On the practical usefulness of the Hardware Efficient Ansatz

Leone, Lorenzo; Oliviero, Salvatore F.E.; Cincio, Lukasz; Cerezo de la Roca, Marco Vinicio Sebastian

doi:10.22331/q-2024-07-03-1395

On the practical usefulness of the Hardware Efficient Ansatz

Journal Article · Wed Jul 03 00:00:00 EDT 2024 · Quantum

DOI:https://doi.org/10.22331/q-2024-07-03-1395· OSTI ID:2391064

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Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); University of Massachusetts, Boston, MA (United States); Freie Univ., Berlin (Germany)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); University of Massachusetts, Boston, MA (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Variational Quantum Algorithms (VQAs) and Quantum Machine Learning (QML) models train a parametrized quantum circuit to solve a given learning task. The success of these algorithms greatly hinges on appropriately choosing an ansatz for the quantum circuit. Perhaps one of the most famous ansatzes is the one-dimensional layered Hardware Efficient Ansatz (HEA), which seeks to minimize the effect of hardware noise by using native gates and connectives. The use of this HEA has generated a certain ambivalence arising from the fact that while it suffers from barren plateaus at long depths, it can also avoid them at shallow ones. In this work, we attempt to determine whether one should, or should not, use a HEA. We rigorously identify scenarios where shallow HEAs should likely be avoided (e.g., VQA or QML tasks with data satisfying a volume law of entanglement). More importantly, we identify a Goldilocks scenario where shallow HEAs could achieve a quantum speedup: QML tasks with data satisfying an area law of entanglement. We provide examples for such scenario (such as Gaussian diagonal ensemble random Hamiltonian discrimination), and we show that in these cases a shallow HEA is always trainable and that there exists an anti-concentration of loss function values. Our work highlights the crucial role that input states play in the trainability of a parametrized quantum circuit, a phenomenon that is verified in our numerics.

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

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: 89233218CNA000001; 20230049DR

OSTI ID:: 2391064

Alternate ID(s):: OSTI ID: 2500882

Report Number(s):: LA-UR-22-31539

Journal Information:: Quantum, Vol. 8; ISSN 2521-327X

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

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