Noisy intermediate-scale quantum (NISQ) processors are entering an early fault-tolerance regime where full quantum error correction carries prohibitive resource costs, yet lightweight error detection can meaningfully improve algorithmic success rates. Existing compilation and error-detection toolchains treat these concerns in isolation, with no principled way to balance detection overhead against success probability under latency constraints. We present an integrated hardware-aware compilation and data-driven quantum error-detection (QED) framework that jointly optimises qubit mapping, SWAP insertion, and syndrome-schedule placement via a noise-weighted cost function and a learned multi-objective scheduler. Simulation experiments on an HPC cluster using GPU-accelerated density-matrix simulation (NVIDIA cuQuantum SDK) across VQE, phase-estimation, and Grover benchmarks, three noise profiles, and circuit sizes of 6-20 qubits (depths 10-160), show that joint co-design raises algorithmic success probability by up to 68 percent (95 percent CI: 60 percent to 76 percent) over SABRE on an 8-qubit VQE instance with post-selection.
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16 pages, 15 figures, Springer LNCS format. Code available at https://github.com/Sumitchongder/quantum-hw-aware-pipeline
Noisy intermediate-scale quantum (NISQ) processors are entering an early fault-tolerance regime where full quantum error correction carries prohibitive resource costs, yet lightweight error detection can meaningfully improve algorithmic success rates. Existing compilation and error-detection toolchains treat these concerns in isolation, with no principled way to balance detection overhead against success probability under latency constraints. We present an integrated hardware-aware compilation and data-driven quantum error-detection (QED) framework that jointly optimises qubit mapping, SWAP insertion, and syndrome-schedule placement via a noise-weighted cost function and a learned multi-objective scheduler. Simulation experiments on an HPC cluster using GPU-accelerated density-matrix simulation (NVIDIA cuQuantum SDK) across VQE, phase-estimation, and Grover benchmarks, three noise profiles, and circuit sizes of 6-20 qubits (depths 10-160), show that joint co-design raises algorithmic success probability by up to 68 percent (95 percent CI: 60 percent to 76 percent) over SABRE on an 8-qubit VQE instance with post-selection.
Quantum error detection (QED) offers a promising pathway to fault tolerance in near-term quantum devices by balancing error suppression with minimal resource overhead. However, its practical utility hinges on optimizing design parameters-such as syndrome measurement frequency-to avoid diminishing returns from detection overhead. In this work, we present a comprehensive framework for fault-tolerant compilation and simulation of quantum algorithms using [[n, n-2, 2]] codes, which enable low-qubit-overhead error detection and a simple nearly fault-tolerant universal set of operations. We demonstrate and analyze our pipeline with a purely statistical interpretation and through the implementation of Grover's search algorithm. Our results are used to answer the question is quantum error detection a worthwhile avenue for early-term fault tolerance, and if so how can we get the most out of it? Simulations under the circuit-level noise model reveal that finding optimal syndrome schedules improves algorithm success probabilities by an average of 6.7x but eventual statistical limits from post-selection in noisy/resource-limited regimes constrain scalability. Furthermore, we propose a simple data-driven approach to predict fault tolerant compilation parameters, such as optimal syndrome schedules, and expected fault tolerant performance gains based on circuit and noise features. These results provide actionable guidelines for implementing QED in early-term quantum experiments and underscore its role as a pragmatic, constant-overhead error mitigation layer for shallow algorithms. To aid in further research, we release all simulation data computed for this work and provide an experimental QED compiler at https://codeqraft.xyz/qed.
Noisy Intermediate-Scale Quantum (NISQ) devices represent current quantum computing technology with 50-1000 qubits operating without comprehensive fault-tolerant error correction. The fundamental challenge lies in balancing error correction necessity against prohibitive resource overhead. Conventional quantum error correction codes require 10:1 to 1000:1 qubit ratios and syndrome extraction circuits exceeding 50 gates, consuming entire NISQ capacities. This work presents a comprehensive low-overhead quantum error correction framework specifically designed for NISQ constraints. Our approach combines three elements: optimised stabiliser codes which get qubit ratios of 3:1 to 10:1, adaptive syndrome extraction which works with circuits with less than 20 gates and machine learning-enhanced decoding which is specific to the noise profiles of the hardware. Experimental validation on IBM Quantum (127- qubit Eagle), IonQ trapped-ion systems, and Google Sycamore simulation demonstrates successful quantum state protection achieving 2.7× error suppression with 60% overhead reduction versus conventional surface codes. The proposed code achieves logical error rates of 0.0065 using only 10 physical qubits compared to 25 qubits for equivalent surface codes. Machine learning decoder attains 94.3% accuracy with 12-microsecond inference latency, enabling real-time error correction. Break-even performance achieved at 0.8% physical error rates establishes practical pathways for near-term quantum advantage in variational algorithms and quantum simulation applications.
Real-time decoding is a major bottleneck in scaling quantum error correction (QEC) from noisy intermediate-scale quantum (NISQ) devices to fault-tolerant quantum computing. We present an adaptive confidence-gated decoding framework for the rotated surface code that treats decoding as a two-stage inference problem. A lightweight feed-forward neural network performs fast-path decoding for the majority of syndrome measurements, while only low-confidence predictions are escalated to a minimum-weight perfect matching (MWPM) refinement stage. We benchmark the framework on rotated surface codes with distances d∈{3,5,7,9,11} under circuit-level depolarising noise using the Stim stabiliser simulator. The evaluation characterises logical accuracy, confidence-controlled accuracy-latency trade-offs, decoding throughput, per-shot latency, and decoding-graph resource scaling. Routing only 3.3%-6.2% of syndromes to the refinement stage improves logical accuracy from 99.21% for the neural-only baseline to 99.81% at a confidence threshold of 0.95 while incurring only a bounded increase in average decoding cost. Neural-decoder throughput saturates near 4.6×105 samples s−1 at batch size 512 on commodity CPU hardware, indicating that the neural fast path is not the dominant throughput bottleneck beyond code distance d=7. We release the complete benchmarking pipeline, trained models, raw benchmark data, and source code, and explicitly distinguish the experimentally validated contributions from the broader hardware-aware QEC co-design roadmap, including hardware-constrained code discovery, GPU-accelerated inference, and multi-noise optimisation, which remain directions for future work.
Noisy Intermediate-Scale Quantum (NISQ) devices represent current quantum computing technology with 50-1000 qubits operating without comprehensive fault-tolerant error correction. The fundamental challenge lies in balancing error correction necessity against prohibitive resource overhead. Conventional quantum error correction codes require 10:1 to 1000:1 qubit ratios and syndrome extraction circuits exceeding 50 gates, consuming entire NISQ capacities. This work presents a comprehensive low-overhead quantum error correction framework specifically designed for NISQ constraints. Our approach combines three elements: optimised stabiliser codes which get qubit ratios of 3:1 to 10:1, adaptive syndrome extraction which works with circuits with less than 20 gates and machine learning-enhanced decoding which is specific to the noise profiles of the hardware. Experimental validation on IBM Quantum (127- qubit Eagle), IonQ trapped-ion systems, and Google Sycamore simulation demonstrates successful quantum state protection achieving 2.7× error suppression with 60% overhead reduction versus conventional surface codes. The proposed code achieves logical error rates of 0.0065 using only 10 physical qubits compared to 25 qubits for equivalent surface codes. Machine learning decoder attains 94.3% accuracy with 12-microsecond inference latency, enabling real-time error correction. Break-even performance achieved at 0.8% physical error rates establishes practical pathways for near-term quantum advantage in variational algorithms and quantum simulation applications.
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.
The rapid evolution of Noisy Intermediate-Scale Quantum (NISQ) devices has intensified the need for robust compilation strategies capable of mitigating hardware-induced errors while maximizing computational efficiency. Quantum compilers play a pivotal role in translating high-level quantum algorithms into hardware-executable instructions, yet they face significant challenges related to qubit connectivity constraints, limited coherence times, and stochastic noise. This paper examines error-resilient quantum compiler design for efficient qubit mapping, gate optimization, and noise mitigation in NISQ-era devices, proposing a framework that integrates topology-aware mapping, adaptive gate synthesis, and probabilistic error suppression techniques. By synthesizing advances in quantum circuit optimization, hardware-aware scheduling, and hybrid classical–quantum error correction strategies, the study evaluates how compiler-level innovations can substantially enhance execution fidelity and resource efficiency. The findings suggest that intelligent compiler architectures are critical enablers of practical quantum advantage during the transitional NISQ phase, bridging theoretical algorithm design with real-world hardware constraints.