One of the main drivers for growing the field of quantum computation has been the prospect of creating a quantum computer capable of carrying out Shor's algorithm for huge numbers.Nonetheless, it is critical to recognise that quantum computers will probably only significantly speed up a small subset of issues if one wants to acquire a more comprehensive perspective on them.Building a system that can accommodate a lot of qubits while preserving stability and coherence is one of the biggest problems in quantum computing.Due to their extreme sensitivity to noise and mistakes, quantum systems are particularly susceptible to computing errors.Building a usable quantum computer requires error mitigation and correction, but the techniques for doing this are still in the early phases of research.In quantum computing, all processes and schemes must be reversible in accordance with the law of unitary development.The circuit model is taken into account in the NISQ framework, but there is also the one-way or measurement-based quantum computation approach, which is not reversible but is demonstrated to be comparable to the circuit model.Noisy suggests that the computing capacity of such quantum computers is constrained because of sufficiently high error and decoherence rates.While they are likely too huge to be replicated by traditional computers using brute force, Intermediate-Scale suggests that they are still too small to be mistake corrected, which also adds to the preceding argument about how noisy they are.P stands for the usage of perfect qubits with perfect quantum gates and no decoherence.The capability to control and protect our qubits in a quantum computer to the degree necessary to run such algorithms is commonly described as fault-tolerant quantum computation.This review paper examines the numerous quantum computing strategies, such as Noisy Intermediate Scale Computing (NISQ) , Perfect Intermediate Scale Computing (PISQ), and Fault Tolerant Intermediate Scale Computing (FTISQ), as well as potential future lines of inquiry.
One of the main drivers for growing the field of quantum computation has been the prospect of creating a quantum computer capable of carrying out Shor's algorithm for huge numbers.Nonetheless, it is critical to recognise that quantum computers will probably only significantly speed up a small subset of issues if one wants to acquire a more comprehensive perspective on them.Building a system that can accommodate a lot of qubits while preserving stability and coherence is one of the biggest problems in quantum computing.Due to their extreme sensitivity to noise and mistakes, quantum systems are particularly susceptible to computing errors.Building a usable quantum computer requires error mitigation and correction, but the techniques for doing this are still in the early phases of research.In quantum computing, all processes and schemes must be reversible in accordance with the law of unitary development.The circuit model is taken into account in the NISQ framework, but there is also the one-way or measurement-based quantum computation approach, which is not reversible but is demonstrated to be comparable to the circuit model.Noisy suggests that the computing capacity of such quantum computers is constrained because of sufficiently high error and decoherence rates.While they are likely too huge to be replicated by traditional computers using brute force, Intermediate-Scale suggests that they are still too small to be mistake corrected, which also adds to the preceding argument about how noisy they are.P stands for the usage of perfect qubits with perfect quantum gates and no decoherence.The capability to control and protect our qubits in a quantum computer to the degree necessary to run such algorithms is commonly described as fault-tolerant quantum computation.This review paper examines the numerous quantum computing strategies, such as Noisy Intermediate Scale Computing (NISQ) , Perfect Intermediate Scale Computing (PISQ), and Fault Tolerant Intermediate Scale Computing (FTISQ), as well as potential future lines of inquiry.
A paradigm shift in computation is being brought about by quantum computing, which uses the concepts of quantum mechanics to tackle problems that even the most powerful conventional supercomputers cannot solve. This review provides an in-depth overview of the field, covering everything from basic concepts to the cutting edge. The three fundamental building blocks of quantum processing—the qubit, superposition, and entanglement—are first described.These ideas enable quantum computers to concurrently explore large computational domains. After that, the paper examines the various physical implementations, highlighting the advantages and disadvantages of the top hardware platforms, such as neutral atoms, trapped ions, photonic systems, and superconducting circuits, in terms of coherence and scalability. Shor's method for integer factorization and Grover's algorithm for unstructured search are two examples of groundbreaking quantum algorithms that are highlighted for their potential to achieve exponential and quadratic speedups over their classical counterparts. We also examine how programming languages that bridge the gap between abstract algorithms and physical hardware are being developed, as well as the new quantum software stack. The paper also explores how quantum computing can revolutionize a number of fields, such as machine learning, materials research, medication development, and cryptography. subsequently, we discuss two of the biggest challenges impeding the development of large-scale, fault-tolerant quantum computers: the requirement for robust quantum error correction and decoherence. In the end, a view of the current period of Noisy Intermediate-Scale Quantum (NISQ) and the path towards quantum advantage is presented. Researchers, students, and professionals looking for a comprehensive grasp of this quickly developing and revolutionary topic are expected to find this review to be an invaluable asset.
Quantum computing represents a foundational paradigm shift from traditional classical computational models, leveraging the intrinsic mechanics of quantum physics—specifically superposition, entanglement, and unitary interference—to execute parallel processing frameworks at an exponential operational scale. This state-of-the-art review systematically deconstructs the mathematical framework of quantum bit (qubit) state vectors within complex Hilbert spaces and details pioneering algorithms like Shor's and Grover's operations. Furthermore, we evaluate dominant contemporary hardware frameworks, specifically contrasting superconducting circuits against trapped-ion architectures across critical indices of coherence metrics, operational speeds, and thermal constraints. Finally, this review highlights systemic algorithmic barriers including phase-flip/bit-flip noise profiles, decoherence phenomena, and real-world deployment challenges across cryptographic infrastructure and biochemical modeling matrices, charting the roadmap from Noisy Intermediate-Scale Quantum (NISQ) systems toward scalable, fault-tolerant ecosystems.
In 2017, John Preskill defined Noisy Intermediate Scale Quantum (NISQ) computers as an intermediate step on the road to large scale error corrected fault-tolerant quantum computers (FTQC). The NISQ regime corresponds to noisy qubit quantum computers with the potential to solve actual problems of some commercial value faster than conventional supercomputers, or consuming less energy. Over five years on, it is a good time to review the situation. While rapid progress is being made with quantum hardware and algorithms, and many recent experimental demonstrations, no one has yet successfully implemented a use case matching the original definition of the NISQ regime. This paper investigates the space, fidelity and time resources of various NISQ algorithms and highlights several contradictions between NISQ requirements and actual as well as future quantum hardware capabilities. It then covers various techniques which could help like qubit fidelities improvements, various breeds of quantum error mitigation methods, analog/digital hybridization, using specific qubit types like multimode photons as well as quantum annealers and analog quantum computers (aka quantum simulators or programmable Hamiltonian simulators) which seem closer to delivering useful applications although they have their own mid to longer-term scalability challenges. Given all the constraints of these various solutions, it seems possible to expect some practical use cases for NISQ systems, but with a very narrow window before various scaling issues show up. Turning to the future, a scenario can be envisioned where NISQ will not necessarily be an intermediate step on the road to FTQC. Instead, the two may develop along different paths, due to their different requirements. This leaves open a key question on the trade-offs that may be necessary to make between qubit scale and qubit fidelities in future quantum computers designs.
Quantum systems operate using quantum bits (qubits), which are highly sensitive to external noises and disturbances and they are easily prone to errors. In the Noisy Intermediate-Scale Quantum (NISQ) era, these errors make difficult to build reliable, fault tolerant quantum circuits for real world deployment. This work provides an overview of need for Quantum Error Correction (QEC) in NISQ devices, as qubits commonly get affected by bit-flip, phase-flip, and combined errors that degrades system performance and examines Quantum Error Correction Code (QECC) techniques usage in communication, computation, and quantum multimedia applications such as image and video transmission. In addition, a simple three-qubit repetition circuit is introduced to demonstrate an error-mitigation approach. These findings, also show how QEC improves fidelity, reduces logical errors, and improves noise tolerance. The analysis also identifies challenges and outlines the future research direction aimed at achieving efficient and scalable fault tolerant quantum circuits.
Quantum systems operate using quantum bits (qubits), which are highly sensitive to external noises and disturbances and they are easily prone to errors. In the Noisy Intermediate-Scale Quantum (NISQ) era, these errors make difficult to build reliable, fault tolerant quantum circuits for real world deployment. This work provides an overview of need for Quantum Error Correction (QEC) in NISQ devices, as qubits commonly get affected by bit-flip, phase-flip, and combined errors that degrades system performance and examines Quantum Error Correction Code (QECC) techniques usage in communication, computation, and quantum multimedia applications such as image and video transmission. In addition, a simple three-qubit repetition circuit is introduced to demonstrate an error-mitigation approach. These findings, also show how QEC improves fidelity, reduces logical errors, and improves noise tolerance. The analysis also identifies challenges and outlines the future research direction aimed at achieving efficient and scalable fault tolerant quantum circuits.
Quantum computing is entering a transitional regime between noisy intermediate-scale quantum (NISQ) processing and early fault-tolerant quantum computation (FTQC), in which increasingly capable hardware is beginning to support repeated syndrome measurements, partial error correction, and logical-qubit operations, while residual physical and logical errors remain non-negligible. In this regime, error suppression, error mitigation, and quantum error correction are increasingly better viewed as complementary layers of a unified error-reduction strategy rather than as separate approaches, with each acting at a different stage of the quantum computation to improve simulation reliability. Thus, in this review, we provide a practical and forward-looking overview of the principal hardware error sources and the corresponding error suppression and mitigation methods for reducing their impact across the current NISQ-FTQC transition. We discuss hardware-aware circuit design, coherent-error suppression, readout mitigation, noise extrapolation, classical inference, and software-supported workflows, with particular emphasis on their implementation on actual quantum processors. We further examine how error mitigation techniques can be adapted to encoded and logical-qubit settings so that they can operate alongside quantum error correction to suppress residual logical errors and improve the accuracy of computation in the early fault-tolerant regime.