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Bulletin of the American Physical Society

Branching Quantum Convolutional Neural Networks: A Variational Ansatz with Mid-Circuit Measurements

Ian MacCormack, Conor Patrick Delaney, Alexey Galda, Prineha Narang

Published Mar 19, 2021• 0 citations
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Variational quantum circuits have become a widely used tool for performing quantum machine learning (QML) tasks on labeled quantum states. In some specific tasks or for specific variational ansätze, one may perform measurements on a restricted part of the overall input state. This is the case for, e.g., quantum convolutional neural networks (QCNNs), where after each layer of the circuit a subset of qubits of the processed state is measured or traced out, and at the end of the network one typically measures a local observable. In this work, we demonstrate that measuring observables with restricted support results in larger label prediction variance in regression QML tasks. We show that the reason for this is, essentially, the number of distinct eigenvalues of the observable one measures after the application of a variational circuit.
ABSTRACT While Quantum Convolutional Neural Networks (QCNNs) offer a structured framework for data processing in the noisy intermediate‐scale quantum (NISQ) regime, conventional architectures often rely on over‐parameterized ansätze that hinder trainability and increase sensitivity to hardware noise. Furthermore, standard quantum pooling strategies frequently discard useful coherent correlations. To address these limitations, we propose a parameter‐efficient QCNN architecture integrating a ‐equivariant convolutional ( Eq‐Conv ) kernel with a guided variational pooling ( Guided Var‐Pool ) scheme. By enforcing continuous symmetry via Schur's Lemma, the Eq‐Conv kernel requires only five trainable parameters, significantly reducing circuit complexity compared to full‐rank operations while maintaining competitive expressivity. For dimensionality reduction, the Guided Var‐Pool introduces an Information‐Bottleneck‐inspired penalty that actively drives discarded qubits toward the ground state, ensuring task‐relevant features are concentrated within the retained subsystem prior to truncation. To maintain NISQ compatibility, the architecture strictly adheres to the Principle of Deferred Measurement, eliminating the need for mid‐circuit measurements. Numerical experiments on MNIST and Fashion‐MNIST datasets demonstrate that our approach achieves competitive classification accuracy while exhibiting superior robustness against depolarizing noise. Compared to over‐parameterized baselines, the proposed model establishes a favorable depth‐for‐robustness trade‐off, providing a resource‐efficient pathway for scalable quantum machine learning.