Detecting nonequilibrium phase transitions via continuous monitoring of space-time trajectories and autoencoder-based clustering

TL;DR

This paper introduces a machine learning method that detects nonequilibrium phase transitions in quantum systems by analyzing space-time measurement data, reducing the need for complex quantum state estimation.

Contribution

It presents a novel approach combining continuous monitoring data with autoencoder-based clustering to identify phase transitions in quantum systems.

Findings

Successfully detects phase transitions in the quantum contact process

Reduces experimental complexity by avoiding full quantum state tomography

Demonstrates effectiveness on a challenging nonequilibrium quantum model

Abstract

The characterization of collective behavior and nonequilibrium phase transitions in quantum systems is typically rooted in the analysis of suitable system observables, so-called order parameters. These observables might not be known a priori, but they may in principle be identified through analyzing the quantum state of the system. Experimentally, this can be particularly demanding as estimating quantum states and expectation values of quantum observables requires a large number of projective measurements. However, open quantum systems can be probed in situ by monitoring their output, e.g. via heterodyne-detection or photon-counting experiments, which provide space-time resolved information about their dynamics. Building on this, we present a machine-learning approach to detect nonequilibrium phase transitions from the measurement time-records of continuously-monitored quantum systems. We benchmark our method using the quantum contact process, a model featuring an absorbing-state phase transition, which constitutes a particularly challenging test case for the quantum simulation of nonequilibrium processes.