Multiclass classification of dephasing channels

TL;DR

This paper explores neural network-based classification of environmental parameters in single-qubit dephasing channels, demonstrating high accuracy with noiseless data and reasonable performance with noisy measurements, focusing on classical and quantum noise sources.

Contribution

It introduces neural network approaches for classifying dephasing channel parameters from limited tomographic data, highlighting their effectiveness and limitations in noisy conditions.

Findings

Neural networks can exactly classify noiseless data into 16 classes.

Classification accuracy drops to about 70% for noisy data in detailed parameter classification.

Coarse classification between macro-classes achieves up to 96% accuracy.

Abstract

We address the use of neural networks (NNs) in classifying the environmental parameters of single-qubit dephasing channels. In particular, we investigate the performance of linear perceptrons and of two non-linear NN architectures. At variance with time-series-based approaches, our goal is to learn a discretized probability distribution over the parameters using tomographic data at just two random instants of time. We consider dephasing channels originating either from classical 1/f{\alpha} noise or from the interaction with a bath of quantum oscillators. The parameters to be classified are the color {\alpha} of the classical noise or the Ohmicity parameter s of the quantum environment. In both cases, we found that NNs are able to exactly classify parameters into 16 classes using noiseless data (a linear NN is enough for the color, whereas a single-layer NN is needed for the Ohmicity). In the presence of noisy data (e.g. coming from noisy tomographic measurements), the network is able to classify the color of the 1/f{\alpha} noise into 16 classes with about 70% accuracy, whereas classification of Ohmicity turns out to be challenging. We also consider a more coarse-grained task, and train the network to discriminate between two macro-classes corresponding to {\alpha} \lessgtr 1 and s \lessgtr 1, obtaining up to 96% and 79% accuracy using single-layer NNs.