ER-AAE: A quantum state preparation approach based on entropy reduction

Kaining Zhang, Liu Liu, Min-Hsiu Hsieh, Dacheng Tao

Keywords: quantum machine learning, amplitude encoding, state preparation

TL;DR: We developed an approximate amplitude encoding approach for real-world data.

Abstract: Amplitude encoding of classical vectors serves as a cornerstone for numerous quantum machine learning algorithms in real-world applications. Nevertheless, achieving exact amplitude encoding for general vectors needs an exponential number of gates, which negates the potential quantum advantages. To address the challenge of large gate number in the state preparation phase, we propose an approximate amplitude encoding algorithm based on entropy reduction (ER-AAE) within the classical framework. Given a target vector, the ER-AAE algorithm generates a sequence of gates, comprising single-qubit rotations and CZ gates, that approximates the amplitude encoding of the target vector. The structure of encoding circuits in ER-AAE is built inductively using a greedy search strategy that maximally reduces the linear entropy. We further prove that the state produced by ER-AAE approximates to the target state with the infidelity bounded by the linear entropy of intermediate states. Experimental results, including state preparations on random quantum circuit states, random vectors, MNIST digits, and CIFAR-10 images, validate our method. Specifically, real-world data reveals a noteworthy trend where linear entropy decays significantly faster compared to random vectors. Furthermore, the ER-AAE algorithm surpasses the best existing encoding techniques, achieving lower error with an equivalent or fewer number of CNOT or CZ gates.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 9304