High-performance syndrome extraction circuits for quantum codes

Abstract:We present a fast and effective framework for analysing and designing syndrome extraction circuits (SECs). Our approach is based on left--right circuits, a general SEC design that maintains low depth and avoids gate interleaving constraints by staggering $X$ and $Z$ stabiliser checks. Initially proposed for specific classes of codes, we generalise this construction to arbitrary CSS codes and optimise the circuit structure to achieve low qubit idling time, large effective distance, and reduced minimum-weight failure mechanisms. A key component of our framework is the formal notion of residual errors and their associated distance metrics, which form lightweight proxies for capturing error propagation and quantifying the potential harm of circuit-level errors. Applying our automated framework to diverse classes of codes, we observe consistent improvements in logical performance of up to an order of magnitude compared to existing single-ancilla SEC designs. Moreover, by directly applying these proxies, we prove that no non-interleaving SEC can achieve circuit distance $12$ for the gross code, and we identify an explicit circuit that we conjecture achieves distance $11$, exceeding previously known constructions.

arXiv:2603.05481 [quant-ph]

(or arXiv:2603.05481v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.05481 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.