Neural-Network Decoders for Quantum Error Correction Using Surface Codes: A Space Exploration of the Hardware Cost-Performance Tradeoffs

Ramon W.J. Overwater*, Masoud Babaie, Fabio Sebastiano*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)
132 Downloads (Pure)


Quantum error correction (QEC) is required in quantum computers to mitigate the effect of errors on physical qubits. When adopting a QEC scheme based on surface codes, error decoding is the most computationally expensive task in the classical electronic back-end. Decoders employing neural networks (NN) are well-suited for this task but their hardware implementation has not been presented yet. This work presents a space exploration of fully connected feed-forward NN decoders for small distance surface codes. The goal is to optimize the NN for the high-decoding performance, while keeping a minimalistic hardware implementation. This is needed to meet the tight delay constraints of real-time surface code decoding. We demonstrate that hardware-based NN-decoders can achieve the high-decoding performance comparable to other state-of-the-art decoding algorithms whilst being well below the tight delay requirements (\approx 440\ ns) of current solid-state qubit technologies for both application-specific integrated circuit designs (< \!30\ ns) and field-programmable gate array implementations (<\! 90\ ns). These results indicate that NN-decoders are viable candidates for further exploration of an integrated hardware implementation in future large-scale quantum computers.

Original languageEnglish
Article number3101719
Number of pages19
JournalIEEE Transactions on Quantum Engineering
Publication statusPublished - 2022


  • Qubit
  • Decoding
  • Codes
  • Hardware
  • Quantum computing
  • Logic gates
  • Artificial neural networks
  • Application-specific integrated circuit (ASIC)
  • complementary metal-oxide semiconductor (CMOS)
  • CMOS integrated circuits
  • combinational circuits
  • cryo-CMOS decoding
  • cryogenic electronics
  • digital integrated circuits
  • error correction codes
  • feedforward neural networks (NNs)
  • field programmable gate array (FPGA)
  • fixed-point arithmetic
  • machine learning
  • NNs
  • pareto analysis
  • quantum computing
  • quantum-error-correction (QEC) codes
  • supervised learning
  • surface codes (SCs)


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