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

TL;DR

This paper introduces a quantum state preparation method leveraging reflection symmetry and matrix product states, significantly enhancing accuracy and scalability for encoding probability distributions on noisy quantum devices.

Contribution

A novel quantum state preparation technique using reflection symmetry to reduce entanglement and improve approximation accuracy with matrix product states.

Findings

Achieved two orders of magnitude improvement in accuracy over existing methods.

Demonstrated the method on a real quantum processor with 10 and 20 qubits.

Showed that approximation accuracy depends mainly on bond dimension, not qubit number.

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.