Few-Shot Cross-Device Transfer for Quantum Noise Modeling on Real Hardware

Abstract: In the noisy intermediate-scale quantum (NISQ) regime, quantum devices contain hardware-specific noise sources which restrict device-invariant error mitigation strategies. We explore transfer learning approaches to apply noise models learned on one quantum device to a different device with the help of a small amount of data. We create a real-hardware dataset from two IBM quantum devices, ibm_fez (source) and ibm_marrakesh (target), comprising 170 noisy and ideal circuit output distributions, with device calibration features added. We train a residual neural network on the source device to map noisy to ideal outcomes. The zero-shot transfer test shows a KL divergence of 1.6706 (up from 0.3014), establishing device specificity. With K = 20 fine-tuning samples, KL drops to 1.1924 (28.6% improvement over zero-shot), recovering 34.9% of the gap between zero-shot and in-domain KL. Ablation studies reveal that the major cause of mismatches across devices is CX gate error, followed by readout error. The results show quantum noise can be learned and fine-tuned with minimal samples, and provide a plausible approach to cross-device quantum error mitigation.

• The paper's main contribution is the development of a few-shot transfer method that adapts a neural quantum noise model from one IBM device to another with minimal new data.
• It employs a residual learning architecture and selective fine-tuning of network layers to significantly reduce KL divergence in cross-device scenarios.
• The study emphasizes the critical role of device-specific calibration, notably the CX gate error, in influencing noise modeling and mitigation performance.

Few-Shot Cross-Device Transfer for Quantum Noise Modeling on Real Hardware

Introduction and Motivation

Quantum computation in the NISQ era is critically challenged by device-specific and temporally varying noise profiles, rendering device-agnostic error mitigation strategies ineffective. Existing quantum error mitigation (QEM) methods, including ZNE, PEC, and classical machine learning models, largely assume noise homogeneity or require extensive per-device calibration, leading to fragile or resource-intensive deployments. The paper "Few-Shot Cross-Device Transfer for Quantum Noise Modeling on Real Hardware" (2604.24397) examines the feasibility of using few-shot transfer learning to adapt a neural quantum noise model, initially trained on data from one superconducting platform, to operate with minimal data on a different IBM quantum chip exhibiting a distinct noise landscape. This work situates itself at the confluence of data-driven QEM and transfer learning, addressing the challenge of scalability and generalization in realistic, hardware-constrained quantum settings.

Experimental Design

The study constructs a controlled dataset sampled from two IBM Quantum backends: ibm_fez (source) and ibm_marrakesh (target). It comprises paired collections of 85 quantum circuits per device—spanning random, Bell, GHZ, and QFT circuit families with 2–5 qubits and depths 2–8—yielding a total of 170 (noisy, ideal) distribution pairs. For each realization, the dataset also annotates device calibration statistics: mean $T_1$, $T_2$, readout error, and CX gate error. These features are standardized using source-device statistics to ensure consistent interpretability during transfer.

Each data sample is encoded as a 41-dimensional vector, with scalar calibration and structure features concatenated to the noisy output distribution over 32 computational basis states (zero-padded for shorter circuits). The neural noise-correction task is formulated as supervised distribution regression, with the aim to map from (noisy output, circuit, calibration) to the corresponding ideal computational distribution.

Model Architecture and Training Protocol

The core model, denoted as the Residual Noise Adapter (RNA), is an MLP with residual structure: rather than predicting the ideal distribution outright, the network learns corrections to the noisy input distribution. Formally, the output is: $$\hat{\mathbf{y}} = \mathrm{softmax}\left(\mathbf{x}_{\text{noisy}} + f_\theta(\mathbf{x})\right)$$ where $\mathbf{x}_{\text{noisy}}$ is the noisy probability distribution subvector and $f_\theta$ is the network’s learned correction.

The backbone architecture consists of three hidden layers with residual connections, LayerNorm, GELU activations, and dropout, enforcing an inductive bias toward sample efficiency and stable convergence. The design ensures that in the absence of data, the network defaults to the identity map, outputting the noisy distribution unchanged.

Training proceeds exclusively on ibm_fez data (A), using standard supervised minimization of the KL divergence between predicted and ideal distributions. The model is validated with held-out data to monitor overfitting. Post-training, transfer protocols are established: (1) in-domain (A→A), (2) zero-shot (A→B), and (3) few-shot with $K$ adaptation samples (A→B, $K = \{5,10,20\}$). For few-shot fine-tuning, only the output head (and, for $K=20$, the final hidden block) is updated, with a replay buffer of source samples to prevent catastrophic forgetting.

Main Results

The primary contribution is the quantitative analysis of transfer performance under limited adaptation data:

• Zero-shot transfer: Applying the source-trained model to the target device yields a KL divergence of 1.6706, in stark contrast to 0.3014 in-domain—a 5.5× degradation—demonstrating the pronounced device specificity of learned noise models.
• Few-shot adaptation: With $K=20$ target-device circuits, fine-tuning recovers 28.6% of the KL loss relative to zero-shot, corresponding to 34.9% closure of the domain shift gap. This adaptation is monotonic in $K$ and robust to sampling seeds.
• Improvements in KL divergence primarily target low-probability regions, not always reflected in the total variation (TV) metric, which sometimes increases marginally due to overcorrection in high-probability states.
• An ablation analysis indicates that the principal factor underlying failed transfer is the large (70.7%) cross-device disparity in CX gate error, followed by smaller but notable effects from readout error. Removal of CX gate error from input features during zero-shot transfer decreases KL, indicating that the mapping learned is device-regime specific and miscalibrated on the target.

Theoretical and Practical Implications

Scalability: The results directly demonstrate that quantum noise models can be effectively repurposed across devices with minimal overhead, provided that a structured few-shot adaptation protocol is used. In practice, this enables reference noise models to be trained centrally and then rapidly customized to new backends or calibration states with a handful of real-hardware executions, exponentially reducing calibration and data collection costs.

Error Physics and Model Design: The residual learning architecture is justified not only statistically—since most quantum noise manifests as parametric deviations from the ideal—but also physically: gate and measurement errors act as structured, device-specific distortions, for which distributional residual learning is both unbiased and sample-efficient. The model’s bias towards near-identity at initialization avoids catastrophic overfitting in the small-$T_2$0 regime.

Device Calibration Features: The ineffectiveness of mean-aggregated $T_2$1, $T_2$2, and the dominant role played by CX error in adaptation highlight the limitations of using only coarse calibration summaries; future models will benefit from more granular, perhaps topological, noise descriptors.

Comparison with Classical QEM: Unlike ZNE and PEC, which are limited by sample cost and/or require explicit device characterization, the RNA-based approach amortizes adaptation cost across arbitrary circuits and scales efficiently via transfer. It sits orthogonally to hardware-extrapolation and quasi-probability approaches.

Limitations and Future Directions

The work is quantitatively robust within its dataset but is subject to the typical constraints of quantum hardware experimentation: limited sample size, circuit widths, and calibration timepoints. Calibration features are mean-aggregated, ignoring qubit-resolved and connectivity-specific effects. Temporal drift and deeper circuits remain unexplored. The choice of an MLP backbone, although justified for isolating transfer effects, may be suboptimal, and integrating GNNs or attention mechanisms would likely capture circuit-noise interactions more effectively.

Crucially, the empirical evidence supports that source-to-target device transfer is viable with limited data, but generalization across a broader array of devices, longer temporal spans, and more complex circuits will require both architectural and dataset enhancements.

Conclusion

The study provides rigorous, numerically substantiated evidence that quantum noise mitigation models in the NISQ domain are inherently device-specific but can be efficiently adapted to new hardware contexts with few-shot training. By leveraging residual distribution learning and layer-selective fine-tuning, up to one-third of the performance gap induced by hardware transfer can be closed with minimal data. The approach operationalizes practical, scalable deployment of data-driven QEM in multi-device, cloud-based quantum computation settings and identifies clear avenues for increased generalization through richer calibration features, advanced architectures, and temporal adaptation protocols.