A New Framework Containing Convolution and Pooling Circuits for Image Processing and Deep Learning Applications with Quantum Computing Implementation

Abstract

The resource need for deep learning and quantum computers' high computing power potential encourage collaboration between the two fields. Today, variational quantum circuits are used to perform the convolution operation with quantum computing. However, the results produced by variational circuits do not show a direct resemblance to the classical convolution operation. Because classical data is encoded into quantum data with their exact values in value-encoded methods, in contrast to variational quantum circuits, arithmetical operations can be applied with high accuracy. In this study, value-encoded quantum circuits for convolution and pooling operations are proposed to apply deep learning in quantum computers in a traditional and proven way. To construct the convolution and pooling operations, some modules such as addition, multiplication, division, and comparison are created. In addition, a window-based framework for quantum image processing applications is proposed. The generated convolution and pooling circuits are simulated on the IBM QISKIT simulator in parallel thanks to the proposed framework. The obtained results are verified by the expected results. Due to the limitations of quantum simulators and computers in the NISQ era, the used grayscale images are resized to 8x8 and the resolution of the images is reduced to 3 qubits. With developing the quantum technologies, the proposed approach can be applied for bigger and higher resolution images. Although the proposed method causes more qubit usage and circuit depth compared to variational convolutional circuits, the results they produce are exactly the same as the classical convolution process.

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

“…The number of qubits and gates required for different window sizes (N × N) and resolutions (M) are listed in table 6. It is considered that 29 and 94 basic quantum gates are required for the 3-qubit and 8-qubit self-adder respectively [9].…”

“…When calculating the total number of qubits, it is assumed that the operations are performed on the input qubits and no extra qubits are required. The quantum circuit for the self-adder operation is given in [9]. Here, 9 CNOT and 4 Toffoli gates are used for 3-qubit inputs.…”

“…Quantum computing is attracting attention for applications in the field of machine learning due to its promising computational potential. Because arithmetic operations can be applied to the data encoded using value-based encoding methods, the convolution operation can also be performed in a classical sense [9]. However, quantum circuits created in this manner require a large number of qubits and quantum gates.…”

“…For example, according to this method, 8 qubits are required to encode numbers with a maximum value of 255. Although arithmetic operations are relatively easy to implement using this method, it requires a large number of quantum gates [9]. Image coding methods such as novel enhanced quantum representation are based on this basis, and images are represented using multiple controlled Toffoli notations [10,11].…”

A YOLO-Based Method for Detection of Gate and Input in Quantum Circuits

“…Günümüzde kuantum bilgisayarlar için özel olarak tasarlanmış algoritmalar mevcuttur [2]. Genetik algoritmalar [3], Back Tracking algoritması [4], derin öğrenme [5], kenar çıkarım algoritması [6], ve sinyal işleme [7] gibi algoritmalar geliştirilmiştir.…”