Syndrome Subgraph Algorithm for Distributed Decoding of Surface Codes

Large scale fault tolerant quantum computers require sophisticated quantum error correction to overcome the inherent noise of physical qubits and operations thereon. For active quantum error correction this requires readout and classical processing of the error syndrome. To avoid a growing backlog of unprocessed syndrome data and ensure fast logical clock speed of a quantum computer, hardware based decoders have been introduced.

Here we introduce the subgraph algorithm as a new decoding algorithm for surface codes. Unlike previous algorithms, the subgraph algorithm has been designed to efficiently decode a single logical qubit across multiple FPGA, requiring limited inter-device communication. It finds an approximation to the minimum weight perfect matching problem, getting closer by either taking more time or using more computational resources in parallel. Numerical simulations show reduction of logical error rate for increasing code distance when using current state-of-the-art qubit fidelities. The flexible nature of the subgraph algorithm allows it to be tuned to different error models, use different methods in its sub-stages and allow resource vs. time tradeoff at various levels.