskit (Quantum Information Science toolKIT) for Python. We perform classification with both classifiers in almost similar environments and study the effects of circuit depths while comparing the results of both classifiers. We also use these classification results with our own rule-based QA system and observe significant performance improvement. Hence, this experiment has helped in improving the quality of QA in general.