A supplemental investigation of non-linearity in quantum generative models with respect to simulatability and optimization

TL;DR

This paper investigates whether non-linearity introduced by RUS sub-routines in quantum generative models affects their classical simulability and training stability, finding it does not simplify simulation but can cause training instability.

Contribution

It demonstrates that RUS-based non-linearity does not enable classical simulation of the quantum models and evaluates the stability of training larger models across different datasets.

Findings

RUS sub-routines do not allow trivial classical simulation.

Models without RUS can be mapped to classical Bayesian networks.

Training stability varies across datasets and trials.

Abstract

Recent work has demonstrated the utility of introducing non-linearity through repeat-until-success (RUS) sub-routines into quantum circuits for generative modeling. As a follow-up to this work, we investigate two questions of relevance to the quantum algorithms and machine learning communities: Does introducing this form of non-linearity make the learning model classically simulatable due to the deferred measurement principle? And does introducing this form of non-linearity make the overall model's training more unstable? With respect to the first question, we demonstrate that the RUS sub-routines do not allow us to trivially map this quantum model to a classical one, whereas a model without RUS sub-circuits containing mid-circuit measurements could be mapped to a classical Bayesian network due to the deferred measurement principle of quantum mechanics. This strongly suggests that the proposed form of non-linearity makes the model classically in-efficient to simulate. In the pursuit of the second question, we train larger models than previously shown on three different probability distributions, one continuous and two discrete, and compare the training performance across multiple random trials. We see that while the model is able to perform exceptionally well in some trials, the variance across trials with certain datasets quantifies its relatively poor training stability.