Better Than Worst-Case Decoding for Quantum Error Correction

The overheads of classical decoding for quantum error correction grow rapidly with the number of logical qubits and their code distance. Decoding at room temperature is bottle-necked by refrigerator I/O bandwidth while cryogenic on-chip decoding is limited by area/power/thermal budget.

To overcome these overheads, we are motivated by the observation that the common case error signatures are fairly trivial with high redundancy / sparsity. If suitably exploited, these trivial signatures can be decoded and corrected with insignificant overhead, alleviating the above bottlenecks, while still handling worst-case complex signatures by state-of-the-art means.

Our proposal, targeting Surface Codes, consists of:

1) A lightweight decoder for decoding and correcting trivial common-case errors, designed for the cryogenic domain. The decoder is implemented for SFQ logic.

2) A statistical confidence-based technique for off-chip decoding bandwidth allocation, to efficiently handle rare complex decodes which are not covered by the on-chip decoder.

3) A method for stalling circuit execution, for the worst-case scenarios in which the provisioned off-chip bandwidth is insufficient to complete all requested off-chip decodes.

In all, our proposal enables 70-99+% off-chip bandwidth elimination across a range of error rates, while achieving a 15-37x resource overhead reduction compared to prior on-chip-only decoding.