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Measurement-induced phase transition (MIPT) is a novel non-equilibrium phase transition characterized by entanglement entropy. The scrambling dynamics induced by random unitary gates can protect information from low-rate measurements. However, common decoherence noises, such as dephasing, are detrimental to the volume law phase, posing a significant challenge for observing MIPT in current noisy intermediate-scale quantum devices. Here, we demonstrate that incorporating quantum-enhanced operations can effectively protect MIPT from environmental noise. The conditional entanglement entropy is associated with a statistical mechanics model wherein noise and quantum-enhanced operations act as two competing external random fields. Then we show that an average apparatus-environment exchange symmetry ensures the conditional entanglement entropy is a valid probe of entanglement. Furthermore, we provide numerical evidence on a (2+1)-d quantum circuit under dephasing noise, demonstrating that MIPT can indeed be observed with the aid of quantum-enhanced operations. This result not only serves as a concrete example of the power of quantum enhancement in combating noise but also holds experimental relevance, as the protocol is straightforward to implement in practice.
Qian et al. (Thu,) studied this question.