Morphing new Quantum Error Correcting Codes

Supervisors

Suitable for

Abstract

Recent advances in quantum error correction have led to discoveries of novel quantum code families with large numbers of logical qubits and low parity-check weights. These include bivariate bicycle codes [1] and 2BGA codes [2], among many others. Additionally, a recent technique called morphing [3] has shown how to construct new codes with desirable properties such as reduced connectivity or better code parameters by treating an existing code as being halfway through the syndrome extraction process of an unknown code, and then computing what the unknown code must be. By combining morphing with recently-discovered families of low density parity check codes known as mirror codes [4], this project would study how those codes are related under morphing and what new code families can be created by using this technique. 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] Shaw, M. H., & Terhal, B. M. (2025). Lowering connectivity requirements for bivariate bicycle codes using morphing circuits. Physical review letters, 134(9), 090602.
[4] Khesin, A. B., & Lu, J. Z. (2026). Mirror codes: High-threshold quantum LDPC codes beyond the CSS regime. Manuscript in preparation.