Mitigating Temporal Fragilities in the XY Surface Code During State Preparation and Logical Measurements

As an example of Clifford-deformed quantum surface code, XY codes reduces to a repetition code under pure phase-flip noise and achieves code capacity threshold of 50%. An important problem that has to be overcome to fully utilize the XY code for biased Pauli noise is the phenomena of fragile temporal boundaries [1] that arise during the standard logical state preparation and measurement processes. We proposed a logical state preparation protocol by locally entangling qubits into small GHZ states prior to stabilizer measurements that project qubits onto XY code states. In this protocol, the number of lowest-weight error configurations that cause a logical failure reduces quadratically compared to the standard approach, mitigating the effect of fragile boundaries. Moreover, the code becomes equivalent to a repetition code under pure phase-flip noise, guaranteeing a 50% code-capacity threshold during state preparation. Numerically, we confirm that our protocol outperforms the standard one in terms of both threshold and logical error rate in the fault-tolerant regime with noisy measurement and at experimentally realistic biases. We also discuss how our state-preparation protocol can be inverted for similar fragile-boundary-mitigated logical-state measurements.

[1] O. Higgott, et al., Phys. Rev. X 13, 031007 (2023)