Protect Measurement-Induced Phase Transition from Noise

Scrambling dynamics induced by random unitary gates can protect information from low-rate measurements, which underpins the phenomenon known as the measurement-induced phase transition (MIPT). However, typical decoherence noise disrupts the volume-law phase, complicating the observation of the MIPT on noisy intermediate-scale quantum devices. Here, we demonstrate that incorporating quantum-enhanced operations can effectively protect the MIPT from environmental noise, thereby enabling its detection in experiment. The transition is characterized by conditional entanglement entropy, which is associated with a statistical mechanics model wherein noise and quantum-enhanced operations act as competing external random fields. When the net external field is zero, a ferromagnetic-paramagnetic phase transition is expected, resulting in the MIPT. This zero-field condition also ensures an average apparatus-environment symmetry, making conditional entanglement entropy a valid probe of entanglement and establishing the transition as a genuine entanglement phase transition. Additionally, we provide numerical results that demonstrate the MIPT in a (2+1)-dimensional quantum circuit under dephasing noise. We also propose a method to estimate the noise rate, enabling the zero-field condition to be achieved experimentally and ensuring the feasibility of our protocol. Our result serves as a concrete example of the power of quantum enhancement in combating noise.