Protect Measurement-Induced Phase Transition from Noise

TL;DR

This paper demonstrates that quantum-enhanced operations can protect measurement-induced phase transitions from environmental noise, enabling their detection in noisy quantum devices through a novel entanglement-based phase transition analysis.

Contribution

It introduces a method using quantum-enhanced operations to preserve MIPT under noise, with a new probe based on conditional entanglement entropy and numerical validation in noisy quantum circuits.

Findings

Quantum-enhanced operations protect MIPT from noise.

Conditional entanglement entropy effectively characterizes the transition.

Numerical evidence of MIPT in noisy (2+1)D quantum circuits.

Abstract

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 noises disrupts the volume law phase, complicating the observation of MIPT on noisy intermediate-scale quantum devices. Here, we demonstrate that incorporating quantum-enhanced operations can effectively protect MIPT from environmental noise, thereby enabling its detection in experiment. The transition is characterized by the conditional entanglement entropy (CEE), 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 CEE a valid probe of entanglement and establishing the transition as a genuine entanglement phase transition. Additionally, we provide numerical results 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.