We introduce layered Quantum Architecture Search (layered-QAS), a strategy inspired by classical network morphism that designs Parametrised Quantum Circuit (PQC) architectures by progressively growing and adapting them. PQCs offer strong expressiveness with relatively few parameters, yet they lack standard architectural layers (e.g., convolution, attention) that encode inductive biases for a given learning task. To assess the effectiveness of our method, we focus on 3D point cloud classification as a challenging yet highly structured problem. Whereas prior work on this task has used PQCs only as feature extractors for classical classifiers, our approach uses the PQC as the main building block of the classification model. Simulations show that our layered-QAS mitigates barren plateau, outperforms quantum-adapted local and evolutionary QAS baselines, and achieves state-of-the-art results among PQC-based methods on the ModelNet dataset.
Layered-QAS aims to design Parametrised Quantum Circuit (PQC) architectures for QML models. We experiment on a model for 3D point cloud classification and first describe the encoding of the point cloud into a quantum state.
We fit the point cloud into a unit cube and rescale its coordinates. We then subdivide this cube into \(2^k\) voxels along each axis, where \(k\) is the number of qubits available for the encoding. Each point is assigned to a voxel based on its coordinates. Finally, we encode the occupancy of each voxel into the amplitude of the corresponding basis state of the quantum system.
The QML model's workflow is shown on first figure above. The input point cloud is encoded into a quantum state using the described encoding scheme. This quantum state is then processed by a PQC, whose architecture is designed using layered-QAS. Finally, measurements are performed on the output quantum state to obtain classical information, which is then used for classification.
Layered-QAS progressively grows and adapts PQC architectures by adding layers inspired by classical network morphism. This approach allows the PQC to better capture the structure of the data and improve its performance on the classification task.
We begin with a trivial identity circuit \(\mathbf {U}_0 (\boldsymbol \theta_0) = \mathbf {I}\) of \(n\) which consists of data encoding followed by measurement. At each generation \((i+1)\), the existing circuit \(\mathbf {U}_i(\boldsymbol \theta_i)\) is expanded by adding a new layer \(\mathbf {L}_{i+1}(\theta_{i+1})\). To explore the best possible architecture, different designs of the same layer type are tested, each yielding a new PQC candidate: \begin{equation} \mathbf {U}_{\text{candidate}}(\boldsymbol \theta_{i+1}) = \mathbf {L}_{i+1}(\theta_{i+1}) \mathbf {U}_i(\boldsymbol \theta_i). \end{equation} The type of layer alternates across generations. For a fair comparison, the parameters of the previous generation remain unchanged in all candidate PQCs. Furthermore, newly added layers are designed to almost preserve the accuracy of \(\mathbf {U}_i(\boldsymbol \theta_i)\) at the start of the training. This is achieved, for example, by initializing the parameters of added layers to zero, ensuring that they initially act as the identity. Each PQC candidate \(\mathbf {U}_{\text{candidate}}(\boldsymbol \theta_{i+1})\) undergoes a few training epochs. After training, candidates are ranked based on their highest performance on the validation set during the last training epoch. The most effective circuit \begin{equation} \mathbf {U}(\boldsymbol \theta_{i+1})= \arg \max_{\mathbf {U} \in \{\mathbf {U}_{\text{candidate}}\}} \ \text{Best}(\mathbf {U}_{\text{candidate}}(\boldsymbol \theta_{i+1})), \end{equation} along with its optimised parameters \(\boldsymbol \theta_{i+1}\), is selected for the next generation. Our ranking metric \(\text{Best}(\cdot)\) is the classification accuracy on the validation data.
Accross generations, we alternate between adding single-qubit layers (Architectures 0-2), entanglement layers (Architectures 3-9) and pruning layers (red).
Comparing the accuracicies vs. the number of parameters in the quantum (NPQ) and classical (NPC) backbones of the models, we observe that layered-QAS outperforms both the sQCNN-3D quantum model and the classical vanilla CNN on both datasets. This demonstrates the effectiveness of our layered-QAS approach in designing PQC architectures that are well-suited for the 3D point cloud classification task.
Layered-QAS consistently outperforms both evolutionary QAS and local QAS across generations, achieving higher classification accuracy on the validation set. This highlights the advantage of our progressive layer addition strategy in effectively exploring the PQC architecture space.
We finally benchmark the best models obtained from each QAS method on the test set.
Again, layered-QAS achieves the highest test accuracy among all QAS methods, demonstrating its superior capability in designing PQCs for 3D point cloud classification.
@inproceedings{meli2026layered,
title={Layered Quantum Architecture Search for 3D Point Cloud Classification},
author={Natacha Kuete Meli and Jovita Lukasik and Vladislav Golyanik and Michael Moeller},
booktitle={3DV},
pages={xxx--xxx},
year={2026}
}