# Connecting ansatz expressibility to gradient magnitudes and barren plateaus

@article{Holmes2021ConnectingAE, title={Connecting ansatz expressibility to gradient magnitudes and barren plateaus}, author={Zoe Holmes and Kunal Sharma and Mar{\'i}a Cerezo and Patrick J. Coles}, journal={ArXiv}, year={2021}, volume={abs/2101.02138} }

Parameterized quantum circuits serve as ansätze for solving variational problems and provide a ﬂexible paradigm for programming near-term quantum computers. Ideally, such ansätze should be highly expressive so that a close approximation of the desired solution can be accessed. On the other hand, the ansatz must also have suﬃciently large gradients to allow for training. Here, we derive a fundamental relationship between these two essential properties: expressibility and trainability. This is…

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