Input-Output Optics as a Causal Time Series Mapping: A Generative Machine Learning Solution

TL;DR

This paper demonstrates that neural networks, especially variational auto-encoders, can effectively model and simulate the complex input-output optical responses of many-body quantum systems, providing a new data-driven approach.

Contribution

It introduces the use of neural networks, including generative models, to learn and characterize the complex mappings in quantum optical systems, outperforming traditional auto-encoders.

Findings

Variational auto-encoders outperform traditional auto-encoders in modeling quantum system responses.

The complexity of the input-output mapping correlates with the size of the minimal latent space.

The model achieves less than 10% error for over 90% of test inputs.

Abstract

The response of many-body quantum systems to an optical pulse can be extremely challenging to model. Here we explore the use of neural networks, both traditional and generative, to learn and thus simulate the response of such a system from data. The quantum system can be viewed as performing a complex mapping from an input time-series (the optical pulse) to an output time-series (the systems response) which is often also an optical pulse. Using both the transverse and non-integrable Ising models as examples, we show that not only can temporal convolutional networks capture the input/output mapping generated by the system but can also be used to characterize the complexity of the mapping. This measure of complexity is provided by the size of the smallest latent space that is able to accurately model the mapping. We further find that a generative model, in particular a variational auto-encoder, significantly outperforms traditional auto-encoders at learning the complex response of many-body quantum systems. For the example that generated the most complex mapping, the variational auto-encoder produces outputs that have less than 10% error for more than 90% of inputs across our test data.