Exploiting the coherence and entanglement of quantum many-qubit states, quantum computing can significantly surpass classical algorithms, making it possible to factor large numbers, solve linear equations, simulate many-body quantum systems, etc., in a reasonable time. With the rapid development of quantum computing hardware, many attention has been drawn to explore how quantum computers could go beyond the limit of classical computation. Owing to the need of a universal fault-tolerant quantum computer for many existing quantum algorithms, such as Shor’s factoring algorithm, and considering the limit of near-term quantum devices with small qubit numbers and short coherence times, many recent works focused on the exploration of demonstrating quantum advantages using noisy intermediate-scaled quantum devices and shallow circuits, and hence some sampling problems have been proposed as the candidates for quantum advantage demonstration. This review summarizes quantum advantage problems that are realizable on current quantum hardware. We focus on two notable problems—random circuit simulation and boson sampling—and consider recent theoretical and experimental progresses. After the respective demonstrations of these two types of quantum advantages on superconducting and optical quantum platforms, we expect current and near-term quantum devices could be employed for demonstrating quantum advantages in general problems.
Identify, Transform, Benchmark, Show Quantum Advantage (ITBQ): Evaluating use cases for quantum computers. We introduce a four-step framework for assessing quantum computing applications -- from identifying relevant industry problems to demonstrating quantum advantage -- addressing steps often overlooked in the literature, such as rigorous benchmarking against classical solutions and the challenge of translating real-world tasks onto quantum hardware. Applying this framework to cases like NMR, multireference chemistry, and radicals reveals both significant opportunities and key barriers on the path to practical advantage. Our results highlight the need for transparent, structured criteria to focus research, guide investment, and accelerate meaningful quantum progress.
Abstract Quantum computing (QC) is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum‐mechanical principles such as entanglement and superposition. It is anticipated that this computational advantage of QC will help to solve many complex and computationally intractable problems in several application domains such as drug design, data science, clean energy, finance, industrial chemical development, secure communications, and quantum chemistry. In recent years, tremendous progress in both quantum hardware development and quantum software/algorithm has brought QC much closer to reality. Indeed, the demonstration of quantum supremacy marks a significant milestone in the Noisy Intermediate Scale Quantum (NISQ) era—the next logical step being the quantum advantage whereby quantum computers solve a real‐world problem much more efficiently than classical computing. As the quantum devices are expected to steadily scale up in the next few years, quantum decoherence and qubit interconnectivity are two of the major challenges to achieve quantum advantage in the NISQ era. QC is a highly topical and fast‐moving field of research with significant ongoing progress in all facets. A systematic review of the existing literature on QC will be invaluable to understand the state‐of‐the‐art of this emerging field and identify open challenges for the QC community to address in the coming years. This article presents a comprehensive review of QC literature and proposes taxonomy of QC. The proposed taxonomy is used to map various related studies to identify the research gaps. A detailed overview of quantum software tools and technologies, post‐quantum cryptography, and quantum computer hardware development captures the current state‐of‐the‐art in the respective areas. The article identifies and highlights various open challenges and promising future directions for research and innovation in QC.