On the practical usefulness of the Hardware Efficient Ansatz
1Theoretical Division (T-4), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
2Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
3Physics Department, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
4Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
5Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| Published: | 2024-07-03, volume 8, page 1395 |
| Eprint: | arXiv:2211.01477v2 |
| Doi: | https://doi.org/10.22331/q-2024-07-03-1395 |
| Citation: | Quantum 8, 1395 (2024). |
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Abstract
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.
Featured image: Our results show that QML tasks using Hardware-Efficient Ansatz (HEA) with input data sets composed of states possessing an area law of entanglement are trainable, whereas tasks with data sets composed of states possessing a volume law of entanglement are untrainable.
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