Treating vertical pairs of highlighted vertices in a matching graph of a surface code

Abstract

Techniques for reducing a syndrome density of a plurality of rounds of syndrome measurements following a first decoding stage (e.g., via a local decoder) for quantum error correction of circuit-level noise within quantum surface codes are disclosed. Such techniques for reducing syndrome density may include syndrome collapse and/or vertical cleanup techniques. In a syndrome collapse technique, a measurement results volume may be partitioned into sheets and the respective sheets collapsed, causing vertical pairs of highlighted vertices to be removed. In a vertical cleanup technique, vertical pairs of highlighted vertices may be removed directly from a matching graph following a first decoding stage. Following the removal of vertical pairs of highlighted vertices, the measurement results are then decoded in a second, global decoding stage. Such techniques allow for fast decoding throughout and low latency times for error correction of rounds of syndrome measurements for quantum algorithms implemented using quantum surface codes.