We consider how to forecast progress in the domain of quantum computing. For this purpose we collect a dataset of quantum computer systems to date, scored on their physical qubits and gate error rate, and we define an index combining both metrics, the generalized logical qubit. We study the relationship between physical qubits and gate error rate, and tentatively conclude that they are positively correlated (albeit with some room for doubt), indicating a frontier of development that trades-off between them. We also apply a log-linear regression on the metrics to provide a tentative upper bound on how much progress can be expected over time. Within the (generally optimistic) assumptions of our model, including the key assumption that exponential progress in qubit count and gate fidelity will continue, we estimate that that proof-of-concept fault-tolerant computation based on superconductor technology is unlikely (<5% confidence) to be exhibited before 2026, and that quantum devices capable of factoring RSA-2048 are unlikely (<5% confidence) to exist before 2039. It is of course possible that these milestones will in fact be reached earlier, but that this would require faster progress than has yet been seen.
We consider how to forecast progress in the domain of quantum computing. For this purpose we collect a dataset of quantum computer systems to date, scored on their physical qubits and gate error rate, and we define an index combining both metrics, the generalized logical qubit. We study the relationship between physical qubits and gate error rate, and tentatively conclude that they are positively correlated (albeit with some room for doubt), indicating a frontier of development that trades-off between them. We also apply a log-linear regression on the metrics to provide a tentative upper bound on how much progress can be expected over time. Within the (generally optimistic) assumptions of our model, including the key assumption that exponential progress in qubit count and gate fidelity will continue, we estimate that that proof-of-concept fault-tolerant computation based on superconductor technology is unlikely (<5% confidence) to be exhibited before 2026, and that quantum devices capable of factoring RSA-2048 are unlikely (<5% confidence) to exist before 2039. It is of course possible that these milestones will in fact be reached earlier, but that this would require faster progress than has yet been seen.
Quantum computers pose a long-term threat to classical cryptographic systems, including those used in blockchain platforms. While prior work has estimated the number of logical qubits required to compromise cryptographic schemes such as RSA and ECDSA, relatively few studies have modeled when such quantum capacity might realistically be achieved. In this paper, we construct a time-series dataset of publicly documented gate-based quantum processors developed between 2016 and 2025. We estimate the number of logical qubits under three fault-tolerance scenarios and apply forecasting models based on exponential trend analysis. Our results provide year-by-year projections for when quantum computers may reach logical qubit thresholds associated with widely used cryptographic schemes. These projections are mapped to specific blockchain security mechanisms, offering a practical timeline for transition planning toward post-quantum systems. These projections should be interpreted as indicators of logical qubit availability rather than precise estimates of full cryptanalytic execution timelines.
Quantum computing has reached a pivotal inflection point with the recent demonstration ofbelow-threshold quantum error correction and the emergence of logical qubits that outperformtheir physical counterparts. This review synthesizes the remarkable progress achieved between2024 and 2026 across multiple quantum hardware platforms, including superconducting circuits,trapped ions, and neutral atom arrays. We examine the theoretical foundations of quantumerror correction codes, with particular emphasis on surface codes and the rapidly advancingquantum low-density parity-check (qLDPC) codes. Key experimental milestones are analyzed,including Google’s Willow chip demonstration of exponential error suppression, IBM’s modularfault-tolerant roadmap culminating in the Starling system, IonQ’s achievement of 48 logicalqubits with a 2:1 encoding ratio, and QuEra’s record-efficiency neutral atom error correctionapproaching the Teraquop regime. The review further explores critical enabling technologiessuch as real-time decoding architectures, magic state distillation protocols, and fault-tolerant gateimplementations. We discuss the remaining challenges in scaling to hundreds of logical qubits,achieving practical logical error rates of 10−10 to 10−15, and realizing end-to-end fault-tolerantalgorithms. By synthesizing these developments, this article provides a comprehensive assessmentof the field’s trajectory toward practical fault-tolerant quantum computing and identifies the keymilestones that will define the next phase of progress.
Remarkable experimental advances in quantum computing are exemplified by recent announcements of impressive average gate fidelities exceeding 99.9% for single-qubit gates and 99% for two-qubit gates. Although these high numbers engender optimism that fault-tolerant quantum computing is within reach, the connection of average gate fidelity with fault-tolerance requirements is not direct. Here we use reported average gate fidelity to determine an upper bound on the quantum-gate error rate, which is the appropriate metric for assessing progress towards fault-tolerant quantum computation, and we demonstrate that this bound is asymptotically tight for general noise. Although this bound is unlikely to be saturated by experimental noise, we demonstrate using explicit examples that the bound indicates a realistic deviation between the true error rate and the reported average fidelity. We introduce the Pauli distance as a measure of this deviation, and we show that knowledge of the Pauli distance enables tighter estimates of the error rate of quantum gates.
Quantum computing is an emerging computational paradigm that uses the principles of quantum mechanics, including superposition, entanglement, and quantum interference, to process information in fundamentally different ways from classical computers. During the last decade, quantum computing has progressed from theoretical research toward experimental and cloud-accessible systems. Recent developments have focused on increasing the number and quality of qubits, reducing gate errors, developing quantum error correction, improving quantum software, and integrating quantum processors with classical high-performance computing systems. Despite significant progress, practical large-scale quantum computing remains challenging because quantum states are extremely sensitive to environmental disturbances, resulting in decoherence and computational errors. Other challenges include limited qubit coherence time, gate fidelity, scalability, cryogenic requirements, quantum error correction overhead, hardware connectivity, programming complexity, and the difficulty of demonstrating useful quantum advantage for real-world applications. Recent developments from major research organizations indicate a shift from simply increasing physical qubit counts toward building reliable logical qubits and fault-tolerant quantum systems. Google has reported progress toward error-corrected logical qubits, while IBM\\\'s roadmap focuses on increasingly complex processors, modular architectures, quantum-classical integration, and fault-tolerant systems. Microsoft is pursuing a topological-qubit approach aimed at scalable quantum computing. This paper reviews the current state of quantum computing, examines major technological and scientific challenges, analyzes current research directions, and identifies future opportunities in drug discovery, materials science, optimization, cryptography, artificial intelligence, finance, and scientific simulation. The study concludes that the most realistic future is likely to involve quantum-centric computing, in which quantum processors work together with classical CPUs, GPUs, high-performance computing systems, and quantum networks rather than completely replacing classical computers.
This study explores the logical aspects of quantum computation through a detailed analysis of key performance parameters, including qubit number, gate depth, entanglement rate, and logical error rate. Using a dataset of 50 quantum circuit observations, we investigate the relationships between these important metrics that determine computational power and system stability. To model gate depth prediction and evaluate quantum system performance, the research uses two machine learning approaches - Gaussian process regression and gradient boosting regression. Statistical analysis reveals significant correlations between the parameters, in particular a strong negative correlation between qubit number and logical error rate (-0.65), and a moderate positive correlation between gate depth and logical error rate (0.62). Both regression models show excellent performance, with Gaussian process regression reaching R² = 0.9776 on the experimental data and gradient boosting regression reaching R² = 0.9436. The findings indicate that while increasing the number of qubits generally reduces logical errors, deep gate circuits introduce additional error sensitivity. The entanglement rates show minimal correlation with other parameters, indicating independent optimization potential. The research contributes to the understanding of quantum computational logic by providing quantitative insights into the parameter relationships essential for fault-tolerant quantum system design. These results have practical implications for quantum algorithm development, circuit optimization, and error correction strategies. The study demonstrates that machine learning approaches can effectively model quantum computational parameters, providing valuable tools to predict system performance and guide quantum hardware development. This work advances the theoretical foundation for scalable quantum computing by elucidating the logical relationships that govern quantum computational processes. Keywords: Quantum Computation, Fault Tolerance, Machine Learning, Quantum Error Correction, Gate Depth Optimization, Qubit Scaling.
The limitations of classical computing in solving complex problems in cryptography, materials science, and optimization necessitate the development of a new computational paradigm based on the principles of quantum mechanics. This article aimed to analyze the current state of quantum computing hardware, evaluate the primary challenges to achieving fault tolerance, and project a realistic timeline for its practical application. The methodology involved a systematic review and comparative analysis of publicly available empirical data from peer-reviewed literature and corporate technical roadmaps, employing a framework of key performance indicators such as coherence times, gate fidelities, and qubit counts to assess leading qubit modalities, including superconducting circuits, trapped ions, and photonic systems. The analysis confirmed that while superconducting qubits currently lead in scalability, with demonstrations of quantum supremacy using 53-qubit processors, trapped ion platforms maintain a significant advantage in gate fidelity and coherence times. The central finding identifies decoherence and high error rates as the fundamental barriers, necessitating that current Noisy Intermediate-Scale Quantum (NISQ) devices rely on error mitigation techniques rather than robust quantum error correction. The comparative assessment concludes that no single qubit modality yet fulfills all DiVincenzo criteria for fault tolerance simultaneously. The path to scalable quantum computing is shown to depend on the successful implementation of topological error-correcting codes like the surface code, which currently requires thousands of physical qubits to create a single stable logical qubit. Projections based on current progress suggest that while demonstrations of quantum utility on specific problems are imminent, fully fault-tolerant quantum computers capable of breaking RSA encryption or revolutionizing drug discovery remain a long-term endeavor, likely requiring several more decades of intensive research and development. The practical value of this research lies in its synthesized technical overview, which provides a clear, evidence-based roadmap for researchers, engineers, and policymakers to navigate the technological hurdles and strategic investments required to realize the transformative potential of quantum computing.