Variational quantum circuits for convolution and window-based image processing applications

Quantum information processing is gaining popularity in the fields of machine learning and image processing because of its advantages. Quantum convolution is an interesting topic in this field, and studies on this topic can be divided into value-based and angle-based methods. Although quantum convolution studies on angle-based or variational quantum circuits (VQCs) is called convolution, the circuits work differently from classical convolution. In this study, contrary to the literature, the VQC was trained to imitate classical convolution. The differential evolution algorithm (DEA) was used to optimize the VQCs. The proposed method requires as many qubits as the filter size (N× N). The generated circuits contain N× N× 4 quantum gates and N× N × 3 trainable parameters. The generated circuits were tested in Python environment using Cirq simulator. The Cifar10 and MNIST datasets are used as examples. For 2 × 2 filters with different weights, the convolution was successfully modeled with a mean squared error of less than 0.001. In general, the proposed method imitates classic convolution within ±5% tolerance. In conclusion, VQCs that imitate classical convolution with fewer qubits and quantum gates than value-based methods were obtained.