Fault Tolerant Syndrome Extraction in Context

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Abstract

Implementations of various quantum algorithms need to be done fault tolerantly in order to prevent errors on a few qubits propagating to many. Various error correcting codes such as the surface code can sometimes admit circuits for measuring their parities that are not fault-tolerant in general, but propagate errors in a way that is not detrimental in the context of this code. This can allow for much more computationally efficient syndrome extraction circuits. There is evidence to suggest that various other codes also have this property. This project will approach this problem from two directions: first, it will attempt to compute or prove the resistance to certain types of propagating errors of highly structured codes such as bivariate bicycle [1], 2BGA [2], or mirror codes [3]. Second, the project will attempt to design efficient but not fully fault tolerant syndrome extraction circuits and find which codes (or possibly novel ones) as context would make these circuits fault tolerant. Students interested in doing a project are highly encouraged to take the MSc/PartC course Quantum Processes and Computation.

[1] Bravyi, S., Cross, A. W., Gambetta, J. M., Maslov, D., Rall, P., & Yoder, T. J. (2024). High-threshold and low-overhead fault-tolerant quantum memory. Nature, 627(8005), 778-782.
[2] Lin, H. K., & Pryadko, L. P. (2024). Quantum two-block group algebra codes. Physical Review A, 109(2), 022407.
[3] Khesin, A. B., & Lu, J. Z. (2026). Mirror codes: High-threshold quantum LDPC codes beyond the CSS regime. Manuscript in preparation.