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

A method, comprising:

• performing error correction for measurement results of a plurality of rounds of syndrome measurements of a quantum surface code, wherein:
• the measurement results form a measurement results volume bounded by first and second dimensions corresponding to dimensions of the quantum surface code and a third dimension corresponding to a number of rounds included in the plurality of rounds of syndrome measurements;
• and
• said performing the error correction comprises:
• decoding, via a first decoder, a subset of detected syndrome differences of a total number of syndrome differences in the measurement results volume, wherein a syndrome difference:
• indicates measurement differences between consecutive rounds of syndrome measurements;
• and
• corresponds to circuit-level noise of the one or more quantum hardware devices;
• treating vertical pairs of highlighted vertices in the decoded measurement results volume, wherein:
• a vertical pair of highlighted vertices indicates syndrome differences that are temporally separated by a round of syndrome measurements;
• and
• said treating the vertical pairs of highlighted vertices causes a syndrome density in the decoded measurement results volume to be reduced;
• and
• providing a resulting measurement results volume that has had the vertical pairs treated to a global decoder.

A non-transitory, computer-readable, medium storing program instructions that, when executed on or across one or more processors, cause the one or more processors to:

• perform error correction for measurement results of a plurality of rounds of syndrome measurements of a quantum surface code, wherein:
• the measurement results form a measurement results volume bounded by first and second dimensions corresponding to dimensions of the quantum surface code and a third dimension corresponding to a number of rounds included in the plurality of rounds of syndrome measurements;
• and
• to perform the error correction, the program instructions further cause the one or more processors to:
• decode, via a decoder, a subset of detected syndrome differences of a total number of syndrome differences in the measurement results volume, wherein a syndrome difference:
• indicates measurement differences between consecutive rounds of syndrome measurements;
• and
• corresponds to circuit-level noise of the one or more quantum hardware devices;
• treat vertical pairs of highlighted vertices in the decoded measurement results volume, wherein:
• a vertical pair of highlighted vertices indicates syndrome differences that are temporally separated by a round of syndrome measurements;
• and
• to treat the vertical pairs of highlighted vertices causes a syndrome density in the decoded measurement results volume to be reduced;
• and
• provide a resulting measurement results volume that has had the vertical pairs treated to a global decoder.