Performance enhancement of surface codes via recursive MWPM decoding

Abstract

The minimum weight perfect matching (MWPM) decoder is the standard decoding strategy for quantum surface codes. However, it suffers a harsh decrease in performance when subjected to biased or non-identical quantum noise. In this work, we modify the conventional MWPM decoder so that it considers the biases, the non-uniformities and the relationship between $X$, $Y$ and $Z$ errors of the constituent qubits of a given surface code. Our modified approach, which we refer to as the recursive MWPM decoder, obtains an $18\%$ improvement in the probability threshold $p_{th}$ under depolarizing noise. We also obtain significant performance improvements when considering biased noise and independent non-identically distributed (i.ni.d.) error models derived from measurements performed on state-of-the-art quantum processors. In fact, when subjected to i.ni.d. noise, the recursive MWPM decoder yields a performance improvement of $105.5\%$ over the conventional MWPM strategy and, in some cases, it even surpasses the performance obtained over the well-known depolarizing channel.

References in corpus (6)

• Strong quantum computational advantage using a superconducting quantum processor
• Suppressing quantum errors by scaling a surface code logical qubit
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• Fault-Tolerant Computing With Biased-Noise Superconducting Qubits
• A local pre-decoder to reduce the bandwidth and latency of quantum error correction
• Multi-qubit time-varying quantum channels for NISQ-era superconducting quantum processors

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