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

Abstract

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.

11 pages, 15 figures, The current version represents the initial submission and differs significantly from the final published version. Please check the official publication in Physics Letters A for the most up-to-date and comprehensive content

References in corpus (28)

• Quantum Computing in the NISQ era and beyond
• Quantum Machine Learning
• The density-matrix renormalization group in the age of matrix product states
• Quantum algorithm for solving linear systems of equations
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quantum support vector machine for big data classification
• Quantum Convolutional Neural Networks
• Quantum principal component analysis
• Quantum random access memory
• Tensor networks for complex quantum systems
• Transfer learning in hybrid classical-quantum neural networks
• Robust data encodings for quantum classifiers
• An approximate Fourier transform useful in quantum factoring
• The density matrix renormalization group for ab initio quantum chemistry
• Real- and imaginary-time evolution with compressed quantum circuits
• Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment
• A divide-and-conquer algorithm for quantum state preparation
• Generalization in Quantum Machine Learning: a Quantum Information Perspective
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Quantum principal component analysis only achieves an exponential speedup because of its state preparation assumptions
• On the robustness of bucket brigade quantum RAM
• A density-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelity
• Scalable and High-Fidelity Quantum Random Access Memory in Spin-Photon Networks
• Tensor networks for unsupervised machine learning
• Quantum state preparation protocol for encoding classical data into the amplitudes of a quantum information processing register's wave function
• Variational determination of multi-qubit geometrical entanglement in NISQ computers
• Quantum kernels with squeezed-state encoding for machine learning
• Deterministic and Entanglement-Efficient Preparation of Amplitude-Encoded Quantum Registers