Minimum-Weight Perfect Matching (MWPM) | QEC Syndrome Decoder
Quick Technical Answer:
Minimum-Weight Perfect Matching (MWPM) is the standard graph-based syndrome decoding algorithm for surface codes. It pairs defect plaquettes by minimizing total graph distance using Edmonds' Blossom algorithm in O(V³) time.
Formula / Unitary:
\min_{M} \sum_{(u, v) \in M} w(u, v), \quad w(u, v) = -\log(P_{\text{error}}(u, v)) \propto \text{dist}(u, v)
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Frequently Asked Questions
What is the runtime constraint for real-time MWPM decoding on physical quantum chips?
Because superconducting QEC cycles take ~1 microsecond, classical decoding hardware (FPGAs / ASICs) must compute MWPM corrections within 1 µs to prevent syndrome backlog.