Neural-Network Decoders for Quantum Error Correction using Surface Codes:A Space Exploration of the Hardware Cost-Performance Trade-Offs

Abstract

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 neural network for 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 high decoding performance comparable to other state-of-the-art decoding algorithms whilst being well below the tight delay requirements $(\approx 440\mathrm{ns})$ of current solid-state qubit technologies for both ASIC designs $(<30\mathrm{ns})$ and FPGA implementations $(<90\mathrm{ns})$. These results designates NN-decoders as fitting candidates for an integrated hardware implementation in future large-scale quantum computers.

arXiv comment19 pages, 21 figures, 5 papers

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• Real-Time Decoding for Fault-Tolerant Quantum Computing: Progress, Challenges and Outlook
• A scalable and fast artificial neural network syndrome decoder for surface codes
• A real-time, scalable, fast and highly resource efficient decoder for a quantum computer
• Interaction graph-based characterization of quantum benchmarks for improving quantum circuit mapping techniques
• FPGA-based Distributed Union-Find Decoder for Surface Codes
• Data-driven decoding of quantum error correcting codes using graph neural networks
• Neural network decoder for near-term surface-code experiments
• Actis: A Strictly Local Union-Find Decoder
• Artificial Neural Network Syndrome Decoding on IBM Quantum Processors
• Improved Belief Propagation Decoding Algorithms for Surface Codes
• Local Clustering Decoder as a fast and adaptive hardware decoder for the surface code
• Neural network accelerator for quantum control
• Low-overhead quantum error correction codes with a cyclic topology
• Synchronization for Fault-Tolerant Quantum Computers
• Neural Decoders for Universal Quantum Algorithms
• Managing Classical Processing Requirements for Quantum Error Correction