  Composite pulse segmentation has emerged as a promising error mitigation
technique for a wide range of physical systems. In recent years, composite
schemes were applied as mitigation strategies for quantum information
processing and quantum computing. However, most of these strategies assume full
error correlation between segments, which can result in gates with worse
fidelity performance compared to non-composite gates. In our research, we
investigate how error correlations impact the fidelity of quantum gates within
the composite segmentation framework. In our study, we prove the existence of a
critical correlation threshold, above which the composite pulse method
significantly enhances both the mean value and variance of the fidelity. To
gain deeper insights, we analyze various properties of the threshold in the
realm of integrated photonics, including the effects of geometrical variations
and the limit where the number of segments approaches infinity. We numerically
explore diverse scenarios, showcasing different aspects of the critical
threshold within the photonic quantum gates framework. These findings
contribute open new pathways of error mitigation strategies and their
implications in quantum information processing.
