# Geometric quantum machine learning of BQPA protocols and latent graph classifiers

arXiv: https://arxiv.org/abs/2402.03871 · HTML: https://mlsanity.com/paper/2402.03871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 24 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 9 of 9)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Quantum anomaly detection in the latent space of proton collision events at the LHC](https://mlsanity.com/paper/2301.10780/) (2023)
- [Expressive variational quantum circuits provide inherent privacy in federated learning](https://mlsanity.com/paper/2309.13002/) (2023)
- [Blind quantum machine learning with quantum bipartite correlator](https://mlsanity.com/paper/2310.12893/) (2023)
- [What can we learn from quantum convolutional neural networks?](https://mlsanity.com/paper/2308.16664/) (2023)

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

- [Can Geometric Quantum Machine Learning Lead to Advantage in Barcode Classification?](https://mlsanity.com/paper/2409.01496/) (2024)

## Abstract (arXiv)

Geometric quantum machine learning (GQML) aims to embed problem symmetries for learning efficient solving protocols. However, the question remains if (G)QML can be routinely used for constructing protocols with an exponential separation from classical analogs. In this Letter we consider Simon's problem for learning properties of Boolean functions, and show that this can be related to an unsupervised circuit classification problem. Using the workflow of geometric QML, we learn from first principles Simon's algorithm, thus discovering an example of BQPAneqBPP protocol with respect to some dataset (oracle A). Our key findings include the development of an equivariant feature map for embedding Boolean functions, based on twirling with respect to identified bitflip and permutational symmetries, and measurement based on invariant observables with a sampling advantage. The proposed workflow points to the importance of data embeddings and classical post-processing, while keeping the variational circuit as a trivial identity operator. Next, developing the intuition for the function learning, we visualize instances as directed computational hypergraphs, and observe that the GQML protocol can access their global topological features for distinguishing bijective and surjective functions. Finally, we discuss the prospects for learning other BQPA-type protocols, and conjecture that this depends on the ability of simplifying embeddings-based oracles A applied as a linear combination of unitaries.