Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

USDs: A universal stabilizer decoder framework using symmetry

Hoshitaro Ohnishi, Hideo Mukai

TL;DR

This work generalizes a symmetry-based re-optimization approach for neural decoders from the Toric code to arbitrary stabilizer codes by introducing a continuous function f that complements syndrome measurements and can be approximated by a multilayer perceptron. A Transformer encoder-based decoder is first trained to map syndrome patterns to error patterns for Color code and Golay code, then re-optimized using the continuous-function approximation to steer predictions toward the zero-corrected state, with only the decoder weights updated. Experiments show the continuous-function approximation achieves high fidelity (Color: ~0.958 cosine similarity; Golay: ~0.933) and yields a notable, stable improvement for the Color code (≈0.8 percentage points at p = 0.05) and a smaller, less consistent gain for Golay (≈0.1 percentage points). The results suggest that learning geometric code structure is advantageous for re-optimization and that future work should tailor architectures to effectively capture algebraic code symmetries to broaden the benefits across stabilizer codes.

Abstract

Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed within a designated subspace. When applying deep learning to the decoding of quantum error-correcting codes, a key challenge arises from the non-uniqueness between the syndrome measurements provided to the decoder and the corresponding error patterns that constitute the ground-truth labels. Building upon prior work that addressed this issue for the toric code by re-optimizing the decoder with respect to the symmetry inherent in the parity-check structure, we generalize this approach to arbitrary stabilizer codes. In our experiments, we employed multilayer perceptrons to approximate continuous functions that complement the syndrome measurements of the Color code and the Golay code. Using these models, we performed decoder re-optimization for each code. For the Color code, we achieved an improvement of approximately 0.8% in decoding accuracy at a physical error rate of 5%, while for the Golay code the accuracy increased by about 0.1%. Furthermore, from the evaluation of the geometric and algebraic structures in the continuous function approximation for each code, we showed that the design of generalized continuous functions is advantageous for learning the geometric structure inherent in the code. Our results also indicate that approximations that faithfully reproduce the code structure can have a significant impact on the effectiveness of reoptimization. This study demonstrates that the re-optimization technique previously shown to be effective for the Toric code can be generalized to address the challenge of label degeneracy that arises when applying deep learning to the decoding of stabilizer codes.

USDs: A universal stabilizer decoder framework using symmetry

TL;DR

This work generalizes a symmetry-based re-optimization approach for neural decoders from the Toric code to arbitrary stabilizer codes by introducing a continuous function f that complements syndrome measurements and can be approximated by a multilayer perceptron. A Transformer encoder-based decoder is first trained to map syndrome patterns to error patterns for Color code and Golay code, then re-optimized using the continuous-function approximation to steer predictions toward the zero-corrected state, with only the decoder weights updated. Experiments show the continuous-function approximation achieves high fidelity (Color: ~0.958 cosine similarity; Golay: ~0.933) and yields a notable, stable improvement for the Color code (≈0.8 percentage points at p = 0.05) and a smaller, less consistent gain for Golay (≈0.1 percentage points). The results suggest that learning geometric code structure is advantageous for re-optimization and that future work should tailor architectures to effectively capture algebraic code symmetries to broaden the benefits across stabilizer codes.

Abstract

Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed within a designated subspace. When applying deep learning to the decoding of quantum error-correcting codes, a key challenge arises from the non-uniqueness between the syndrome measurements provided to the decoder and the corresponding error patterns that constitute the ground-truth labels. Building upon prior work that addressed this issue for the toric code by re-optimizing the decoder with respect to the symmetry inherent in the parity-check structure, we generalize this approach to arbitrary stabilizer codes. In our experiments, we employed multilayer perceptrons to approximate continuous functions that complement the syndrome measurements of the Color code and the Golay code. Using these models, we performed decoder re-optimization for each code. For the Color code, we achieved an improvement of approximately 0.8% in decoding accuracy at a physical error rate of 5%, while for the Golay code the accuracy increased by about 0.1%. Furthermore, from the evaluation of the geometric and algebraic structures in the continuous function approximation for each code, we showed that the design of generalized continuous functions is advantageous for learning the geometric structure inherent in the code. Our results also indicate that approximations that faithfully reproduce the code structure can have a significant impact on the effectiveness of reoptimization. This study demonstrates that the re-optimization technique previously shown to be effective for the Toric code can be generalized to address the challenge of label degeneracy that arises when applying deep learning to the decoding of stabilizer codes.
Paper Structure (11 sections, 6 equations, 3 figures, 5 tables)

This paper contains 11 sections, 6 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Problem Setting
  4. Continuous Extension of Syndrome Measurements Applicable to Arbitrary Stabilizer Codes
  5. Training and Re-optimization of the Decoder
  6. Results and discussion
  7. Approximation Accuracy of Continuous Functions
  8. Effect of Re-optimization in the Color Code
  9. Effect of Re-optimization in the Golay Code
  10. Comparison and Discussion of Re-optimization Effects Across Codes
  11. Conclusions

Figures (3)

  • Figure 1: Conceptual illustration of the color code with code distance 5. White circles represent data qubits, and each face corresponds to a stabilizer generator acting on the adjacent data qubits.
  • Figure 2: Results of experiments on the Color code.
  • Figure 3: Results of experiments on the Golay code.