# Quantum Geometric Machine Learning for Quantum Circuits and Control

arXiv: https://arxiv.org/abs/2006.11332 · HTML: https://mlsanity.com/paper/2006.11332/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Model-free Distortion Canceling and Control of Quantum Devices](https://mlsanity.com/paper/2407.09877/) (2024)
- [Reverse Map Projections as Equivariant Quantum Embeddings](https://mlsanity.com/paper/2407.19906/) (2024)
- [Bayesian quantum sensing using graybox machine learning](https://mlsanity.com/paper/2601.17465/) (2026)
- [Data-Driven Qubit Characterization and Optimal Control using Deep Learning](https://mlsanity.com/paper/2601.18704/) (2026)

## Abstract (arXiv)

The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be used to enhance geometric approaches to solving problems in quantum information processing. In this work, we review and extend the application of deep learning to quantum geometric control problems. Specifically, we demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems by applying novel deep learning algorithms in order to approximate geodesics (and thus minimal circuits) along Lie group manifolds relevant to low-dimensional multi-qubit systems, such as SU(2), SU(4) and SU(8). We demonstrate the superior performance of greybox models, which combine traditional blackbox algorithms with prior domain knowledge of quantum mechanics, as means of learning underlying quantum circuit distributions of interest. Our results demonstrate how geometric control techniques can be used to both (a) verify the extent to which geometrically synthesised quantum circuits lie along geodesic, and thus time-optimal, routes and (b) synthesise those circuits. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.