Quantum Convolutional Neural Networks with Interaction Layers for Classification of Classical Data

TL;DR

The paper addresses classification of classical data using quantum circuits by extending quantum convolutional neural networks (QCNNs) with novel three-qubit Interaction Layers. It couples an Encoding Subsystem (Amplitude or Angle Encoding) with Convolutional and Pooling layers and an ancilla-based Classifier to achieve high expressibility while keeping parameters small for near-term devices. The authors demonstrate that three-qubit interactions, coupled with an ancilla classifier, yield superior performance on MNIST, Fashion-MNIST, and Iris under constrained parameter budgets, with binary and multiclass results showing strong accuracy and reduced training cost. This work highlights the practical potential of leveraging higher-order qubit interactions in QCNNs and provides a framework for exploring multi-qubit gates on NISQ hardware, along with concrete architectural and dataset benchmarks.

Abstract

Quantum Machine Learning (QML) has come into the limelight due to the exceptional computational abilities of quantum computers. With the promises of near error-free quantum computers in the not-so-distant future, it is important that the effect of multi-qubit interactions on quantum neural networks is studied extensively. This paper introduces a Quantum Convolutional Network with novel Interaction layers exploiting three-qubit interactions, while studying the network's expressibility and entangling capability, for classifying both image and one-dimensional data. The proposed approach is tested on three publicly available datasets namely MNIST, Fashion MNIST, and Iris datasets, flexible in performing binary and multiclass classifications, and is found to supersede the performance of existing state-of-the-art methods.

Figures (13)

• Figure 1: Simplified Block diagram of the proposed architecture showing the Encoding Subsystem followed by the Convolutional Subsystem followed by the Classifier Subsystem. The Quantum System of the architecture comprises quantum gates with trainable parameters, which are optimized classically by minimizing the Cross Entropy loss function. Classical data are embedded on qubits initialized as 0 at the Encoding subsystem of the network. Ancilla qubits with $i=$ number of classes are used in the Classifier Subystem.
• Figure 2: (Top) The Quantum Feature encoding for quantum machine learning maps classical data in the classical data space to quantum states in the Hilbert space. The different shapes denote different data points. On the right side, in the quantum Hilbert space, each shape represents the corresponding quantum composite state (Bottom left) Amplitude Encoding is an example of such an encoding technique where $2^n$ (here n=2) data points can be mapped into n-qubits. (Bottom right) In contrast, Angle Encoding maps the n-datapoints as arguments of $R_y$ gates to n qubits.
• Figure 3: The Convolutional Layers comprises ansatzes, all of which use two-qubit interactions. Each green box represents either convolutional ansatz 1 or 2. Note that in the second vertical line of the Convolutional Layers, the topmost and bottom green boxes denote the two halves of the same ansatz, which means that the first and last qubits are fed as input to the same ansatz. The blue boxes in the Pooling Layer are made up of the pooling ansatz, and they reduce the number of qubits.
• Figure 4: (Top) Ansatz 1 contains 15 trainable parameters. (Middle) Ansatz 2 contains 10 trainable parameters. These two ansatzes are both used for building the Convolutional Layers. (Bottom) The ansatz used for building the Pooling Layer. The gates used to construct the ansatzes are summarized in table \ref{['tab:A']}.
• Figure 5: The proposed Interaction Layer 1 (at the top), which comes after the first Convolutional Layer and is followed by the second Convolutional Layer. The novel Interaction Layer 2 (at the bottom) comes after the second Convolutional Layer and is followed by the final Classifier Subsystem. The graphical representations show the dependency of each state established via Toffoli gates in each layer. Each state depends on two target states. For e.g., a Pauli-X operation will be carried on qubit 4 if both of the 2nd and 3rd qubits are in a state 1.