Optimal Qubit Mapping Search for Encoding Classical Data into Matrix Product State Representation with Minimal Loss

Matrix product state (MPS) offers a framework for encoding classical data into quantum states, enabling the efficient utilization of quantum resources for data representation and processing. This research paper investigates techniques to enhance the efficiency and accuracy of MPS representations specifically designed for encoding classical data. Based on the observations that MPS truncation error depends on the pattern of the classical data, we devised an algorithm that finds optimal qubit mapping for given classical data, thereby improving the efficiency and fidelity of the MPS representation. Furthermore, we evaluate the impact of the optimized MPS in the context of quantum classifiers, demonstrating their enhanced performance compared to the conventional mapping. This improvement confirms the efficacy of the proposed techniques for encoding classical data into quantum states. MPS representation combined with optimal qubit mapping can pave a new way for more efficient and accurate quantum data representation and processing.