Quantum computing has reached a pivotal moment in its evolution. No longer confined to theoretical speculation or laboratory curiosities, it now stands at the threshold of broader scientific and industrial engagement. Yet technology is still very much in its adolescence. The present generation of devices, known as noisy intermediate-scale quantum (NISQ) machines, operate with tens to a few hundred qubits, but these qubits are fragile, error-prone, and difficult to scale. Their circuits cannot yet sustain the depth required for solving truly intractable problems, and so their outputs are often statistical approximations rather than reliable solutions. Despite these limitations, NISQ devices have opened an era of experimentation in which the boundaries between quantum theory and practical application are being actively tested.
Quantum computing has reached a pivotal moment in its evolution. No longer confined to theoretical speculation or laboratory curiosities, it now stands at the threshold of broader scientific and industrial engagement. Yet technology is still very much in its adolescence. The present generation of devices, known as noisy intermediate-scale quantum (NISQ) machines, operate with tens to a few hundred qubits, but these qubits are fragile, error-prone, and difficult to scale. Their circuits cannot yet sustain the depth required for solving truly intractable problems, and so their outputs are often statistical approximations rather than reliable solutions. Despite these limitations, NISQ devices have opened an era of experimentation in which the boundaries between quantum theory and practical application are being actively tested.
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 has the potential to solve complex problems that are outside the scope of classical systems, making it a standard shifter. Current devices, which are considered as Noisy Intermediate-Scale Quantum (NISQ) systems, are insufficient in their practical utility due to hardware limitations, error rates, and qubit counts. The dynamic growths wanted to exceed the NISQ era and grow scalable quantum algorithms and architectures that can achieve useful quantum benefit in real-world applications are reviewed in this research. This research gives a comprehensive examination of the complications in scaling quantum systems, adjacent resource efficacy, qubit connectivity, and error correction. In addition to connecting architectural innovations like modular quantum computing, error-resilient circuit design, and distributed quantum systems, the paper provides new hybrid quantum-classical algorithms planned to exploit performance in noisy environments. Results from benchmarking in arenas like machine learning, optimization, and quantum chemistry show how these methods can provide short-term quantum benefit. Lastly, this paper proposes a research roadmap for quantum computing that highlights the requirement of co-designing algorithms, software, and hardware. The goal of this effort is to straighten the progress of quantum systems that can resolve problems in the real world at scale by addressing the inadequacies of NISQ devices and emphasizing scalable solutions.
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 has moved from a theoretical curiosity to a strategic technological priority for governments, hyperscale technology companies, and a fast-growing ecosystem of specialized start-ups. This survey provides a comprehensive, self-contained overview of the field as it stands in 2026. We first lay out the physical and mathematical foundations of quantum computation, superposition, entanglement, interference, and measurement, and contrast them systematically with classical computing. We then survey the competing hardware modalities (superconducting, trapped-ion, photonic, neutral-atom, topological, and spin qubits) and the logic gates and circuit model that operate on them, before reviewing the canonical quantum algorithms that motivate the field. We classify the major computing paradigms (gate-based, annealing, adiabatic, measurement-based, and topological), and examine the current state of the market, the national strategies of leading countries, and the roles played by IBM, Google, Microsoft, Amazon, NVIDIA, and a cohort of pure-play companies. Dedicated sections map undergraduate and graduate education pathways, including specific universities offering quantum-focused degrees, the domains in which quantum computers are expected to create value, and the career paths now opening in the field. We close with an explicit three-phase roadmap \qtoday{}, \qtomorrow{}, and the \qfuture{} and a candid discussion of the open scientific and engineering problems that stand between the present noisy intermediate-scale quantum (NISQ) era and a fault-tolerant, utility-scale quantum computing industry.
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 has become a promising computing approach because of its capability to solve certain problems, exponentially faster than classical computers. A n -qubit quantum system is capable of providing 2 n computational space to a quantum algorithm. However, quantum computers are prone to errors. Quantum circuits that can reliably run on today’s Noisy Intermediate-Scale Quantum (NISQ) devices are not only limited by their qubit counts but also by their noisy gate operations. In this article, we have introduced i -QER, a scalable machine learning-based approach to evaluate errors in a quantum circuit and reduce these without using any additional quantum resources. The i -QER predicts possible errors in a given quantum circuit using supervised learning models. If the predicted error is above a pre-specified threshold, it cuts the large quantum circuit into two smaller sub-circuits using an error-influenced fragmentation strategy for the first time to the best of our knowledge. The proposed fragmentation process is iterated until the predicted error reaches below the threshold for each sub-circuit. The sub-circuits are then executed on a quantum device. Classical reconstruction of the outputs obtained from the sub-circuits can generate the output of the complete circuit. Thus, i -QER also provides classical control over a scalable hybrid computing approach, which is a combination of quantum and classical computers. The i -QER tool is available at https://github.com/SaikatBasu90/i-QER .