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• W3136233239 abstract "Variational quantum algorithms (VQAs) optimize the parameters $vec{theta}$ of a parametrized quantum circuit $V(vec{theta})$ to minimize a cost function $C$. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming $V(vec{theta})$ is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining $C$ in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when $V(vec{theta})$ is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining $C$ with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of $V(vec{theta})$ is $mathcal{O}(log n)$. Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation." @default.
• W3136233239 created "2021-03-29" @default.
• W3136233239 creator A5016381168 @default.
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• W3136233239 date "2021-03-19" @default.
• W3136233239 modified "2023-10-17" @default.
• W3136233239 title "Cost function dependent barren plateaus in shallow parametrized quantum circuits" @default.
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• W3136233239 doi "https://doi.org/10.1038/s41467-021-21728-w" @default.
• W3136233239 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/7979934" @default.
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• W3136233239 hasPublicationYear "2021" @default.
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