Neural network enhanced cross entropy benchmark for monitored circuits

TL;DR

This paper demonstrates how a neural network can be used with a cross entropy benchmark to reduce measurement requirements in quantum circuit experiments, improving efficiency in observing measurement-induced phase transitions.

Contribution

It introduces a method combining neural networks with the cross entropy benchmark to lower the measurement complexity in quantum experiments involving monitored circuits.

Findings

Neural network models can effectively learn measurement records.

Using the model reduces the number of measurements needed for accurate estimation.

The approach enhances the feasibility of observing MIPT in real quantum devices.

Abstract

We explore the interplay of quantum computing and machine learning to advance experimental protocols for observing measurement-induced phase transitions (MIPT) in quantum devices. In particular, we focus on trapped ion monitored circuits and apply the cross entropy benchmark recently introduced by [Li et al., Phys. Rev. Lett. 130, 220404 (2023)], which can mitigate the post-selection problem. By doing so, we reduce the number of projective measurements -- the sample complexity -- required per random circuit realization, which is a critical limiting resource in real devices. Since these projective measurement outcomes form a classical probability distribution, they are suitable for learning with a standard machine learning generative model. In this paper, we use a recurrent neural network (RNN) to learn a representation of the measurement record for a native trapped-ion MIPT, and show that using this generative model can substantially reduce the number of measurements required to accurately estimate the cross entropy. This illustrates the potential of combining quantum computing and machine learning to overcome practical challenges in realizing quantum experiments.