Abstract Quantum error mitigation is a key enabling technique for extracting reliable computational results from noisy intermediate-scale quantum devices. Among existing approaches, zero-noise extrapolation (ZNE) is widely employed, but its effectiveness deteriorates in high-noise regimes or deep circuits, where measurement outcomes converge to the random-guessing limit. To address this issue, we propose a lightweight, extrapolation-based error mitigation framework that leverages the intrinsic repetitive structure of quantum algorithms. We classify these algorithms into homogeneous and heterogeneous types and efficiently estimate block fidelities using shallow identity sequences of the core operational block, thereby avoiding global circuit folding. Experiments on IBM’s advanced superconducting platform and its corresponding simulator demonstrate that the proposed framework remains effective even in high-noise regimes where folding-based ZNE(f-ZNE) fails due to noise saturation. For a four-qubit Grover search, our approach restores the success probability to near its theoretical value, whereas f-ZNE yields negligible improvement. We further validate the proposed method on a 17-qubit quantum approximate optimization algorithm with layer-dependent parameters, demonstrating robustness beyond fixed-structure circuits. These results indicate that leveraging algorithmic structure provides a practical pathway to extending the performance of extrapolation-based error mitigation on current quantum processors.
Abstract Quantum error mitigation is a key enabling technique for extracting reliable computational results from noisy intermediate-scale quantum devices. Among existing approaches, zero-noise extrapolation (ZNE) is widely employed, but its effectiveness deteriorates in high-noise regimes or deep circuits, where measurement outcomes converge to the random-guessing limit. To address this issue, we propose a lightweight, extrapolation-based error mitigation framework that leverages the intrinsic repetitive structure of quantum algorithms. We classify these algorithms into homogeneous and heterogeneous types and efficiently estimate block fidelities using shallow identity sequences of the core operational block, thereby avoiding global circuit folding. Experiments on IBM’s advanced superconducting platform and its corresponding simulator demonstrate that the proposed framework remains effective even in high-noise regimes where folding-based ZNE(f-ZNE) fails due to noise saturation. For a four-qubit Grover search, our approach restores the success probability to near its theoretical value, whereas f-ZNE yields negligible improvement. We further validate the proposed method on a 17-qubit quantum approximate optimization algorithm with layer-dependent parameters, demonstrating robustness beyond fixed-structure circuits. These results indicate that leveraging algorithmic structure provides a practical pathway to extending the performance of extrapolation-based error mitigation on current quantum processors.
Near term quantum processors operate in a noise dominated regime, motivating error mitigation techniques that recover accurate expectation values without full fault tolerance. Zero Noise Extrapolation (ZNE) is a widely used but biased error mitigation method that lacks rigorous error bounds. Its effective application requires nontrivial technical choices, most notably the selection of noise scaling factors and extrapolation models, making ZNE sensitive to user expertise and often necessitating costly trial and error procedures. Here, we introduce Folding Free Zero Noise Extrapolation (FF-ZNE), a method that removes the need for noise factor selection by achieving effective noise amplification without circuit folding. FF-ZNE exploits isomorphic hardware layouts with distinct native noise profiles, such that executing a fixed circuit across these layouts induces controllable variations in the effective noise strength. Under a depolarizing noise model, we analytically show that the resulting extrapolation admits a fixed linear form, eliminating extrapolator choice and enabling a seamless, user independent mitigation procedure. We further propose two algorithms that identify sets of isomorphic hardware layouts on which a given circuit yields sufficiently distinct expectation values to enable reliable zero noise extrapolation. Experiments on a 133 qubit IBM Quantum device demonstrate that FF-ZNE yields mitigated expectation values with average deviations of ~6% and 4.5% for up to 50 qubit EfficientSU2 (sparse) and Hamiltonian simulation (dense) circuits, respectively. The method is thus scalable and applicable to a broad range of circuits. By eliminating noise factor and extrapolator selection, FF-ZNE transforms zero noise extrapolation from a technique requiring expert tuning into a practical, scalable, and broadly accessible error mitigation method for current quantum hardware.
Recent hundred-qubit processors represent a significant hardware advancement, but current limitations prevent effective quantum error correction (QEC), necessitating reliance on quantum error mitigation (QEM) to enhance result fidelity from quantum computers. Our paper introduces a noise-aware folding technique that enhances Zero-Noise Extrapolation (ZNE) by leveraging the noise characteristics of target quantum hardware to fold circuits more efficiently. Unlike traditional ZNE approaches assuming uniform error distribution, our method redistributes noise using calibration data based on hardware noise models. By employing a noise-adaptive compilation method combined with our proposed folding mechanism, we enhance the ZNE accuracy of quantum gate-based computing using superconducting quantum computers. This paper highlights the uniqueness of our method, summarizes noise accumulation, presents the scaling algorithm, and compares the reliability of our method with those of existing models using linear extrapolation model. Experimental results show that compared to existing folding methods, our approach achieved up to a 23.6% improvement on quantum computer simulators and up to a 44.8% improvement on real quantum computers, with statistical confidence intervals indicating stable performance gains across circuit scales.
Variational quantum circuits (VQCs) are central to near-term quantum computing, yet their practical deployment is severely hindered by noise. While existing error mitigation methods, such as zero-noise extrapolation (ZNE), typically assume static noise, real noisy intermediate-scale quantum (NISQ) systems exhibit dynamic, time-varying noise that remains largely unaddressed. To overcome this critical gap, our work introduces a novel adaptive noise mitigation framework for VQCs that integrates ZNE with contextual multi-armed bandits (CMAB), enabling dynamic, context-aware selection of circuit-folding levels based on ansatz parameters (e.g., depth, parameter count) and the evolving noise environment. Unlike fixed-fold or heuristic ZNE, our approach uses online adaptation to improve the accuracy of ZNE and reduce redundant quantum circuit executions. Our extensive simulations and experiments on real quantum hardware reveal the following important properties: (i) deeper VQCs accumulate noise, degrading accuracy and increasing the number of quantum circuit executions; (ii) ZNE restores estimator fidelity when the folding level is chosen appropriately; and (iii) CMAB-guided folding cuts quantum circuit execution round trips by up to 40\%, bytes exchanged by up to 35\%, and end-to-end cost by up to 30\% under a 10~Mbps budget, with up to 6.9\% higher estimator fidelity (CIFAR-10, depth 3, noise band η=0.05), versus fixed-fold and grid-search ZNE. These results demonstrate substantial performance gains over existing noise mitigation methods, underscoring the effectiveness of our design in supporting robust noise mitigation for VQCs. The source code is also publicly released to support reproducibility.
As quantum computing advances towards practical applications, reducing errors remains a crucial frontier for developing near-term devices. Errors in the quantum gates and quantum state readout could result in noisy circuits, which would prevent the acquisition of the exact expectation values of the observables. Although ultimate robustness to errors is known to be achievable by quantum error correction-based fault-tolerant quantum computing, its successful implementation demands large-scale quantum processors with low average error rates that are not yet widely available. In contrast, quantum error mitigation (QEM) offers more immediate and practical techniques, which do not require extensive resources and can be readily applied to existing quantum devices to improve the accuracy of the expectation values. Here, we report the implementation of a zero-noise extrapolation-based error mitigation technique on a silicon spin qubit platform. This technique has recently been successfully demonstrated for other platforms such as superconducting qubits, trapped-ion qubits, and photonic processors. We first explore three methods for amplifying noise on a silicon spin qubit: global folding, local folding, and pulse stretching, using a standard randomized benchmarking protocol. We then apply global folding-based zero-noise extrapolation to the state tomography and achieve a state fidelity of 99.96% (98.52%), compared to the unmitigated fidelity of 75.82% (82.16%) for different preparation states. The results show that the zero-noise extrapolation technique is a versatile approach that is generally adaptable to quantum computing platforms with different noise characteristics through appropriate noise amplification methods.
The pursuit of practical quantum utility on near-term quantum processors is critically challenged by their inherent noise. Quantum error mitigation (QEM) techniques are leading solutions to improve computation fidelity with relatively low qubit-overhead, while full-scale quantum error correction remains a distant goal. However, QEM techniques incur substantial measurement overheads, especially when applied to families of quantum circuits parameterized by classical inputs. Focusing on zero-noise extrapolation (ZNE), a widely adopted QEM technique, here we devise the surrogate-enabled ZNE (S-ZNE), which leverages classical learning surrogates to perform ZNE entirely on the classical side. Unlike conventional ZNE, whose measurement cost scales linearly with the number of circuits, S-ZNE requires only constant measurement overhead for an entire family of quantum circuits, offering superior scalability. Theoretical analysis indicates that S-ZNE achieves accuracy comparable to conventional ZNE in many practical scenarios, and numerical experiments on up to 100-qubit ground-state energy and quantum metrology tasks confirm its effectiveness. Our approach provides a template that can be effectively extended to other quantum error mitigation protocols, opening a promising path toward scalable error mitigation.
Abstract The practical application of Noisy Intermediate-Scale Quantum (NISQ) hardware is fundamentally limited by gate-level noise, which corrupts computational results. This research addresses this challenge through the development and validation of a modular software framework for Quantum Error Mitigation (QEM). We implement and compare two leading QEM strategies: Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC). The framework is built using the Qiskit library and is validated using a realistic, hardware-calibrated noisy simulator that mimics the error characteristics of a real IBM Quantum device. Our methodology focuses on a robust implementation of ZNE via unitary folding and a proof-of-concept demonstration of the PEC algorithm. The framework's effectiveness is demonstrated on a simulated noisy backend where, for a 3-qubit Greenberger-Horne-Zeilinger (GHZ) state, the baseline state fidelity was increased from 93.5% to 97.3% via ZNE, corresponding to a 59% reduction in the state's infidelity. This work provides a practical demonstration of how software-based error mitigation can enhance the reliability of quantum computations on current noisy hardware.