Neural-network decoders for measurement induced phase transitions

Hossein Dehghani; Ali Lavasani; Mohammad Hafezi; Michael J Gullans

doi:10.1038/s41467-023-37902-1

Neural-network decoders for measurement induced phase transitions

Nat Commun. 2023 May 22;14(1):2918. doi: 10.1038/s41467-023-37902-1.

Authors

Hossein Dehghani^{1

2}, Ali Lavasani^{3

4}, Mohammad Hafezi^{3

5}, Michael J Gullans⁵

Affiliations

¹ Joint Quantum Institute, NIST/University of Maryland, College Park, MD, 20742, USA. hdehghan@umd.edu.
² Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, 20742, USA. hdehghan@umd.edu.
³ Joint Quantum Institute, NIST/University of Maryland, College Park, MD, 20742, USA.
⁴ Condensed Matter Theory Center, University of Maryland, College Park, MD, 20742, USA.
⁵ Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, 20742, USA.

Abstract

Open quantum systems have been shown to host a plethora of exotic dynamical phases. Measurement-induced entanglement phase transitions in monitored quantum systems are a striking example of this phenomena. However, naive realizations of such phase transitions requires an exponential number of repetitions of the experiment which is practically unfeasible on large systems. Recently, it has been proposed that these phase transitions can be probed locally via entangling reference qubits and studying their purification dynamics. In this work, we leverage modern machine learning tools to devise a neural network decoder to determine the state of the reference qubits conditioned on the measurement outcomes. We show that the entanglement phase transition manifests itself as a stark change in the learnability of the decoder function. We study the complexity and scalability of this approach in both Clifford and Haar random circuits and discuss how it can be utilized to detect entanglement phase transitions in generic experiments.