Abstract

Quantum computing has advanced rapidly from theoretical foundations to practical experimentation, entering what is known as the Noisy Intermediate-Scale Quantum (NISQ) era. This article provides an in-depth overview of quantum computing in the NISQ era and explores pathways beyond it. NISQ devices, characterized by tens to a few hundred qubits without full error correction, have enabled the execution of small-scale quantum algorithms, opening possibilities for quantum advantage in specific tasks such as quantum simulation, optimization, and machine learning. However, the limitations of noise, decoherence, and scalability continue to challenge their reliability and usefulness in solving real-world problems. The paper examines current NISQ-era technologies, hardware platforms (like superconducting qubits, trapped ions), and prominent algorithms (such as VQE, QAOA, and quantum machine learning models). It also discusses the transition to the fault-tolerant era, which aims to harness large-scale, error-corrected quantum systems for broader applications in cryptography, materials science, drug discovery, and beyond. Finally, the article highlights ongoing research in quantum error correction, quantum hardware development, and hybrid quantum-classical systems that will shape the future of quantum computing. This comprehensive review serves as a guide to understanding the current landscape and future trajectory of quantum technologies.