On the practical usefulness of the Hardware Efficient Ansatz

Journal Article · Wed Jul 03 04:00:00 EDT 2024 · Quantum

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

Leone, Lorenzo ^[1]; Oliviero, Salvatore F. E. ^[2]; Cincio, Lukasz ^[3]; Cerezo, M. ^[4]

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1. Theoretical Division (T-4), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Physics Department, University of Massachusetts Boston, Boston, Massachusetts 02125, USA, Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
2. Theoretical Division (T-4), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Physics Department, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
3. Theoretical Division (T-4), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
4. Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

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.

• Sponsoring Organization: USDOE
• OSTI ID: 2391064
• Alternate ID(s): OSTI ID: 2500882
• Journal Information: Quantum, Journal Name: Quantum Vol. 8; ISSN 2521-327X
• Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
• Country of Publication: Austria
• Language: English