Clifford-Deformed Compass Codes
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AbstractWe 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 summaryWe 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} }► References [1] A. R. Calderbank and P. W. 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Could not fetch ADS cited-by data during last attempt 2026-04-16 10:26:52: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe 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 summaryWe 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} }► References [1] A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Phys. Rev. A 54, 1098 (1996). https://doi.org/10.1103/PhysRevA.54.1098 [2] E. Knill, R. Laflamme, and W. H. Zurek, Resilient quantum computation, Science 279, 342 (1998). https://doi.org/10.1126/science.279.5349.3 [3] D. Aharonov and M. Ben-Or, Fault-tolerant quantum computation with constant error, in Proceedings of the twenty-ninth annual ACM symposium on Theory of computing (1997) pp. 176–188. https://doi.org/10.48550/arXiv.quant-ph/9906129 arXiv:quant-ph/9906129 [4] H. Bombin, G. Duclos-Cianci, and D. Poulin, Universal topological phase of two-dimensional stabilizer codes, New J. of Physics. 14, 073048 (2012). https://doi.org/10.1088/1367-2630/14/7/073048 [5] Y. Tomita and K. M. Svore, Low-distance surface codes under realistic quantum noise, Phys. Rev. A 90, 062320 (2014). https://doi.org/10.1103/PhysRevA.90.062320 [6] S. Bravyi, M. Suchara, and A. Vargo, Efficient algorithms for maximum likelihood decoding in the surface code, Phys. Rev. A 90, 032326 (2014). https://doi.org/10.1103/PhysRevA.90.032326 [7] K. Sahay and B. J. Brown, Decoder for the triangular color code by matching on a möbius strip, PRX Quantum 3, 010310 (2022). https://doi.org/10.1103/PRXQuantum.3.010310 [8] A. Grimm, N. E. Frattini, S. Puri, S. 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