A theoretical framework for quantum image representation and data loading scheme

Two fundamental problems exist in the use of quantum computation to process an image or signal. The first one is how to represent giant data, such as image data, using quantum state without losing information. The second one is how to load a colossal volume of data into the quantum registers of a quantum CPU from classical electronic memory. Researches on these two questions are rarely reported. Here an entangled state is used to represent an image (or vector) for which two entangled registers are used to store a vector component and its classical address. Using the representation, n1 + n2 + 8 qubits are used to store the whole information of the gray image that has a $2^{n_1 } \times 2^{n_2 } $ size at a superposition of states, a feat is not possible with a classic computer. The way of designing a unitary operation to load data, such as a vector (or image), into the quantum registers of a quantum CPU from electronic memory is defined herein as a quantum loading scheme (QLS). In this paper, the QLS with time complexity O(log2N) is presented where N denotes the number of vector components, a solution that would break through the efficiency bottleneck of loading data. QLS would enable a quantum CPU to be compatible with electronic memory and make possible quantum image compression and quantum signal processing that has classical input and output.