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

arXiv: https://arxiv.org/abs/2302.00788 · HTML: https://mlsanity.com/paper/2302.00788/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## Builds on (most cited first, 15 of 15)

- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2001.06937/) (2020)
- [An Introduction to Deep Generative Modeling](https://mlsanity.com/paper/2103.05180/) (2021)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Bias and Generalization in Deep Generative Models: An Empirical Study](https://mlsanity.com/paper/1811.03259/) (2018)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Quantum Vision Transformers](https://mlsanity.com/paper/2209.08167/) (2022)
- [Quantum Neuron: an elementary building block for machine learning on quantum computers](https://mlsanity.com/paper/1711.11240/) (2017)
- [Do Quantum Circuit Born Machines Generalize?](https://mlsanity.com/paper/2207.13645/) (2022)
- [Learnability of the output distributions of local quantum circuits](https://mlsanity.com/paper/2110.05517/) (2021)
- [Introducing Non-Linear Activations into Quantum Generative Models](https://mlsanity.com/paper/2205.14506/) (2022)
- [Image Restoration from Parametric Transformations using Generative Models](https://mlsanity.com/paper/2005.14036/) (2020)

## Built on by (most cited first, 1 of 1)

- [QonFusion -- Quantum Approaches to Gaussian Random Variables: Applications in Stable Diffusion and Brownian Motion](https://mlsanity.com/paper/2309.16258/) (2023)

## Abstract (arXiv)

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.