Characterisation and error budget of non-demolition fidelity of measurement pulses on superconducting qubits

Non-demolition measurements are essential in quantum algorithms and error correction, as they project the qubit state without inducing further backaction. Accurately assessing this quantum non-demolition (QND) behavior is critical for maintaining coherence and achieving high-fidelity control. Conventional QND fidelity estimates rely on correlations between consecutive readouts [1,2], but these often neglect leakage effects—similar to traditional classification fidelity. Other approaches attempt indirect leakage inference via randomized bit-flip sequences [3]. In this work, we present a direct and comprehensive framework for quantifying non-demolition fidelity through a full state transition matrix that maps how a measurement pulse transforms the qubit state, incorporating relaxation and leakage. We further develop a rate-equation model that predicts this transition matrix for arbitrary pulse parameters, offering quantitative insight into the relationship between measurement strength, duration, and backaction.

[1] M. F. Dumas et al., Phys. Rev. X 14, 041023 (2024).

[2] M. Khezri et al., Phys. Rev. Appl. 20, 054008 (2023).

[3] S. Hazra et al., Phys. Rev. Lett. 134, 100601 (2025).