quantum noise and error modeling

Addressing the unreliability of quantum measurements under depolarizing noise—dominant in the NISQ era—this paper proposes a statistically driven quantum error mitigation (QEM) method to accurately estimate the most probable noise-free output from noisy measurement samples. The method introduces an innovative two-stage “filtering + EM” framework: first, a heuristic filtering stage explicitly isolates and suppresses non-informative depolarizing noise; second, expectation-maximization (EM) is applied to the denoised data to enhance both interpretability and scalability of maximum-likelihood estimation. Small-scale experiments using Qiskit demonstrate that the approach significantly outperforms existing statistical QEM techniques. Further validation on synthetic datasets confirms its scalability to systems with ~100 qubits. By unifying theoretical rigor with engineering practicality, this work establishes a novel paradigm for error mitigation in intermediate-scale noisy quantum computation.

In the NISQ era, anomalous quantum program behavior arises from the entanglement of software bugs and hardware noise, rendering conventional debugging methods ineffective due to their inability to disentangle these distinct root causes. Method: We propose the first statistically grounded quantum error attribution framework, leveraging probabilistic modeling and hypothesis testing over repeated circuit executions to characterize output distributional properties and construct interpretable, quantitative discriminative metrics that separate software errors from physical noise. Contribution/Results: Evaluated on canonical algorithms—including Grover’s, Deutsch-Jozsa, and Simon’s—the framework achieves significantly higher attribution accuracy than baseline approaches. It transcends the applicability limits of classical debugging paradigms in quantum settings and delivers the first theoretically sound and practically deployable error classification tool for quantum software engineering.

This study addresses the critical lack of systematic investigation into faults in quantum simulators, which has left their reliability risks poorly understood. For the first time, we conduct an empirical analysis of 394 real-world defects across 12 widely used open-source quantum simulators. Through manual classification and root-cause tracing, we systematically characterize failure modes along multiple dimensions—including defect origins, manifestations, affected components, and detection mechanisms. Our findings reveal a prevalence of silent logical errors and critical failures stemming from classical infrastructure issues such as memory management and dependency compatibility, challenging the conventional testing paradigm that focuses narrowly on quantum-specific logic. Notably, most crashes and resource-related errors are reported post-deployment by users, whereas logical errors often produce incorrect outputs without triggering exceptions, offering crucial insights for advancing quantum software testing and verification methodologies.

Quantum error mitigation is crucial for enhancing the performance of noisy intermediate-scale quantum (NISQ) devices, yet existing approaches rely either on prior noise models or access to ideal, noise-free training data. This work proposes a fully noise-agnostic neural-network-based error mitigation framework—requiring neither pre-specified noise parameters nor noiseless reference data. Its core innovation is quantum data augmentation: a self-supervised signal is constructed directly from noisy measurement outcomes to train the mitigator end-to-end. This enables robustness across diverse noise models and hardware platforms. The method applies broadly to quantum circuits, many-body systems, and continuous-variable setups. Extensive validation demonstrates significant improvements in measurement statistical fidelity—both in simulations of noisy quantum circuits and on real superconducting quantum processors. By eliminating the need for device-specific calibration or noise characterization, our approach establishes a practical, general-purpose, and calibration-free paradigm for quantum error mitigation on near-term quantum hardware.

This work addresses the gap between idealized noise-free models and real-world noisy quantum hardware in quantum program verification. It introduces, for the first time, a noise-aware quantum Hoare logic that integrates hardware-specific error models—such as those provided by IBM Qiskit—to define a realistic noisy semantics. The study further demonstrates the critical role of classical probabilistic branching in achieving optimality in quantum programs. Building on this foundation, the authors develop a bounded verification algorithm and an automated synthesis method capable of generating optimal quantum subroutines tailored to specific noise environments, including tasks like parity computation, state preparation, and state discrimination. The efficacy of the proposed approach is validated against actual hardware specifications.

Current quantum computing platforms are constrained by noise and limited qubit counts, hindering the realization of scalable systems. This work proposes a unified analytical framework that rapidly predicts the logical error rates of leading quantum error-correcting codes across mainstream hardware and distributed architectures by modeling two key factors: code structure and two-qubit gate overhead. For the first time, this framework analytically reproduces the qualitative trends observed in large-scale simulations and precisely identifies the dominant sources of logical errors—such as circuit volume, routing overhead, or asymmetric noise—across diverse platforms. Experimental validation confirms its cross-platform predictive accuracy and delineates the optimal design regime for distributed quantum error correction, offering critical guidance for the development of scalable distributed quantum computing systems.

This work addresses the challenge of error propagation and unreliable outcomes in noisy quantum computing, arising from both hardware noise and intrinsic stochasticity. It introduces, for the first time, a systematic uncertainty quantification (UQ) framework into quantum computation by formulating the problem as a statistical inference task. By integrating tools from probabilistic modeling, Bayesian inference, stochastic analysis, and sensitivity analysis, the study establishes a novel paradigm for error characterization and algorithm design tailored to noisy intermediate-scale quantum (NISQ) devices. The proposed uncertainty-aware framework is not only scalable but also provides a unified and mathematically rigorous foundation for error verification, characterization, and mitigation strategies.

Quantum error detection faces significant challenges in scalability, including exponentially growing sampling and post-processing overheads as well as constant resource costs from encoding that may compromise accuracy. This work presents the first systematic benchmarking of repetition and three-qubit bit-flip codes for logical memory and computation on medium-scale real and simulated noisy quantum hardware, encompassing up to 74 physical qubits. The authors introduce a pseudo-threshold estimation method to quantitatively assess code efficacy. Their experiments uncover both the current scalability limitations and the latent potential of existing devices, offering crucial empirical insights to guide the design of future fault-tolerant quantum architectures.

This study addresses the lack of systematic analysis on the combined impact of classical input noise and quantum hardware noise on the performance of variational quantum classifiers. For the first time, it jointly models both noise sources: employing a noisy ZZ feature map for classical data encoding and incorporating quantum noise channels—including depolarizing, amplitude/phase damping, Pauli errors, and readout errors—via Qiskit Aer. The work systematically evaluates model robustness under multi-level composite noise scenarios. Experimental results reveal that classical input noise significantly amplifies quantum decoherence effects, exacerbating training instability and leading to a marked drop in classification accuracy. These findings elucidate the synergistic mechanism through which classical and quantum noise jointly degrade model performance.

Existing quantum programming languages struggle to balance programmability and resource estimation accuracy in fault-tolerant computing: they either expose excessive hardware details or incur resource inefficiencies due to over-abstraction. This work proposes a novel fault-tolerant quantum programming language that introduces programmer-visible error-correction abstractions and integrates a cross-layer hardware-software co-analysis mechanism. This approach enables fine-grained, high-fidelity resource modeling and estimation, significantly reducing the fault-tolerance overhead for large-scale practical quantum algorithms while delivering precise and actionable resource assessments.