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Leveraging biased noise for more efficient quantum error correction at the circuit level with two-level qubits

Josu Etxezarreta Martinez1,2,*, Paul Schnabl1,3, Javier Oliva del Moral1,4, Reza Dastbasteh1, Pedro M. Crespo1, and Ruben M. Otxoa5

  • *Contact author: jetxezarreta@unav.es
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Phys. Rev. Applied 25, 014021 – Published 9 January, 2026

DOI: https://doi.org/10.1103/q7w6-nljp

Abstract

Tailoring quantum-error-correction codes (QECCs) to biased noise has demonstrated significant benefits. However, most of the prior research on this topic has focused on code-capacity noise models. Furthermore, a no-go theorem prevents the construction of controlled-not (cnot) gates for two-level qubits in a bias-preserving manner which may, in principle, imply that noise bias cannot be leveraged in such systems. In this work, we show that a residual bias up to η∼5 can be maintained in cnot gates under certain conditions. Moreover, we employ controlled-Z (cz) gates in syndrome-extraction circuits and show how to natively implement these in a bias-preserving manner for a broad class of qubit platforms. This motivates the introduction of what we call a hybrid biased-depolarizing (HBD) circuit-level noise model that captures these features. We numerically study the performance of the XZZX surface code and observe that bias-preserving cz gates are critical for leveraging biased noise. Accounting for the residual bias present in the cnot gates, we observe an increase in the code threshold up to a 1.27% physical error rate, representing a 90% improvement. Additionally, we find that the required qubit footprint can be reduced by up to 75% at relevant physical error rates.

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Phys. Rev. Applied 25, 014021– Published 9 January, 2026
  • Received 26 May 2025
  • Revised 14 December 2025
  • Accepted 16 December 2025
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