Clifford-Deformed Compass Codes

Julie A. Campos; Kenneth R. Brown

doi:10.22331/q-2026-04-16-2073

Clifford-Deformed Compass Codes

Julie A. Campos^1,2 and Kenneth R. Brown^1,2,3,4

¹Duke Quantum Center, Duke University, Durham, NC 27701, USA
²Department of Physics, Duke University, Durham, NC 27708, USA
³Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
⁴Department of Chemistry, Duke University, Durham, NC 27708, USA

Published:	2026-04-16, volume 10, page 2073
Editor:	Kishor Bharti
Eprint:	arXiv:2412.03808v3
Doi:	https://doi.org/10.22331/q-2026-04-16-2073
Citation:	Quantum 10, 2073 (2026).

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Abstract

We can design efficient quantum error-correcting (QEC) codes by tailoring them to our choice of quantum architecture. Useful tools for constructing such codes include Clifford deformations and appropriate gauge fixings of compass codes. In this work, we find Clifford deformations that can be applied to elongated compass codes resulting in QEC codes with improved performance under noise models with errors biased towards dephasing commonly seen in quantum computing architectures. These Clifford deformations enhance decoder performance by introducing symmetries, while the stabilizers of compass codes can be selected to obtain more information on high-rate errors. As a result, the codes exhibit thresholds that increase with bias and lower logical error rates under both code capacity and phenomenological noise models. One of the Clifford deformations we explore yields QEC codes with better thresholds and logical error rates than those of the XZZX surface code at moderate biases under code capacity noise.

Popular summary

We need effective quantum error-correcting (QEC) protocols to build fault-tolerant quantum computers. One approach is to adapt QEC codes to the noise processes observed in physical hardware. For example, many quantum computing platforms, such as those based on trapped-ion and superconducting qubits, experience noise biased towards dephasing errors. To efficiently mitigate the effects of these dominant errors, we can use techniques such as local Clifford deformations and gauge fixing to design stabilizer codes that extract more detailed information about these errors. Elongated compass codes, for instance, are a family of stabilizer codes whose asymmetry between Puli-$X$ and Pauli-$Z$ stabilizers favors the detection of dephasing errors. However, this asymmetry also restricts the performance of these codes to be optimal only at a specific bias level. In this work, we design Clifford deformations that improve the performance of elongated compass codes by imposing symmetries on their stabilizer structure. The resulting codes exhibit higher thresholds and lower error rates than the undeformed elongated compass codes under various noise models that include memory errors and measurement errors.

► BibTeX data

@article{Campos2026clifforddeformed,
  doi = {10.22331/q-2026-04-16-2073},
  url = {https://doi.org/10.22331/q-2026-04-16-2073},
  title = {Clifford-{D}eformed {C}ompass {C}odes},
  author = {Campos, Julie A. and Brown, Kenneth R.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2073},
  month = apr,
  year = {2026}
}

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