Calibration-Conditioned FiLM Decoders for Low-Latency Decoding of Quantum Error Correction Evaluated on IBM Repetition-Code Experiments

TL;DR

This work introduces a calibration-conditioned FiLM decoder for low-latency quantum error correction, leveraging a graph-based hardware encoder to modulate a lightweight CNN via FiLM so that slow hardware calibration informs fast syndrome decoding without increasing latency. On IBM devices performing 1D repetition codes up to distance $d=11$, the FiLM+CNN model generalizes across unseen qubit chains and recalibrated data, achieving up to 11.1x and 7.41x improvements in logical error rate over MWPM on validation and unseen data, respectively, with negligible latency when FiLM is folded into the CNN weights. The results demonstrate hardware-aware adaptive decoding that maintains high throughput and suggests a path toward scalable, fault-tolerant quantum computation, with future work extending to higher-weight stabilizer codes like the surface code. The study also provides a large real-device dataset to facilitate future research in calibration-conditioned quantum decoding.

Abstract

Real-time decoding of quantum error correction (QEC) is essential for enabling fault-tolerant quantum computation. A practical decoder must operate with high accuracy at low latency, while remaining robust to spatial and temporal variations in hardware noise. We introduce a hardware-conditioned neural decoder framework designed to exploit the natural separation of timescales in superconducting processors, where calibration drifts occur over hours while error correction requires microsecond-scale responses. By processing calibration data through a graph-based encoder and conditioning a lightweight convolutional backbone via feature-wise linear modulation (FiLM), we decouple the heavy processing of device statistics from the low-latency syndrome decoding. We evaluate this approach using the 1D repetition code as a testbed on IBM Fez, Kingston, and Pittsburgh processors, collecting over 2.7 million experimental shots spanning distances up to d = 11. We demonstrate that a single trained model generalizes to unseen qubit chains and new calibration data acquired days later without retraining. On these unseen experiments, the FiLM-conditioned decoder achieves up to an 11.1x reduction in logical error rate relative to modified minimum-weight perfect matching. We observe that by employing a network architecture that exploits the highly asynchronous nature of system calibration and decoding, hardware-conditioned neural decoding demonstrates promising, adaptive performance with negligible latency overhead relative to unconditioned baselines.

Figures (7)

• Figure 1: Architecture of the Calibration-Conditioned FiLM Neural Decoder. The framework consists of three core components. (Upper Left) Hardware Encoder: An experimental shot defines a calibration subgraph $G=(V,E)$, extracted from the target IBM Heavy Hex topology device, where node features include normalized $T_1, T_2$, and gate errors. This graph is processed by a 3-layer Graph Convolutional Network (GCN) and pooled to form a latent calibration embedding $\mathbf{z} \in \mathbb{R}^{256}$. (Upper Right) FiLM Generator: A Multi-Layer Perceptron (MLP) projects the latent embedding $\mathbf{z}$ into layer-wise modulation parameters $\boldsymbol{\gamma}^{(\ell)}$ (scale) and $\boldsymbol{\beta}^{(\ell)}$ (shift). (Right) Decoder Arm: The error syndrome tensor $\chi \in \{0, 1\}^{r \times (d-1)}$ is processed by a Convolutional Neural Network (CNN). The feature maps of the CNN layers are modulated via the Feature-wise Linear Modulation (FiLM) operation: $Z^{(\ell)} = \sigma(\boldsymbol{\gamma}^{(\ell)} \odot \text{Conv}(Z^{(\ell-1)}) + \boldsymbol{\beta}^{(\ell)})$. The output CNN features are flattened and mapped to per-qubit correction probabilities via a dense output head.
• Figure 2: Compiled syndrome extraction circuit onto device hardware for $X$-repetition code for a distance $d$ repetition code with $r$ syndrome extraction rounds. State prep in this example prepares the logical $|+\rangle$ state.
• Figure 3: Overall repetition code process deployed, where PREP initializes the logical code word, either $\ket{0}_L$ or $\ket{1}_L$ for a $Z-$ repetition code, or $\ket{+}_L$ or $\ket{-}_L$ for an $X-$ repetition code. Syndrome extraction is repeated $r$ times, after which the data qubits are Measured. See Figure \ref{['fig:synd_ext_example']} for a compiled example over IBM Fez basis gates.
• Figure 4: Validation results: logical error rates in the X-basis as a function of measurement rounds. Logical states $|+\rangle_L$ and $|-\rangle_L$ are tested. Results are shown for code distances $d={3,5,7,9,11}$ for experiment rounds $r={1,3,..d}$ states. We compare the performance of the proposed FiLM + CNN decoder (solid lines) against a standard CNN (dashed lines) and Modified MWPM (dash-dotted lines).
• Figure 5: Validation results: logical error rates in the Z-basis as a function of measurement rounds. Logical states $|0\rangle_L$ and $|1\rangle_L$ are tested. Results are shown for code distances $d={3,5,7,9,11}$ for experiment rounds $r={1,3,..d}$ states. We compare the performance of the proposed FiLM + CNN decoder (solid lines) against a standard CNN (dashed lines) and Modified MWPM (dash-dotted lines).