In recent years, quantum computers have become one of most attractive machines based on the principles of quantum mechanics. We make use of quantum superposition, quantum entanglement and so on in the calculation process. Expectations have increased enormously since the announcement of Quantum supremacy1, 2 in October 2019 and December 2020 by superconducting and photonic quantum computers. There are three types of quantum computing devices: quantum annealing3, quantum gates and optical Continuous-Variable2, 4. Quantum gate quantum computing devices include the superconducting type5, 6, trapped ion type7, 8, semiconductor quantum type9, 10, diamond NV centre type11 and Rydberg atom type12. The performance of quantum devices has been rapidly improving day by day in recent years because of severe development competition. In putting them into practical use, software implementation techniques that make the most of the characteristics of each quantum computer are becoming increasingly important. Applications to cryptographic security13, 14, quantum simulation15, 16, mathematical optimisation for solving graphical problems17, 18 and machine learning19–23 are especially promising areas.
With the progress of the internet, computers and various sensors, a variety of information has been collected from the IoT, and vast amounts of data have been stored. Attempts to solve social problems are being made by these stored data. The needs for classification are getting stronger in accordance with the goal.
For example, classification includes image data, text, and sound. Image classification is widely used in remote sensing24, biological inspection25–27, building and civil engineering28 and manufacturing29–31.
Support vector machine (SVM) 24, 32–34 is the most often used method in various machine learning. This method is based on statistical machine learning, which allows the construction of training models with relatively little data. In recent years, kernel SVM35–37 has been widely used as one method of kernel estimation. Kernel SVM is widely used for pattern recognition and other imaging applications, as we can separate non-linear feature spaces by using inner products.
However, we have two issues with the kernel estimation. One is calculation cost. We need a huge calculation cost as the embedding function into the feature space increases dramatically when the feature volume increases. The other is the limitation of the embedding function. We must treat a complicated function when we use the kernel trick in SVM. However, we have the limitation of an embedded function into the feature space.
As a means of solving the above problems, there are two attempts to use kernel estimation to embed feature maps with quantum entanglement in the quantum Hilbert space. One is the quantum kernel SVM, which introduced quantum entanglement and Z feature maps in an exponentially large feature space38. The other is the kernel estimation neural network, and the results show the potential of quantum advantage39.
The inspection of defective products is a very important issue in the inspection process in the manufacturer. The learning model of two-class classification is used in such inspection processes. Recently, we have limited the training size (good and defective products), as many products have been produced in small quantities and in many varieties. Therefore, we need a machine learning model that enables limited and small data for classification. Our purpose is to obtain a highly accurate learning model that classifies small-size imaging data in shipping inspection.
In related work38, they developed a method to solve by using Z-feature maps using quantum entanglement. However, they have not yet presented the quantum advantage over the classical learning model. The quantum advantage of machine learning has been reported in several journal38, 40–43. However, we cannot watch comparisons between classical and quantum kernel estimation on machine learning.
In this work, we have investigated the learning model construction process for quantum and classical kernel SVM and demonstrated the quantum advantage over the classical learning model in the classifier. We have revealed the quantum advantage of constructing a learning model by investigating the effect of various feature maps and the training process by using an evaluation index and ROC space.