Abstract Quantum computers have made extraordinary progress over the past decade, and significant milestones have been achieved along the path of pursuing universal fault-tolerant quantum computers. Quantum advantage, the tipping point heralding the quantum era, has been accomplished along with several waves of breakthroughs. Quantum hardware has become more integrated and architectural compared to its toddler days. The controlling precision of various physical systems is pushed beyond the fault-tolerant threshold. Meanwhile, quantum computation research has established a new norm by embracing industrialization and commercialization. The joint power of governments, private investors, and tech companies has significantly shaped a new vibrant environment that accelerates the development of this field, now at the beginning of the noisy intermediate-scale quantum era. Here, we first discuss the progress achieved in the field of quantum computation by reviewing the most important algorithms and advances in the most promising technical routes, and then summarizing the next-stage challenges. Furthermore, we illustrate our confidence that solid foundations have been built for the fault-tolerant quantum computer and our optimism that the emergence of quantum killer applications essential for human society shall happen in the future.
Abstract Quantum computers have made extraordinary progress over the past decade, and significant milestones have been achieved along the path of pursuing universal fault-tolerant quantum computers. Quantum advantage, the tipping point heralding the quantum era, has been accomplished along with several waves of breakthroughs. Quantum hardware has become more integrated and architectural compared to its toddler days. The controlling precision of various physical systems is pushed beyond the fault-tolerant threshold. Meanwhile, quantum computation research has established a new norm by embracing industrialization and commercialization. The joint power of governments, private investors, and tech companies has significantly shaped a new vibrant environment that accelerates the development of this field, now at the beginning of the noisy intermediate-scale quantum era. Here, we first discuss the progress achieved in the field of quantum computation by reviewing the most important algorithms and advances in the most promising technical routes, and then summarizing the next-stage challenges. Furthermore, we illustrate our confidence that solid foundations have been built for the fault-tolerant quantum computer and our optimism that the emergence of quantum killer applications essential for human society shall happen in the future.
The quest for quantum advantage, wherein quantum computers surpass the computational capabilities of classical computers executing state-of-the-art algorithms on well-defined tasks, represents a pivotal race in the domain of quantum computing. NISQ (Noisy Intermediate-Scale Quantum) computing has witnessed remarkable advancements, culminating in significant milestones on the journey towards the realization of universal fault-tolerant quantum computers. This transformative turning point, known as quantum supremacy, has been achieved amid a series of breakthroughs, signifying the dawn of the quantum era. Quantum hardware has undergone substantial integration and architectural evolution, contrasting with its nascent stages. In this review, we critically examine the quantum supremacy experiments conducted thus far, shedding light on their implications and contributions to the evolving landscape of quantum computing. Additionally, we endeavor to illuminate a range of cutting-edge proof-of-principle investigations in the realm of applied quantum computing, providing an insightful overview of the current state of applied quantum research and its prospective influence across diverse scientific, industrial, and technological frontiers.
Quantum computing has transitioned from a theoretical curiosity to an emerging technological paradigm with demonstrable computational advantages in specific problem domains. This paper presents a comprehensive review of current advances in quantum computing hardware, software, and near-term applications within the Noisy Intermediate-Scale Quantum (NISQ) era. We examine the architectural evolution of leading quantum platforms, including superconducting, trapped-ion, and photonic systems, analyzing their qubit counts, gate fidelities, and coherence times. The paper evaluates key quantum algorithms Shor's factoring algorithm [1], Grover's search algorithm [2], the Variational Quantum Eigensolver (VQE) [3], and the Quantum Approximate Optimization Algorithm (QAOA) [4] in the context of their practical applicability to real-world problems. We further discuss the milestone of quantum computational advantage demonstrated by Google's Sycamore processor [5] and IBM's ambitious hardware roadmap toward fault-tolerant quantum computing [6]. Our analysis reveals that while universal fault-tolerant quantum computing remains a long-term objective, NISQ-era devices are already yielding valuable results in quantum chemistry simulation, combinatorial optimization, and quantum machine learning. We conclude by identifying the critical challenges—error correction, scalability, and algorithm design that must be addressed to realize the full potential of quantum computing.
Quantum computing represents a paradigm shift in computational capabilities, promising to solve complex problems that remain intractable for classical architectures. Tracing its roots from the theoretical propositions of the 1980s to the Noisy Intermediate-Scale Quantum (NISQ) era of the present, the field is rapidly transitioning from academic curiosity to industrial reality. This manuscript explores the historical trajectory of quantum computing, examining foundational milestones such as Shor’s and Grover’s algorithms. It evaluates the current state of hardware platforms, including superconducting circuits, trapped ions, and photonic systems, highlighting the persistent challenges of decoherence and quantum error correction. Furthermore, the paper analyzes the future trajectory of the technology, focusing on the race toward large-scale fault-tolerant quantum computing (FTQC) and the critical transition to post-quantum cryptography. By synthesizing current roadmaps and industry projections, this study underscores that while significant technical hurdles remain, the realization of scalable quantum advantage will fundamentally disrupt sectors ranging from drug discovery to global cybersecurity.
Quantum computing is advancing rapidly, offering the potential to transform computational paradigms and tackle problems that are intractable for classical systems. Realizing practical quantum systems demands the development of an entirely new computing stack—from qubits and quantum processors to components, wiring and control electronics, transpilers, error handling, software, algorithms, and the compute architecture to integrate quantum and classical resources at scale. This plenary will provide an overview of the current state of quantum computing and outline the milestones on the path toward building a large-scale, fault-tolerant quantum computer by 2029. The significant improvements in hardware, software, and system integration, pushing the performance of quantum computing to reach quantum utility and advance toward quantum advantage, will be presented. Breakthroughs in error correction and a modular approach indicated in the IBM Quantum Roadmap outline a clear path to quantum systems using 200 logical qubits and 100 million quantum operations by 2029 and 2,000 logical qubits a few years later. Furthermore, advances in quantum algorithms, combined with the integration of quantum systems and high-performance computing (HPC), will unlock powerful synergies—accelerating the timeline for applications previously considered to be far in the future.
The transition from classical to quantum computation marks a shift from deterministic binary logic to a probabilistic, entanglement‑driven framework able to address problems beyond classical reach. Today’s Noisy Intermediate ‑ Scale Quantum era features devices that lack full error correction yet already point toward larger, modular systems designed for fault‑tolerant operation. This paper examines the evolving paradigm shift from classical and NISQ ‑ era machines toward practical fault‑tolerant quantum computing, focusing on how advances in physical qubit technologies, control architectures, and error‑correction strategies are converging to bridge noisy prototypes and scalable, useful machines. We synthesize insights from historical semiconductor scaling trends, contemporary roadmaps from leading institutions and industry, and emerging modular designs with real‑time error decoding. Our analysis shows that while challenges around decoherence, connectivity, and classical co‑processing remain, coordinated progress in hardware, control, and software is laying a coherent foundation for future quantum platforms. The work concludes that quantum computing is maturing into a strategically significant paradigm, poised to redefine the limits of computation in simulation, optimization, and secure communication.
Quantum computing is a paradigm shift in computational science, where computational tasks that cannot be computationally tackled with binary computing systems can be tackled using quantum mechanics principles, including superposition, entanglement, and quantum interference. The present paper gives a comprehensive summary of the present condition of quantum computing, including the most advanced hardware systems, such as topological qubits, photonics processors, trapped-ion systems and superconducting qubits, and their corresponding advantages and technical challenges. Also, quantum algorithms, including the Quantum Approximate Optimization Algorithm (QAOA) and the variational quantum eigen solvers (VQE), include a summary of the first algorithm, Shor's factorization method, and the second algorithm, Grover's search algorithm. Applications of such algorithms are evaluated in such areas as financial modeling, machine learning, material science, drug discovery, and cryptography. Taking into account the information provided by large research facilities and technology firms, the conditions under which quantum systems can outperform conventional technology, such a concept as quantum advantage is given specific focus in this review. Moreover, this paper pays particular attention to the key barriers to effective implementation, such as qubit decoherence, large error rates, scalability issues, and the lack of fault-tolerant quantum devices that can be sold commercially. Regarding the noisy intermediate-scale quantum (NISQ) devices that are expected to be available in the near future, we discuss novel approaches to quantum error correction, especially surface code and concatenated code. The quantum software industry, such as IBM Qiskit, Google Cirq, and Microsoft Q, and an evaluation of quantum workforce and research facility readiness across the globe is also discussed. In the end, this work highlights essential potential future paths, such as standards for post-quantum cryptography, hybrid quantum-classical computation, quantum networking and the quantum internet, and the long-term aims for universal fault- tolerant quantum computers. The review should provide researchers, graduate students, and practitioners with a systematic and up-to-date base to understand the fast-growing discipline of quantum computing and its extensive implications on science and business.