Dimensionality Reduction Using Quantum Computation and Data Transformation

In this article, we present a dimensionality reduction method based on data transformation and quantum computation. The proposed approach is implemented using a cascade quantum circuit comprising three key stages: quantum state preparation (QSP), quantum data transformation (QDT), and quantum measurement. The main steps of the method are as follows: First, the QSP circuit is designed using elementary quantum gates to encode the given data into a quantum register, enabling efficient data transformation. Next, the QDT circuit processes the encoded data, compressing it into a more compact representation with fewer significant features. This study explores two types of data transformations: dataindependent transforms (DIT), commonly used in digital signal compression, such as the discrete cosine transform (DCT), discrete Walsh transform (DWT), and discrete Haar transform (DHT); and data-dependent transforms (DDT), which leverage statistical properties of the data, such as the Karhunen-Loeve transform (KLT) which is also known as principal component analysis (PCA). Finally, quantum measurement is performed to extract the transformed data, where small-valued coefficients are discarded to achieve dimensionality reduction. To validate the effectiveness of the proposed method, experiments are conducted using real-world Fisher's iris flower data set.