Distributed Quantum Neural Networks via Partitioned Features Encoding

TL;DR

This work tackles the limitations of near-term quantum neural networks by introducing distributed QNNs that encode partitioned input features across multiple smaller circuits and aggregate their predictions via the sum of their expectation values, reducing qubit count and circuit depth. The method is validated on Semeion and MNIST datasets, showing improved performance over a single QNN on Semeion and achieving over 0.961 accuracy on MNIST with 14 QNNs. The results demonstrate the viability and scalability of distributed QNNs for practical quantum machine learning on near-term devices, while highlighting the trade-off that excessive partitioning can degrade performance. Overall, distributed QNNs emerge as a promising architecture for advancing quantum inference on large, real-world datasets.

Abstract

Quantum neural networks are expected to be a promising application in near-term quantum computing, but face challenges such as vanishing gradients during optimization and limited expressibility by a limited number of qubits and shallow circuits. To mitigate these challenges, an approach using distributed quantum neural networks has been proposed to make a prediction by approximating outputs of a large circuit using multiple small circuits. However, the approximation of a large circuit requires an exponential number of small circuit evaluations. Here, we instead propose to distribute partitioned features over multiple small quantum neural networks and use the ensemble of their expectation values to generate predictions. To verify our distributed approach, we demonstrate ten class classification of the Semeion and MNIST handwritten digit datasets. The results of the Semeion dataset imply that while our distributed approach may outperform a single quantum neural network in classification performance, excessive partitioning reduces performance. Nevertheless, for the MNIST dataset, we succeeded in ten class classification with exceeding 96\% accuracy. Our proposed method not only achieved highly accurate predictions for a large dataset but also reduced the hardware requirements for each quantum neural network compared to a large single quantum neural network. Our results highlight distributed quantum neural networks as a promising direction for practical quantum machine learning algorithms compatible with near-term quantum devices. We hope that our approach is useful for exploring quantum machine learning applications.

Figures (3)

• Figure 1: This figure shows the flow of our distributed approach over $n_\text{qc}$ QNNs. First, we equally partition features $\bm{x}_i$ into $\{\bm{x}_{i,j}\}_{j=1}^{n_\text{qc}}$. We input partitioned features $\{\bm{x}_{i,j}\}_{j=1}^{n_\text{qc}}$ to variational quantum circuits $\{U(\bm{x}_{i,j},\bm{\phi}_j)\}_{j=1}^{n_\text{qc}}$. Then, we evaluate a loss function using the sum of expectation values as outputs from the quantum circuits and optimize the parameters $\{\bm{\phi}_j\}_{j=1}^{n_\text{qc}}$ in quantum circuits to minimize the loss function.
• Figure 2: This figure shows our QNN architecture. The detail is described in Appendix \ref{['secA:model_description']}.
• Figure 3: This figure shows the example of our QNN architecture used for classifying the $8 \times 8$ reduced sized Semeion dataset with two QNNs. Note that we excluded the CZ transformations $U_\text{ent}$ just before the measurement, as we mentioned in Appendix \ref{['secA:model_description']}.