The authors present a scalable approach for variational quantum compilation (VQC) of quantum dynamics, leveraging recent advances in quantum machine learning (QML). The key insight is to rephrase the quantum compilation problem as a supervised machine learning task, where the goal is to learn the action of a given many-body dynamics on a small dataset of random product states.
The authors show that the PQC only requires a few training samples to accurately learn the dynamics, and crucially, this learned circuit also generalizes to highly entangled states like Haar random states. This out-of-distribution generalization effectively measures the trace distance between the target unitary and the variational circuit, which is the ultimate goal of VQC.
To enable scalability, the authors employ tensor network techniques to efficiently compute the overlaps between low-entanglement states required during training. They also devise effective initialization strategies to mitigate the barren plateau problem. The combination of QML and tensor network methods allows the authors to explore a wide range of system sizes, significantly outperforming previous VQC results.
The authors benchmark their approach on 1D Heisenberg and Ising models, demonstrating accurate long-time dynamics simulation. Comparing to optimized Trotterization, the VQC-generated circuits require orders of magnitude fewer CNOT gates to achieve the same level of accuracy, highlighting the effectiveness of their approach for large, complex quantum systems across one and higher dimensions.
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by Yuxuan Zhang... a las arxiv.org 09-26-2024
https://arxiv.org/pdf/2409.16346.pdfConsultas más profundas