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Formal Methods for Quantum Software Engineering
Abstract
The characteristic difficulty in creating pure quantum software is mainly due to the inaccessibility to intermediate states, which makes debugging practically impossible. However, the use of formal methods, which apply rigorous mathematical models to ensure error-free software, can overcome this barrier and enable the production of reliable quantum algorithms and applications right out of the box.
... F-QSE can rigorously analyze and verify the correctness of quantum algorithms, with a verification example of the Deutsch Algorithm. (Cartiere, 2022) Quantum Formal Method A survey introducing several techniques and tools for the formal verification of quantum programs to mitigate errors and bugs. Methods include quantum weakest preconditions, quantum Hoare logic, quantum computation tree logic, and ZX-Calculus Path. ...
Research in software engineering is essential for improving development practices, leading to reliable and secure software. Leveraging the principles of quantum physics, quantum computing has emerged as a new computational paradigm that offers significant advantages over classical computing. As quantum computing progresses rapidly, its potential applications across various fields are becoming apparent. In software engineering, many tasks involve complex computations where quantum computers can greatly speed up the development process, leading to faster and more efficient solutions. With the growing use of quantum-based applications in different fields, quantum software engineering (QSE) has emerged as a discipline focused on designing, developing, and optimizing quantum software for diverse applications. This paper aims to review the role of quantum computing in software engineering research and the latest developments in QSE. To our knowledge, this is the first comprehensive review on this topic. We begin by introducing quantum computing, exploring its fundamental concepts, and discussing its potential applications in software engineering. We also examine various QSE techniques that expedite software development. Finally, we discuss the opportunities and challenges in quantum-driven software engineering and QSE. Our study reveals that quantum machine learning (QML) and quantum optimization have substantial potential to address classical software engineering tasks, though this area is still limited. Current QSE tools and techniques lack robustness and maturity, indicating a need for more focus. One of the main challenges is that quantum computing has yet to reach its full potential.
... Because of that an extension will also be necessary to apply specification language to quantum software. In this line, we can highlight the article by Cartiere [13], which introduces a formal specification that can represent the basic notations of quantum computing and the work by Feng et al. [14] that proposes an extension of the computational logic tree to consider superposition and entanglement (Q-CTL). However, given the early stage of quantum software, the use of quantum computation logic has not yet been widely adopted or integrated into existing tools and frameworks. ...
Quantum computing represents a revolutionary computational paradigm with the potential to address challenges beyond classical computers’ capabilities. The development of robust quantum software is indispensable to unlock the full potential of quantum computing. Like classical software, quantum software is expected to be complex and extensive, needing the establishment of a specialized field known as Quantum Software Engineering. Recognizing the regional focus on Latin America within this special issue, we have boarded on an in-depth inquiry encompassing a systematic mapping study of existing literature and a comprehensive survey of experts in the field. This rigorous research effort aims to illuminate the current landscape of Quantum Software Engineering initiatives undertaken by universities, research institutes, and companies across Latin America. This exhaustive study aims to provide information on the progress, challenges, and opportunities in Quantum Software Engineering in the Latin American context. By promoting a more in-depth understanding of cutting-edge developments in this burgeoning field, our research aims to serve as a potential stimulus to initiate pioneering initiatives and encourage collaborative efforts among Latin American researchers.
... The latter was addressed by the recent development of the high-level quantum programming language Silq [2] by implementing automatic uncomputation. While the focus of this paper is Silq and its practical implementation of quantum algorithms, recently published surveys [5,1,8] provide detailed analyses of different quantum programming languages and are a strong recommendation for a reader choosing the tool for their project needs. ...
Quantum computing, with its vast potential, is fundamentally shaped by the intricacies of quantum mechanics, which both empower and constrain its capabilities. The development of a universal, robust quantum programming language has emerged as a key research focus in this rapidly evolving field. This paper explores Silq, a recent high-level quantum programming language, highlighting its strengths and unique features. We aim to share our insights on designing and implementing high-level quantum algorithms using Silq, demonstrating its practical applications and advantages for quantum programming.
... In the same way that extensions of the language used for modeling are necessary for the architectural model, an extension will also be necessary to apply specification language to quantum software. In this line, we can highlight the article by Cartiere [14], which introduces a formal specification that can represent the basic notations of quantum computing. ...
Quantum computing represents a revolutionary computational paradigm with the potential to address challenges beyond classical computers' capabilities. The development of robust quantum software is indispensable to unlock the full potential of quantum computing. Like classical software, quantum software is expected to be complex and extensive, needing the establishment of a specialized field known as Quantum Software Engineering. Recognizing the regional focus on Latin America within this special issue, we have boarded on an in-depth inquiry encompassing a systematic mapping study of existing literature and a comprehensive survey of experts in the field. This rigorous research effort aims to illuminate the current landscape of Quantum Software Engineering initiatives undertaken by universities, research institutes, and companies across Latin America. This exhaustive study aims to provide information on the progress, challenges, and opportunities in Quantum Software Engineering in the Latin American context. By promoting a more in-depth understanding of cutting-edge developments in this burgeoning field, our research aims to serve as a potential stimulus to initiate pioneering initiatives and encourage collaborative efforts among Latin American researchers.
... The right level of requirement specification is, of course, formal specification languages, like Z notation (Object Z, Z++) (Cartiere 2022) or B method. Another alternative that has a low level of obscure syntax is logic programming languages like Prolog. ...
As bigger quantum processors with hundreds of qubits become increasingly available, the potential for quantum computing to solve problems intractable for classical computers is becoming more tangible. Designing efficient quantum algorithms and software in tandem is key to achieving quantum advantage. Quantum software engineering is challenging due to the unique counterintuitive nature of quantum logic. Moreover, with larger quantum systems, traditional programming using quantum assembly language and qubit-level reasoning is becoming infeasible. Automated Quantum Software Engineering (AQSE) can help to reduce the barrier to entry, speed up development, reduce errors, and improve the efficiency of quantum software. This article elucidates the motivation to research AQSE (why), a precise description of such a framework (what), and reflections on components that are required for implementing it (how).
... The right level of requirement specification is, of course, formal specification languages, like Z notation (Object Z, Z++) [31] or B method. Another alternative that has a low level of obscure syntax is logic programming languages like Prolog. ...
This article provides a personal perspective on research in Automated Quantum Software Engineering (AQSE). It elucidates the motivation to research AQSE (why?), a precise description of such a framework (what?), and reflections on components that are required for implementing it (how?).
Until now, the quality problems of quantum software have been largely ignored. This chapter analyzes the applicability of models and metrics for quantum software and, to mitigate this lack of attention to quality issues, presents a set of metrics that have been proposed and empirically validated to characterize the complexity of quantum circuits in terms of their understandability. The validation experiment design, execution, and results are reported. In addition, the main functionalities of a prototype tool that has been created for the automatic computation of the metrics are briefly presented.
Context: Quantum software development is a complex and intricate process that diverges significantly from traditional software development. Quantum computing and quantum software are deeply entangled with quantum mechanics, which introduces a different level of abstraction and a deep dependence on quantum physical properties. The classical requirements engineering methods must be adapted to encompass the essential quantum features in this new paradigm. Aim: This study aims to systematically identify and analyze challenges, opportunities, developments, and new lines of research in requirements engineering for quantum computing. Method: We conducted a systematic literature review, including three research questions. This study included 105 papers published from 2017 to 2024. Results: The main results include the identification of problems associated with defining specific requirements for quantum software and hybrid system requirements. In addition, we identified challenges related to the absence of standards for quantum requirements engineering. Finally, we can see the advances in developing programming languages and simulation tools for developing software in hybrid systems. Conclusions: This study presents the challenges and opportunities in quantum computing requirements engineering, emphasizing the need for new methodologies and tools. It proposes a roadmap for future research to develop a standardized framework, contributing to theoretical foundations and practical applications.
Hyperparameter optimization (HPO) and neural architecture search (NAS) of machine learning (ML) models are in the core implementation steps of AI-enabled systems. With multi-objective and multi-level optimization of complex ML models, it is agreed-on that HPO and NAS are NP-hard problems. That is, the size of the search space grows exponentially with the number of hyperparameters, possible architecture elements, and configurations. In 2017, the first proposal of QC-enabled HPO and NAS optimization was proposed. Simultaneously, advancements related to quantum neural networks (QNNs) resulted in more powerful ML due to their deployment on QC infrastructure. For such, quantum architecture search (QAS) problem arose as a similar problem, aiming to achieve optimal configuration of quantum circuits. Although classical approaches to solve these problems were thoroughly studied in the literature, a systematic overview that summarizes quantum-based methods is still missing. Our work addresses this gap and provides the first Systemization of Knowledge (SoK) to differentiate, and bridge the gap between the utilization of QC for optimizing ML rather than learning. Specifically, we provide qualitative and empirical analysis of related works, and we classify the properties of QC-based HPO, NAS, and QAS optimization systems. Additionally, we present a taxonomy of studied works, and identify four main types of quantum methods used to address the aforementioned problems. Finally, we set the agenda for this new field by identifying promising directions and open issues for future research.
Computer software technology is also undergoing corresponding innovation and reform. Due to low work efficiency, there are still deficiencies and problems in the unlimited accumulation and explosion of big data digital technology, which need to be continuously strengthened, improved and improved. Only in this way can we promote the development of computer software technology and maximize work efficiency and speed. On this basis, this paper attempts to study the development direction of computer software testing methods under the background of big data era, so as to provide reference value for the development of business.KeywordsSoftware testingBig dataComputer
We present Qibo, a new open-source software for fast evaluation of quantum circuits and adiabatic evolution which takes full advantage of hardware accelerators. The growing interest in quantum computing and the recent developments of quantum hardware devices motivates the development of new advanced computational tools focused on performance and usage simplicity. In this work we introduce a new quantum simulation framework that enables developers to delegate all complicated aspects of hardware or platform implementation to the library so they can focus on the problem and quantum algorithms at hand. This software is designed from scratch with simulation performance, code simplicity and user friendly interface as target goals. It takes advantage of hardware acceleration such as multi-threading CPU, single GPU and multi-GPU devices.
The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits.
The execution of a quantum algorithm typically requires various classical pre- and post-processing tasks. Hence, workflows are a promising means to orchestrate these tasks, benefiting from their reliability, robustness, and features, such as transactional processing. However, the implementations of the tasks may be very heterogeneous and they depend on the quantum hardware used to execute the quantum circuits of the algorithm. Additionally, today’s quantum computers are still restricted, which limits the size of the quantum circuits that can be executed. As the circuit size often depends on the input data of the algorithm, the selection of quantum hardware to execute a quantum circuit must be done at workflow runtime. However, modeling all possible alternative tasks would clutter the workflow model and require its adaptation whenever a new quantum computer or software tool is released. To overcome this problem, we introduce an approach to automatically select suitable quantum hardware for the execution of quantum circuits in workflows. Furthermore, it enables the dynamic adaptation of the workflows, depending on the selection at runtime based on reusable workflow fragments. We validate our approach with a prototypical implementation and a case study demonstrating the hardware selection for Simon’s algorithm.
Nowadays, we are at the dawn of a new age, the quantum era. Quantum computing
is no longer a dream; it is a reality that needs to be adopted. But this new
technology is taking its first steps, so we still do not have models, standards, or
methods to help us in the creation of new systems and the migration of current
ones. Given the current state of quantum computing, we need to go back to the
path software engineering took in the last century to achieve the new golden age
for quantum software engineering.
Principles and methodologies of quantum algorithmic gates design for master course and PhD students in computer science, control engineering and intelligent robotics described. The possibilities of quantum algorithmic gates simulation on classical computers discussed. Applications of quantum gate of nanotechnology in intelligent quantum control introduced. Anew approach to a circuit implementation design of quantum algorithm gates for fast quantum massive parallel computing presented. The main attention focused on the development of design method of fast quantum algorithm operators as superposition, entanglement and interference, which are in general time-consuming operations due to the number of products that have performed. SW & HW support sophisticated smart toolkit of supercomputing accelerator of quantum algorithm simulation on small quantum programmable computer algorithm gate (that can program in SW to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates) described. As example, the method for performing Grover’s interference operator without product operations introduced. The background of developed information technology is the "Quantum / Soft Computing Optimizer" (QSCOptKBTM) SW based on soft and quantum computational intelligence toolkit.
Quantum computing has become one of the most
interesting areas of research, training and
investment, particularly in the IT-related business
sector. This technology will inevitably cause a
disruptive innovation effect in the efficiency,
economy and efficacy of processes, services and
products, thus providing an enormous competitive
edge to organizations that use it. However, it
requires knowledge of very different areas of
scientific disciplines such as mathematics,
quantum mechanics, particle physics, electronics
and computer science. Of course, it is inevitable
that other scientific disciplines and business
sectors that are not related to IT will also be
affected either directly or indirectly. Organizations
such as Google and the US National Aeronautics
and Space Agency (NASA) have already begun to
use Qbit, which is a new hard and soft technology
with new algorithms and an IT environment to
handle large-size data. There is now even a search
engine that has been developed with quantum
computers. As is shown in figure 1, Rigetti
Computing has been developing and granting
access to an online platform of 8- and 19-qbit
processors and, in August 2018, the company
committed to developing a 128-qbit quantum
computer by August 2019.1
In distributed quantum computing architectures, with the network and communications functionalities provided by the Quantum Internet, remote quantum processing units (QPUs) can communicate and cooperate for executing computational tasks that single NISQ devices cannot handle by themselves. To this aim, distributed quantum computing requires a new generation of quantum compilers, for mapping any quantum algorithm to any distributed quantum computing architecture. With this perspective, in this paper, we first discuss the main challenges arising with compiler design for distributed quantum computing. Then, we analytically derive an upper bound of the overhead induced by quantum compilation for distributed quantum computing. The derived bound accounts for the overhead induced by the underlying computing architecture as well as the additional overhead induced by the sub-optimal quantum compiler -- expressly designed through the paper to achieve three key features, namely, general-purpose, efficient and effective. Finally, we validate the analytical results and we confirm the validity of the compiler design through an extensive performance analysis.
Quantum computing is gaining serious momentum in these days. With increasing capabilities of corresponding devices also comes the need for efficient and automated tools to design them. Verification, i.e., ensuring that the originally intended functionality of a quantum algorithm/circuit is preserved throughout all layers of abstraction during the design process, is a vital part of the quantum software stack. In this work, we present QCEC, a tool for quantum circuit equivalence checking which is part of the JKQ toolset for quantum computing. By exploiting characteristics unique to quantum computing, the tool allows users to efficiently verify the equivalence of two quantum circuits using a variety of methods and strategies.
This article outlines our point of view regarding the applicability, state-of-the-art, and potential of quantum computing for problems in finance. We provide an introduction to quantum computing as well as a survey on problem classes in finance that are computationally challenging classically and for which quantum computing algorithms are promising. In the main part, we describe in detail quantum algorithms for specific applications arising in financial services, such as those involving simulation, optimization, and machine learning problems. In addition, we include demonstrations of quantum algorithms on IBM Quantum back-ends and discuss the potential benefits of quantum algorithms for problems in financial services. We conclude with a summary of technical challenges and future prospects.
With quantum computers on the brink of practical applicability, there is a lively community that develops toolkits for the designof corresponding quantum circuits. Many of the problems to betackled here are similar to design problems from the classical realm for which sophisticated design automation tools have been developed in the previous decades. In this paper, we present JKQ—a set of tools for quantum computing developed at the Johannes Kepler University (JKU) Linz which utilizes this design automation expertise. By this, we offer complementary approaches for many design problems in quantum computing such as simulation, compilation, or verification. In the following, we provide an introduction of the tools for potential users who would like to work with them as well as potential developers aiming to extend them.
A hybrid quantum–classical approach to model continuous classical probability distributions using a variational quantum circuit is proposed. The architecture of this quantum generator consists of a quantum circuit that encodes a classical random variable into a quantum state and a parameterized quantum circuit trained to mimic the target distribution. The model allows for easy interfacing with a classical function, such as a neural network, and is trained using an adversarial learning approach. It is shown that the quantum generator is able to learn using either a classical neural network or a variational quantum circuit as the discriminator model. This implementation takes advantage of automatic differentiation tools to perform the optimization of the variational circuits employed. The framework presented here for the design and implementation of the variational quantum generators can serve as a blueprint for designing hybrid quantum–classical models for other machine learning tasks.
This document describes the Scaffold programming language, its design goals, and related tools. Scaffold is a programming language for expressing quantum algorithms. A quantum algorithm can consist of a wide variety of components (including classical and quantum routines) which will be defined using different coding techniques. As a quantum programming language (QPL), Scaffold was formulated to make it easy to express an algorithm with so many disparate components in a clean and efficient manner. It is from this notion of "putting things together" that Scaffold derives its name.
Quantum computers are available to use over the cloud, but the recent explosion of quantum software platforms can be overwhelming for those deciding on which to use. In this paper, we provide a current picture of the rapidly evolving quantum computing landscape by comparing four software platforms - Forest (pyQuil), Qiskit, ProjectQ, and the Quantum Developer Kit (Q#) - that enable researchers to use real and simulated quantum devices. Our analysis covers requirements and installation, language syntax through example programs, library support, and quantum simulator capabilities for each platform. For platforms that have quantum computer support, we compare hardware, quantum assembly languages, and quantum compilers. We conclude by covering features of each and briefly mentioning other quantum computing software packages.
Abstract
This research deals with a vital and important issue in computer
world. It is concerned with the software management processes
that examine the area of software development through the
development models, which are known as software development
life cycle. It represents five of the development models namely,
waterfall, Iteration, V-shaped, spiral and Extreme programming.
These models have advantages and disadvantages as well.
Therefore, the main objective of this research is to represent
different models of software development and make a
comparison between them to show the features and defects of
each model.
Implementing a gate-based quantum algorithm on a NISQ device has several challenges that arise from the fact that such devices are noisy and have limited quantum resources. Thus, various factors contributing to the depth and width as well as to the noise of an implementation of a gate-based algorithm must be understood in order to assess whether an implementation will execute successfully on a given NISQ device. In this contribution, we discuss these factors and their impact on algorithm implementations. Especially, we will cover state preparation, oracle expansion, connectivity, circuit rewriting, and readout: these factors are very often ignored when presenting a gate-based algorithm but they are crucial when implementing such an algorithm on near-term quantum computers. Our contribution will help developers in charge of realizing gate-based algorithms on such machines in (i) achieving an executable implementation, and (ii) assessing the success of their implementation on a given machine.
We describe staq, a full-stack quantum processing toolkit written in standard C++. staq is a quantum compiler toolkit, comprising of tools that range from quantum optimizers and translators to physical mappers for quantum devices with restricted connectives. The design of staq is inspired from the UNIX philosophy of ‘less is more’, i.e. staq achieves complex functionality via combining (piping) small tools, each of which performs a single task using the most advanced current state-of-the-art methods. We also provide a set of illustrative benchmarks.
The Quantum Internet, by enabling quantum communications among remote quantum nodes, is a network capable of
supporting functionalities with no direct counterpart in the classical world. Indeed, with the network and communications
functionalities provided by the Quantum Internet, remote quantum devices can communicate and cooperate for solving
challenging computational tasks by adopting a distributed computing approach. The aim of this study is to provide the reader
with an overview about the main challenges and open problems arising in the design of a distributed quantum computing
ecosystem. We follow a bottom-up approach, from a communications engineering perspective. We start by introducing the Quantum Internet as the fundamental underlying infrastructure of the distributed
quantum computing ecosystem. Then we go further, by elaborating on a high-level system abstraction of the distributed
quantum computing ecosystem. We describe such an abstraction through a set of logical layers. Thereby, we clarify
dependencies among the aforementioned layers and, at the same time, a road-map emerges.
The Variational Quantum Eigensolver (VQE) algorithm is gaining interest for its potential use in near-term quantum devices. In the VQE algorithm, parameterized quantum circuits (PQCs) are employed to prepare quantum states, which are then utilized to compute the expectation value of a given Hamiltonian. Designing efficient PQCs is crucial for improving convergence speed. In this study, we introduce problem-specific PQCs tailored for optimization problems by dynamically generating PQCs that incorporate problem constraints. This approach reduces a search space by focusing on unitary transformations that benefit the VQE algorithm, and accelerate convergence. Our experimental results demonstrate that the convergence speed of our proposed PQCs outperforms state-of-the-art PQCs, highlighting the potential of problem-specific PQCs in optimization problems.
This 1997 book is a self-contained tutorial on Z, a formal notation for modelling, specifying and designing computer systems and software, for experienced professionals and serious students in programming and software engineering. It presents realistic case studies emphasising safety-critical systems, with examples drawn from embedded controls, real-time and concurrent programming, computer graphics, games, text processing, databases, artificial intelligence, and object-oriented programming. It motivates the use of formal methods and discusses practical issues concerning how to apply them in real projects. It also teaches how to apply formal program derivation and verification to implement Z specifications in real programming languages with examples in C. The book includes exercises with solutions, reference materials, and a guide to further reading.
In this chapter, QuantumPath® (QPath® https://www.quantumpath.es/), an agnostic quantum software development platform to support the design, implementation, and execution of quantum software applications is presented, with its advantages and an example of use.
Quantum assembly languages are machine-independent languages that traditionally describe quantum computation in the circuit model. Open quantum assembly language (OpenQASM 2) was proposed as an imperative programming language for quantum circuits based on earlier QASM dialects. In principle, any quantum computation could be described using OpenQASM 2, but there is a need to describe a broader set of circuits beyond the language of qubits and gates. By examining interactive use cases, we recognize two different timescales of quantum-classical interactions: real-time classical computations that must be performed within the coherence times of the qubits, and near-time computations with less stringent timing. Since the near-time domain is adequately described by existing programming frameworks, we choose in OpenQASM 3 to focus on the real-time domain, which must be more tightly coupled to the execution of quantum operations. We add support for arbitrary control flow as well as calling external classical functions. In addition, we recognize the need to describe circuits at multiple levels of specificity, and therefore we extend the language to include timing, pulse control, and gate modifiers. These new language features create a multi-level intermediate representation for circuit development and optimization, as well as control sequence implementation for calibration, characterization, and error mitigation.
Quantum computers are becoming real. Therefore, it is promising to use their potentials in different application areas, which includes research in the humanities. Due to an increasing amount of data that needs to be processed in the digital humanities the use of quantum computers can contribute to this research area. To give an impression on how beneficial such involvement of quantum computers can be when analysing data from the humanities, a use case from the media science is presented. Therefore, both the theoretical basis and the tooling support for analysing the data from our digital humanities project MUSE is described. This includes a data analysis pipeline, containing e.g. various approaches for data preparation, feature engineering, clustering, and classification where several steps can be realized classically, but also supported by quantum computers.KeywordsQuantum computingQuantum humanitiesMachine learningQuantum machine learningDigital humanitiesData analysisArtificial neural networksPattern languages
Quantum computing is expected to exponentially outperform classic computing on a broad set of problems, including encryption, machine learning, and simulations. It has an impact yet to explore on all software lifecycle's processes and techniques. Testing quantum software raises a significant number of challenges due to the unique properties of quantum physics—such as superposition and entanglementand the stochastic behavior of quantum systems. It is, therefore, an open research issue. In this work, we offer a systematic mapping study of quantum software testing engineering, presenting a comprehensive view of the current state of the art. The main identified trends in testing techniques are (1) the statistic approaches based on repeated measurements and (2) the use of Hoare-like logics to reason about software correctness. Another relevant line of research is reversible circuit testing, which is partially applicable to quantum software unitary testing. Finally, we have observed a flourishing of secondary studies and frameworks supporting testing processes from 2018 onwards.
Deep Convolutional Neural Networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose
-Nets, \rebuttal{a new class of function approximators based on polynomial expansions}.
-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. The unknown parameters, which are naturally represented by high-order tensors, are estimated through a collective tensor factorization with factors sharing. We introduce three tensor decompositions that significantly reduce the number of parameters and show how they can be efficiently implemented by hierarchical neural networks. We empirically demonstrate that
-Nets are very expressive and they even produce good results without the use of non-linear activation functions in a large battery of tasks and signals, i.e., images, graphs, and audio. When used in conjunction with activation functions,
-Nets produce state-of-the-art results in three challenging tasks, i.e. image generation, face verification and 3D mesh representation learning. The source code is available at \url{https://github.com/grigorisg9gr/polynomial_nets}.
In this paper, we propose Proq, a runtime assertion scheme for testing and debugging quantum programs on a quantum computer. The predicates in Proq are represented by projections (or equivalently, closed subspaces of the state space), following Birkhoff-von Neumann quantum logic. The satisfaction of a projection by a quantum state can be directly checked upon a small number of projective measurements rather than a large number of repeated executions. On the theory side, we rigorously prove that checking projection-based assertions can help locate bugs or statistically assure that the semantic function of the tested program is close to what we expect, for both exact and approximate quantum programs. On the practice side, we consider hardware constraints and introduce several techniques to transform the assertions, making them directly executable on the measurement-restricted quantum computers. We also propose to achieve simplified assertion implementation using local projection technique with soundness guaranteed. We compare Proq with existing quantum program assertions and demonstrate the effectiveness and efficiency of Proq by its applications to assert two sophisticated quantum algorithms, the Harrow-Hassidim-Lloyd algorithm and Shor’s algorithm.
Quantum Computing is becoming an increasingly mature area, with a simultaneous escalation of investment in many sectors. Quantum technology will revolutionize all the engineering fields. For example, companies will need to add quantum computing progressively to some or all of their daily operations. It is clear that all existing classical information systems cannot be done away with. Rather than that occurring, it is expected that some quantum algorithms will be added, so that they can work alongside classical information systems. There has been no systematic solution offered to deal with this challenge so far. This research proposes a software modernization approach (model-driven reengineering) designed to restructure classical systems to work in conjunction with quantum systems, thereby providing target environments that combine both of these computational paradigms. The approach proposed is systematic, and based on existing software engineering standards like the Knowledge Discovery Metamodel and the Unified Modelling Language. It could therefore be applied in industry in a way that complies with the existing software evolution processes. The independence of this proposal with respect to quantum programming environments is also guaranteed, making its application feasible in the changing environment in today's quantum industry. The main implication of this approach is technical, but also economic, since it enables the reuse of the knowledge embedded in legacy systems, while at the same time the new quantum-based projects are speeded up.
The scheduling problem of social workers is a class of combinatorial optimization problems that can be solved in exponential time at best. Because is belongs to class of problems known as NP-Hard, which have huge impact huge impact on our society. Nowadays, the focus on the quantum computer should no longer be just for its enormous computing capacity but also for the use of its imperfection, (Noisy Intermediate-Scale Quantum (NISQ) era) to create a powerful machine learning device that uses the variational principle to solve the optimization problem by reducing their complexity’s class. We propose a formulation of the Vehicle Rooting Problem (VRP) with time windows to solve efficiently the social workers schedule problem using Variational Quantum Eigensolver (VQE). The quantum feasibility of the algorithm will be modelled with docplex and tested on IBMQ computers.
Quantum computing technologies are advancing, and the class of addressable problems is expanding. Together with the emergence of new ventures and government-sponsored partnerships, these trends will help to lower the barrier for adoption of new technology and provide stability in an uncertain market. Until then, quantum computing presents an exciting testbed for different strategies in an emerging market. Quantum computing technologies are advancing, and the class of addressable problems is expanding. What market strategies are quantum computing companies and start-ups adopting?
Well-designed software systems, with providers only modules, have been rigorously obtained by algebraic procedures from the software Laplacian Matrices or their respective Modularity Matrices. However, a complete view of the whole software system should display, besides provider relationships, also consumer relationships. Consumers may have two different roles in a system: either internal or external to modules. Composite modules, including both providers and internal consumers, are obtained from the joint providers and consumers Laplacian matrix, by the same spectral method which obtained providers only modules. The composite modules are integrated into a whole Software System by algebraic connectors. These algebraic connectors are a minimal Occam’s razor set of consumers external to composite modules, revealed through iterative splitting of the Laplacian matrix by Fiedler eigenvectors. The composite modules, of the respective standard Modularity Matrix for the whole software system, also obey linear independence of their constituent vectors, and display block-diagonality. The spectral method leading to composite modules and their algebraic connectors is illustrated by case studies. The essential novelty of this work resides in the minimal Occam’s razor set of algebraic connectors — another facet of Brooks’ Propriety principle leading to Conceptual Integrity of the whole Software System — within Linear Software Models, the unified algebraic theory of software modularity.
Machine Learning (ML) is becoming a more and more popular field of knowledge, being a term known not only in the academic field due to its successful applications to many real-world problems. The advent of Deep Learning and Big Data in the last decade has contributed to make it even more popular. Many companies, both large ones and SMEs, have created specific departments for ML and data analysis, being in fact their main activity in many cases. This current exploitation of ML should not mislead us; while it is a mature field of knowledge, there is still room for many novel contributions, namely, a better understanding of the underlying Mathematics , proposal and tuning of algorithms suitable for new problems (e.g., Natural Language Processing), automation and optimization of the search of parameters, etc. Within this framework of new contributions to ML, Quantum Machine Learning (QML) has emerged strongly lately, speeding up ML calculations and providing alternative representations to existing approaches. This special session includes six high-quality papers dealing with some of the most relevant aspects of QML, including analysis of learning in quantum computing and quantum annealers, quantum versions of classical ML models-like neural networks or learning vector quantization-, and quantum learning approaches for measurement and control.
Quantum computing, and to an even greater extent quantum technology, is changing the world. Quantum computing is not an evolution of classical computer science; it is actually a revolution that completely changes the computing paradigm. Quantum computers are based on the principles of quantum mechanics, such as superposition and entanglement, and they seek to boost computational power exponentially. Many problems that have until now been impossible to solve, in practical terms, might very well be able to be addressed by means of quantum computing. The fact is that at the present time quantum computing is influencing most business sectors and research fields, due to its various promising applications. To make such applications become reality, quantum algorithms must be specially coded for these extremely different computers. Although some well-known quantum algorithms already exist, the need for quantum software will increase dramatically in the next years. In that context, quantum software has to be produced in a more industrial and controlled way, i.e., aspects such as quality, delivery, project management, or evolution of quantum software must be addressed. We are sure that quantum computing will be the main driver for a new software engineering golden age during the present decade of the 2020s.
Quantum machine learning has recently attracted much attention from the community of quantum computing. In this paper, we explore the ability of generative adversarial networks (GANs) based on quantum computing. More specifically, we propose a quantum GAN for generating classical discrete distribution, which has a classical-quantum hybrid architecture and is composed of a parameterized quantum circuit as the generator and a classical neural network as the discriminator. The parameterized quantum circuit only consists of simple one-qubit rotation gates and two-qubit controlled-phase gates that are available in current quantum devices. Our scheme has the following characteristics and potential advantages: (i) It is intrinsically capable of generating discrete data (e.g., text data), while classical GANs are clumsy for this task due to the vanishing gradient problem. (ii) Our scheme avoids the input/output bottlenecks embarrassing most of the existing quantum learning algorithms that either require to encode the classical input data into quantum states, or output a quantum state corresponding to the solution instead of giving the solution itself, which inevitably compromises the speedup of the quantum algorithm. (iii) The probability distribution implicitly given by data samples can be loaded into a quantum state, which may be useful for some further applications.
