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 quantum state-preparation method for probability distributions 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 improve the accuracy by 2 orders of magnitude over existing methods. Our approach, which scales linearly with qubit count, is highly advantageous for noisy quantum devices. Our results also demonstrate 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.

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• Quantum circuits
• Quantum computation
• Quantum simulation
• Tensor network methods