Quantum computers are still infrequent and expensive. They have a great potential for research and industry, but they are noisy, limited, and not always easy to access. All this is preventing rapid and widespread access to the whole potential of this field. To overcome this bottleneck and foster advances in quantum computing, a large plethora of Quantum Computer Simulators (QCS) have emerged, allowing quantum studies on classical machines, and ultimately on quantum devices as well. In addition to being numerous, these simulators differ from each other in an overwhelming number of aspects, which hardens any attempt to categorise/profile them: making a choice is really difficult for a researcher. This work presents a systematic literature review and a public web repository QoverC of the existing QCS for quantum computation in general, and the leading ones for optimisation in particular. To the best of the authors' knowledge, this is the largest QCS study to date, where we include 199 web, desktop, and hybrid simulators, over 22 programming languages. We also provide a comprehensive comparison spanning over 10 metrics. We aim to bring structure to this domain, foster quantum computing, study their particular features, and ease their use and research in the future.
Quantum computers are still infrequent and expensive. They have a great potential for research and industry, but they are noisy, limited, and not always easy to access. All this is preventing rapid and widespread access to the whole potential of this field. To overcome this bottleneck and foster advances in quantum computing, a large plethora of Quantum Computer Simulators (QCS) have emerged, allowing quantum studies on classical machines, and ultimately on quantum devices as well. In addition to being numerous, these simulators differ from each other in an overwhelming number of aspects, which hardens any attempt to categorise/profile them: making a choice is really difficult for a researcher. This work presents a systematic literature review and a public web repository QoverC of the existing QCS for quantum computation in general, and the leading ones for optimisation in particular. To the best of the authors' knowledge, this is the largest QCS study to date, where we include 199 web, desktop, and hybrid simulators, over 22 programming languages. We also provide a comprehensive comparison spanning over 10 metrics. We aim to bring structure to this domain, foster quantum computing, study their particular features, and ease their use and research in the future.
Developing state-of-the-art classical simulators of quantum circuits is of utmost importance to test and evaluate early quantum technology and understand the true potential of full-blown error-corrected quantum computers. In the past few years, multiple theoretical and numerical advances have continuously pushed the boundary of what is classically simulable, hence the development of a plethora of tools which are often limited to a specific purpose or designed for a particular hardware (e.g. CPUs vs. GPUs). Moreover, such tools are typically developed using tailored languages and syntax, which makes it hard to compare results from, and create hybrid approaches using, different simulation techniques. To support unified and optimized use of these techniques across platforms, we developed HybridQ , a highly extensible platform designed to provide a common framework to integrate multiple state-of-the-art techniques to run on a variety of hardware. The philosophy behind its development has been driven by three main pillars: Easy to Use, Easy to Extend, and Use the Best Available Technology. The powerful tools of HybridQ allow users to manipulate, develop, and extend noiseless and noisy circuits for different hardware architectures. HybridQ supports large-scale high-performance computing (HPC) simulations, automatically balancing workload among different processor nodes and enabling the use of multiple backends to maximize parallel efficiency. Everything is then glued together by a simple and expressive language that allows seamless switching from one technique to another as well as from one hardware to the next, without the need to write lengthy translations, thus greatly simplifying the development of new hybrid algorithms and techniques.
Quantum Computing (QC) and Artificial Intelligence (AI) have emerged as key technologies in the evolution of Industry 6.0, driving advancements in automation and advanced analytics, and process optimization. Their integration holds the potential to revolutionize sectors such as data science, healthcare, finance, and cybersecurity by enabling faster and more efficient computations through qubits, superposition, and quantum entanglement. However, the lack of structured knowledge regarding specific QC methodologies and applications in AI hinders its optimal implementation and development. Consequently, this study aims to identify the applications and variables associated with QC-AI integration. To this end, a systematic literature review was conducted following the PRISMA 2020 methodology, drawing on studies from Scopus and Web of Science databases. This enabled the analysis of trends, limitations, and opportunities in this technological convergence. This study aims to systematically examine the intersection of quantum computing and artificial intelligence by identifying the key technological features, integration requirements, and sectoral applications that define the current state of the field. The review contributes by mapping existing research, highlighting methodological approaches, and revealing gaps that may guide targeted advancements in hybrid quantum AI systems. The insights generated have the potential to accelerate innovation in high-impact domains such as healthcare, finance, energy, and cybersecurity. The findings indicate that the main advances in QC applied to AI focus on quantum optimization, Quantum Machine Learning (QML), and post-quantum cryptography. Notably, sectors such as energy, healthcare, and finance have shown significant progress in adopting these technologies. For example, in healthcare, QML has been applied to simulate molecular interactions to accelerate drug discovery, and in finance, it enhances predictive models for market behavior. The study concludes that although QC demonstrates substantial potential to enhance AI, its broader adoption remains constrained by reliance on NISQ hardware, the need for effective error correction, and the limited scalability of hybrid quantum classical algorithms. Addressing these challenges will be essential to establishing QML as a cornerstone of technological innovation and digital transformation. Additionally, this review introduces an integrative framework that categorizes key AI QC convergence dimensions and proposes a classification of application areas based on technical requirements and algorithmic capabilities. These contributions aim to guide future experimental validations and hybrid model development.
This review offers the first available overview of progress in the field of quantum computer simulation. As research interest in quantum computation grows, together with the number of field researchers, it seems certain that quantum computer simulators will play a major role in this research. The review discusses quantum computer simulators and their role in the study of quantum computation. Currently available simulators are described and compared and recommendations are offered as to the most appropriate uses for specific purposes. An awareness of the functions and features of existing simulators is essential for researchers in the field, to avoid duplication of effort and build on the foundations of previous work. This document is an ongoing project, the latest version will always be available at http://www.dcs.exeter.ac.uk/~jwallace A shorter version of this review is available as Department of Computer Science Technical Report 387. Comments, criticisms and suggestions a...
The technology of Quantum Computing (QC) is continuously evolving, as researchers explore new technologies and the public gains access to quantum computers with an increasing number of qubits. In addition, the research community and industry are increasingly interested in the potential use, application, and contribution of QCs to large-scale problems in the real world as a result of this technological enhancement. QCs operations are based on quantum mechanics, and their special properties are mainly exploited to solve computationally intensive problems in polynomial time, problems that are commonly unsolvable, even by High-Performance Computing systems (HPCs) in a feasible time. However, since QCs cannot perform as general-purpose computing machines, alternative computational approaches aiming to boost further their enormous computing abilities are requested, and their combination as an additional computing resource to HPC systems is considered as one of the most promising ones. In the proposed hybrid HPCs, the Quantum Processing Units (QPUs), similar to GPUs and CPUs, target specific problems that, through Quantum Algorithms, can exploit quantum properties like quantum entanglement and superposition to achieve substantial performance gains from the HPC point of view. This interconnection between classical HPC systems and QCs towards the creation of Hybrid Quantum-Classical computing systems is neither straightforward nor standardized while crucial for unlocking the real potential of QCs and achieving real performance improvements. The interconnection between the classical and quantum systems can be performed in the hardware, software (system), or application layer. In this study, a concise overview of the existing architectures for the interconnection interface between HPCs and QCs is provided, focusing mainly on hardware approaches that enable effective hybrid quantum-classical operation.
We present a comprehensive study of quantum simulation methods and quantum simulators for classical computers. We first study an exhaustive set of 150+ simulators and quantum libraries. Then, we short-list the simulators that are actively maintained and enable simulation of quantum algorithms for more than 10 qubits. As a result, we realize that most efficient and actively maintained simulators have been developed after 2010. We also provide a taxonomy of the most important simulation methods, namely Schrodinger-based, Feynman path integrals, Heisenberg-based, and hybrid methods. We observe that most simulators fall in the category of Schrodinger-based approaches. However, there are a few efficient simulators belonging to other categories. We also make note that quantum frameworks form their own class of software tools that provide more flexibility for algorithm designers with a choice of simulators/simulation method. Another contribution of this study includes the use and classification of optimization methods used in a variety of simulators. We observe that some state-of-the-art simulators utilize a combination of software and hardware optimization techniques to scale up the simulation of quantum circuits. We summarize this study by providing a roadmap for future research that can further enhance the use of quantum simulators in education and research.
Quantum computing has the potential to revolutionise multiple fields by solving complex problems that cannot be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its early stages and the available systems have still very limited resources. As such, currently, the most practical way to develop and test quantum algorithms is to use classical simulators of quantum computers. In addition, the development of new quantum computers and their components also depends on simulations. Given the characteristics of a quantum computer, their simulation is a very demanding application in terms of both computation and memory. As such, simulations do not scale well in current classical systems. Thus different optimisation and approximation techniques need to be applied at different levels. This review provides an overview of the components of a quantum computer, the levels at which these components and the whole quantum computer can be simulated, and an in-depth analysis of different state-of-the-art acceleration approaches. Besides the optimisations that can be performed at the algorithmic level, this review presents the most promising hardware-aware optimisations and future directions that can be explored for improving the performance and scalability of the simulations.