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Leveraging biased noise for more efficient quantum error correction at the circuit-level with two-level qubits
Josu Etxezarreta Martinez, Paul Schnabl, Javier Oliva del Moral, Reza Dastbasteh, Pedro M. Crespo, Ruben M. Otxoa
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Tailoring quantum error correction codes (QECC) 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 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-phase (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 which 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 a 75% at relevant physical error rates.
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