Learning to Decode in Parallel: Self-Coordinating Neural Network for Real-Time Quantum Error Correction

TL;DR

This work confronts the real-time decoding bottleneck in quantum error correction by introducing a self-coordinating neural network that performs parallel, per-window decoding without explicit local-merging. By predicting a single bit per decoding window and enforcing cross-window consistency through joint training and a Soft-XOR end-to-end fine-tuning method, it achieves high accuracy while meeting stringent throughput requirements. The approach is validated on Zuchongzhi 3.2 hardware for surface codes up to distance $d=7$, and on TPU v6e hardware it demonstrates real-time decoding up to distance $d=25$ per round, outperforming traditional decoders in both accuracy and speed. This parity between accuracy and throughput suggests a practical path toward scalable, real-time fault-tolerant quantum computation, with further potential when combined with larger neural decoders like AQ2 and lattice-surgery-aware extensions.

Abstract

Fast, reliable decoders are pivotal components for enabling fault-tolerant quantum computation (FTQC). Neural network decoders like AlphaQubit have demonstrated potential, achieving higher accuracy than traditional human-designed decoding algorithms. However, existing implementations of neural network decoders lack the parallelism required to decode the syndrome stream generated by a superconducting logical qubit in real time. Moreover, integrating AlphaQubit with sliding window-based parallel decoding schemes presents non-trivial challenges: AlphaQubit is trained solely to output a single bit corresponding to the global logical correction for an entire memory experiment, rather than local physical corrections that can be easily integrated. We address this issue by training a recurrent, transformer-based neural network specifically tailored for parallel window decoding. While it still outputs a single bit, we derive training labels from a consistent set of local corrections and train on various types of decoding windows simultaneously. This approach enables the network to self-coordinate across neighboring windows, facilitating high-accuracy parallel decoding of arbitrarily long memory experiments. As a result, we overcome the throughput bottleneck that previously precluded the use of AlphaQubit-type decoders in FTQC. Our work presents the first scalable, neural-network-based parallel decoding framework that simultaneously achieves SOTA accuracy and the stringent throughput required for real-time quantum error correction. Using an end-to-end experimental workflow, we benchmark our decoder on the Zuchongzhi 3.2 superconducting quantum processor on surface codes with distances up to 7, demonstrating its superior accuracy. Moreover, we demonstrate that, using our approach, a single TPU v6e is capable of decoding surface codes with distances up to 25 within 1us per decoding round.

Figures (14)

• Figure 1: (a) Surface code example for $d = 7$. Data qubits are represented by gray circles. Z stabilizers and X stabilizers are represented by the purple and blue squares (or semi-circle), respectively. Logical Z/X operators are illustrated as red/green rectangles. (b) Memory experiment example that contains multiple syndrome extraction rounds. We use light yellow shading to indicate the time boundaries of the initial and final rounds, as they are physically distinct from the intermediate rounds.
• Figure 2: Influence of decoding parallelism. The decoding latency is the time difference between the decoder response and the syndrome generation. For parallel decoders with insufficient throughput, the latency also grows nearly linearly and becomes unacceptable. In contrast, for a decoder with sufficient throughput, the latency remains asymptotically constant regardless of the number of measurement rounds.
• Figure 3: Decoding window visualization for $d = 5$ and degeneracy example in merge seam with logical error in the core region or the buffer region.
• Figure 4: Overview of our parallel decoding scheme. Each decoding window containing $n$ syndrome measurement rounds will be embedded and go through the RNN for $n$ times, exactly the same as AlphaQubit, while the final output logit is designed to predict the logical error only in the core region of this decoding window.
• Figure 5: Neural network architecture. The basic network architecture is consistent with that of AlphaQubit, with the key modification being that the supervisions are changed from the global logical error to the local logical error within a decoding window.

Theorems & Definitions (4)

• Theorem 1
• proof : Proof
• Conjecture 1
• proof : Proof