Noise-adaptive hybrid quantum convolutional neural networks based on depth-stratified feature extraction

TL;DR

A noise-adaptive hybrid QCNN that improves classification under noise by exploiting depth-stratified intermediate measurements and mitigates the scaling limitations of standard architectures is proposed.

Abstract

Hierarchical quantum classifiers, such as quantum convolutional neural networks (QCNNs), represent recent progress toward designing effective and feasible architectures for quantum classification. However, their performance on near-term quantum hardware remains highly sensitive to noise accumulation across circuit depth, calling for strategies beyond circuit-architecture design alone. We propose a noise-adaptive hybrid QCNN that improves classification under noise by exploiting depth-stratified intermediate measurements. Instead of discarding qubits removed during pooling operations, we measure them and use the resulting outcomes as classical features that are jointly processed by a classical neural network. This hybrid hierarchical design enables noise-adaptive inference by integrating quantum intermediate measurements with classical post-processing. Systematic experiments across multiple circuit sizes and noise settings, including hardware-calibrated noise models derived from IBM Quantum backend data, demonstrate more stable convergence, reduced loss variability, and consistently higher classification accuracy compared with standard QCNNs. Moreover, we observe that this performance advantage significantly amplifies as the circuit size increases, confirming that the hybrid architecture mitigates the scaling limitations of standard architectures. Notably, the multi-basis measurement variant attains performance close to the noiseless limit even under realistic noise. While demonstrated for QCNNs, the proposed depth-stratified feature extraction applies more broadly to hierarchical quantum classifiers that progressively discard qubits.

Figures (9)

• Figure 1: Schematic overview of the proposed noise-robust framework and evaluation pipeline. The workflow initiates with classical input preprocessing (PCA) and quantum encoding (angle encoding) to map data into the quantum state. To rigorously evaluate model performance, a target backend profile is configured to emulate realistic hardware conditions using real device calibration data. The central diagram illustrates the hierarchical architecture: the inner gray block represents the baseline architecture (QCNN), which outputs predictions solely from the final qubit readout, while the enclosing blue block indicates the proposed model (HQCNN-EZ and HQCNN-EM). The proposed architecture recovers information from discarded trash qubits via depth-stratified measurements, processing these outcomes through a classical neural network to compute the output. The surrounding yellow rectangular region delineates the noise-adaptive training loop, where the circuit is transpiled and executed under noise to compute the output and evaluate the loss, enabling the joint update of model parameters directly under noisy execution conditions.
• Figure 1: Training and validation loss curves of the regression models under varying simulation conditions. The plots display the loss trajectories for (a) a four-qubit circuit and (b) an eight-qubit circuit across three environments: noiseless, FakeGuadalupeV2, and AerSimulator (configured with the IBM_Yonsei backend). Solid lines with filled markers represent the mean training loss, while dotted lines with open markers indicate the mean validation loss, averaged over five independent iterations. The shaded bands around the training loss curves indicate one standard deviation ($\pm \sigma$) around the mean. The insets provide a magnified view of the final training epochs to illustrate the convergence details of the hybrid models.
• Figure 2: Training and validation loss curves for eight-qubit classification models under different noise settings. The plots display the loss trajectories across three simulation environments: noiseless, FakeGuadalupeV2, and AerSimulator configured with the IBM_Yonsei backend. Solid and dotted lines with filled markers represent the mean of training loss, while dotted lines with open markers indicate the mean validation loss, averaged over five independent iterations. The shaded bands around the training loss curves indicate one standard deviation ($\pm \sigma$) around the mean.
• Figure 2: Mean performance improvements of hybrid QCNN models relative to the baseline QCNN across circuit sizes and noise settings. Results are reported for the regression task using four- and eight-qubit circuits (denoted as 4q and 8q) under varying simulation conditions: noiseless, FakeGuadalupeV2, and AerSimulator configured with the IBM_Yonsei backend. Metrics include the relative improvement in Mean Squared Error (MSE, top row) and Coefficient of Determination ($R^2$, bottom row), reported as mean $\pm$ one standard deviation over five independent training trials. Blue circles with solid lines denote HQCNN-EZ, while orange squares with dashed lines represent HQCNN-EM. Positive values of the relative improvement indicate a performance gain (i.e., lower MSE or higher $R^2$) over the baseline.
• Figure 3: Mean performance improvements of hybrid QCNN models relative to the baseline QCNN across circuit sizes and noise settings. Results are reported for the classification task using four-, eight-, and ten-qubit circuits (denoted as 4q, 8q, and 10q) under varying simulation conditions: noiseless, FakeGuadalupeV2, and AerSimulator configured with the IBM_Yonsei backend. Metrics include the relative improvement in Binary Cross-Entropy (BCE) loss (top row) and classification accuracy (bottom row), reported as mean $\pm$ one standard deviation over five independent training trials. Blue circles with solid lines denote HQCNN-EZ, while orange squares with dashed lines represent HQCNN-EM. Positive values of the relative improvement indicate a performance gain (i.e., lower loss or higher accuracy) over the baseline.