Cost function dependent barren plateaus in shallow parametrized quantum circuits

Cerezo de la Roca, Marco Vinicio Sebastian; Sone, Akira; Volkoff, Tyler James; Cincio, Lukasz; Coles, Patrick Joseph

doi:10.1038/s41467-021-21728-w

Cost function dependent barren plateaus in shallow parametrized quantum circuits

Journal Article · Fri Mar 19 00:00:00 EDT 2021 · Nature Communications

DOI:https://doi.org/10.1038/s41467-021-21728-w· OSTI ID:1826512

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) 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(θ) 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(θ) 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(θ) is Ο(logn). 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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1826512

Report Number(s):: LA-UR--19-32681

Journal Information:: Nature Communications, Journal Name: Nature Communications Journal Issue: 1 Vol. 12; ISSN 2041-1723

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

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