Quantum State Preparation for Probability Distributions with Reflection Symmetry Using Matrix Product States

Abstract

Quantum circuits for loading probability distributions into quantum states are essential subroutines in quantum algorithms used in physics, finance engineering, and machine learning. The ability to implement these with high accuracy in low-depth quantum circuits is a critical issue. We propose a novel quantum state preparation method for probability distribution with reflection symmetry using matrix product states. By considering reflection symmetry, our method reduces the entanglement of probability distributions and improves the accuracy of approximations by matrix product states. As a result, we improved the accuracy by two orders of magnitude over existing methods using matrix product states. Our approach, characterized by linear scalability with qubit count, is highly advantageous for noisy quantum devices. Also, our demonstration results reveal that the approximation accuracy in tensor networks depends heavily on the bond dimension, with minimal reliance on the number of qubits. Our method is demonstrated for a normal distribution encoded into 10 and 20 qubits on a real quantum processor.