1 Introduction
Quantum computing is entering a critical transition from demonstrating computational advantage to delivering practical utility. Over the past few years, multiple experimental platforms have achieved quantum advantage on carefully designed computational tasks [
1–
8], establishing quantum computation as a physically realizable paradigm for beyond-classical information processing. These achievements mark a significant milestone, but they also highlight a more fundamental question:
what is required for quantum computation to become practically useful?Answering this question requires a shift in perspective. The notion of quantum advantage, as demonstrated in benchmark settings, does not directly imply practical relevance. Bridging this gap involves moving beyond isolated demonstrations of computational superiority toward a systems-level understanding of what makes quantum computation useful in realistic settings. This includes not only the identification of meaningful application domains, but also a re-examination of the algorithmic and hardware assumptions under which quantum advantages are expected to emerge.
From this viewpoint, the central challenge of the field is no longer the existence of quantum advantage, but its transformation into a robust and scalable computational resource. This transition is shaped by three intertwined aspects: the alignment between quantum computation and real-world problems, the conditions under which quantum algorithms provide genuine and sustainable advantages, and the extent to which physical hardware can support these requirements.
In this perspective, we discuss how recent developments across quantum hardware, algorithm design, and quantum-classical co-design are beginning to reshape this landscape (see Fig. 1). Rather than focusing on individual milestones or isolated progress, we emphasize the emerging structural convergence that may ultimately enable practical quantum advantage. We further analyze where such advantages are most likely to appear first, and argue that their realization will depend on the co-evolution of hardware capabilities, algorithmic understanding, and application-driven discovery.
2 The gap between quantum advantage and practical utility
Demonstrations of quantum advantage have convincingly shown that quantum computers can outperform classical machines on carefully designed computational tasks. However, such demonstrations do not automatically translate into practical utility.
A key limitation is the utility gap. Most existing demonstrations are based on benchmark problems, such as random circuit sampling and boson sampling, which are designed primarily to maximize quantum-classical separation rather than to address real-world needs. While these experiments represent important milestones, their direct relevance to scientific or industrial applications remains limited. Practical quantum advantage, in contrast, requires solving problems of genuine scientific and technological importance, including quantum simulation, electronic structure calculation, materials discovery, optimization, and machine learning.
A second limitation is the algorithmic gap. Even for practically relevant problems, quantum advantage is not guaranteed. Many quantum algorithms provide asymptotic speedups that are weakened in realistic settings due to resource overheads, finite-size effects, data-loading costs, and implementation constraints. Bridging this gap requires not only new algorithms, but also a more precise understanding of when quantum resources can yield robust and measurable advantages under realistic assumptions.
A third limitation is the
hardware gap. Current quantum devices remain in the noisy intermediate-scale quantum (NISQ) regime [
9,
10], where limited coherence, imperfect gates, and measurement errors constrain circuit depth and computational accuracy. As a result, many theoretically promising algorithms remain experimentally inaccessible. Progress toward scalable and fault-tolerant architectures, together with advances in error mitigation, compilation, and system-level optimization, is essential for expanding the range of achievable computations.
These three gaps are tightly interconnected. Practical quantum advantage will require their simultaneous reduction through co-design of applications, algorithms, and hardware.
3 Emerging routes toward practical quantum advantage
Recent progress in quantum computing is increasingly driven by three mutually reinforcing trends: hardware scaling toward fault tolerance, a shift toward practically meaningful quantum algorithms, and deeper integration with classical computation.
One defining trend is the rapid maturation of quantum hardware [
11–
13]. Quantum processors have evolved from laboratory prototypes to programmable systems with hundreds to thousands of qubits across multiple physical platforms. This progress is driven by advances in fabrication, cryogenic engineering, control electronics, and automated calibration. Importantly, hardware progress is no longer measured only by qubit count: improvements in gate fidelity and coherence have enabled early demonstrations of logical qubits and error suppression below threshold. In parallel, advances in error correction codes, decoding, and architecture design are steadily reducing the overhead required for scalable quantum computation.
A second trend is the growing emphasis on practical quantum algorithms. While quantum algorithms often provide asymptotic advantages, realizing these gains in practice requires careful accounting of quantum resources [
14] and implementation costs. This has shifted the field from asking whether quantum speedups exist in principle to understanding when such speedups survive under realistic constraints. Quantum-inspired algorithms [
15] have clarified that some expected advantages rely critically on assumptions such as efficient state preparation, sharpening the boundary between classical and quantum computation. Meanwhile, research on variational quantum algorithms has moved beyond classical analogues toward studying the intrinsic properties of parameterized quantum circuits, including expressibility, trainability, and generalization. At the same time, increasing attention to resource estimation, hardware-aware compilation, and native-gate implementation reflects a shift toward practically realizable quantum computation.
A third trend is the integration of classical computation into the quantum workflow. Classical optimization and machine learning now play essential roles in calibration, control, pulse optimization, and error decoding. At the algorithmic level, error mitigation, classical shadows, tensor-network methods, surrogate models [
16], and learning-based techniques [
17] reduce quantum resource requirements while improving performance. This reflects an emerging quantum-classical co-design paradigm, where classical and quantum resources are jointly optimized rather than treated separately.
4 Where might practical quantum advantage first emerge?
A central question is not whether practical quantum advantage will emerge, but where it is most likely to appear first. While inherently uncertain, structural considerations suggest that early breakthroughs are more likely in domains where quantum systems naturally match underlying physical processes and where partial improvements already yield scientific value.
Quantum simulation [
18–
23] is the most natural candidate. Quantum devices are intrinsically suited to representing quantum states and dynamics, making them well matched to strongly correlated materials and many-body systems that are classically intractable. Unlike benchmark tasks, quantum simulation is directly tied to scientific discovery, where even moderate improvements can yield new physical insight.
Chemistry and materials science [
24–
26] are closely related opportunities. These problems are fundamentally governed by quantum mechanics and are central to energy, catalysis, and materials design. While large-scale industrial applications will require fault-tolerant systems, progress in algorithms, error mitigation, and early logical qubits suggests that meaningful scientific advantages may appear at earlier stages for specific problem classes.
Optimization and machine learning [
27–
29] form a more uncertain frontier. Although widely studied and highly relevant to industry, these domains have weaker structural alignment with quantum dynamics, and classical methods continue to improve rapidly. As a result, robust evidence of sustained quantum advantage remains limited, and their role as early applications remains uncertain.
Despite these promising directions, it remains unclear which domain will yield the first definitive practical quantum advantage. A “killer application” has yet to be identified, and its emergence will depend critically on continued advances in hardware. As quantum devices improve, they not only expand computational capabilities but also reshape algorithm design and stimulate broader scientific engagement. Historically, such hardware-driven transitions have often triggered rapid methodological innovation. Whether quantum computing will experience a similar feedback loop — eventually comparable to the rise of large-scale machine learning — remains an open question.
5 Outlook
The past decade has transformed quantum computing from a theoretical concept into an experimental reality, with multiple platforms demonstrating quantum advantage on tasks beyond classical reach. These achievements have established quantum computation as a credible scientific paradigm. The next challenge is no longer demonstrating quantum advantage on benchmarks, but achieving practical quantum utility. This requires generating scientifically or technologically meaningful outcomes that cannot be efficiently reproduced classically.
Achieving this goal will require progress across hardware, algorithms, and applications in a tightly integrated manner. Success will depend not only on scaling qubit numbers, but also on developing reliable workflows and embedding quantum processors into broader computational ecosystems.
Progress is unlikely to be linear. Instead, it will emerge through iterative feedback between hardware advances, algorithmic innovation, and application-driven discovery. Early successes are likely to appear in specialized scientific domains before expanding outward.
Ultimately, practical quantum advantage represents the point at which quantum computing transitions from demonstrating computational possibility to delivering real-world value, enabling new scientific insights and technological capabilities.
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