Trainability of IQP Quantum Circuit Born Machines Under Gaussian Initialization
Abstract
Quantum Circuit Born Machines (QCBMs) offer a natural approach to generative machine learning by leveraging the Born rule. Recent work has provided a method to classically train QCBMs with Instantaneous Quantum Polynomial (IQP) circuits via the Maximum Mean Discrepancy (MMD) loss. Despite the assumed intractability of sampling from IQP circuits classically, their expectation values can be computed classically, enabling training of these IQP QCBMs. However, quantum machine learning (QML) models have various other challenges, including trainability issues caused by exponential concentration or barren plateaus. While these issues have been explored for parameters sampled from a uniform distribution, little work has been done to rigorously treat the use of arbitrary Gaussian initialization schemes. This work leverages Stein's lemma and Lipschitz concentration bounds for Gaussian random variables to provide an analytical lower bound of the variance of the gradient and a probabilistic concentration bound of the deviation of the gradient from its mean. It discusses strategies to either avoid or encourage exponential concentration, as well as the conditions under which barren plateaus are more likely to occur.
Related
- Noise-regularized training of quantum circuit Born machines under a finite shot budget
- Nonstabilizerness of the entangling layer in quantum circuit Born machines
- A Quantum Circuit for Gaussian Elimination
- On Relationship Between Circuit Depth and Trainability of VQAs
- Deployment of Large IQP Circuit Born Machines on Qubit-Limited Hardware Using Noise Injection
BibTeX
@misc{luca2026trainability,
title = {{Trainability of IQP Quantum Circuit Born Machines Under Gaussian Initialization}},
author = {Gennaro De Luca and Vinayak Sharma and Aviral Shrivastava},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.10179},
eprint = {2606.10179},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.10179},
}
RIS
TY - UNPB
TI - Trainability of IQP Quantum Circuit Born Machines Under Gaussian Initialization
AU - Gennaro De Luca
AU - Vinayak Sharma
AU - Aviral Shrivastava
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2606.10179
UR - https://arxiv.org/abs/2606.10179
AB - Quantum Circuit Born Machines (QCBMs) offer a natural approach to generative machine learning by leveraging the Born rule. Recent work has provided a method to classically train QCBMs with Instantaneous Quantum Polynomial (IQP) circuits via the Maximum Mean Discrepancy (MMD) loss. Despite the assumed intractability of sampling from IQP circuits classically, their expectation values can be computed classically, enabling training of these IQP QCBMs. However, quantum machine learning (QML) models have various other challenges, including trainability issues caused by exponential concentration or barren plateaus. While these issues have been explored for parameters sampled from a uniform distribution, little work has been done to rigorously treat the use of arbitrary Gaussian initialization schemes. This work leverages Stein's lemma and Lipschitz concentration bounds for Gaussian random variables to provide an analytical lower bound of the variance of the gradient and a probabilistic concentration bound of the deviation of the gradient from its mean. It discusses strategies to either avoid or encourage exponential concentration, as well as the conditions under which barren plateaus are more likely to occur.
ER -