A generalized floating-point quantum representation of 2-D data and their applications

In the past few decades, quantum computation has become increasingly attractive due to its remarkable performance. However, few results of 2-D data and their transformation based on quantum computation have emerged in recent years. A generalized floating-point representation of 2-D data (QR2-DD) is proposed, which can represent a quantum data with arbitrary size by the element of $p+q$ qubits. And then, we provide a method to convert a 3-D data into 2-D data, which leads to a reduction in the number of qubits for position. Based on QR2-DD, the quantum circuits of elementary transformation of 2-D data are designed, such as interchanging two-row module, multiplying a row by a constant module and adding two-row module. In order to verify the effectiveness of these circuits, an example is given below each module.