New preprint on Fault-Tolerant QLDPC Syndrome Measurement via LDGM Encoding

In order to perform fault-tolerant quantum computing, we need to obtain syndrome information that is robust to bit-flip errors. Typically this is achieved by straightforwardly repeating measurements, but there are other methods that allow for syndrome fault-tolerance. One such method is the use of syndrome measurement codes: classical error-correcting codes that tell us what measurements to perform to obtain the lowest possible overhead. However, the best-known way to do this involves high-weight measurements, which are not suitable for all quantum codes. In particular, quantum low-density parity check (QLDPC) codes rely on their measurements being constant-weight. In order to improve the time overhead of syndrome measurement while retaining the QLDPC property, we construct low-density generator matrix (LDGM) codes using a protograph-based construction method to retain low-weight checks. Compared to traditional repeated measurement, this allows for more errors to be corrected on the syndrome in fewer total measurements, and superior performance under a phenomenological error model.

This work was done by Eren Guttentag, a PhD candidate in the Duke Quantum Center advised by Dr. Ken Brown, in collaboration with Anthony Gómez-Fonseca, who obtained his PhD in mathematics from the University of Notre Dame and is now a postdoctoral fellow at the University of South Florida. Read more about it at arXiv:2605.25317 .