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Variational Quantum Algorithms (VQAs) and Quantum Machine Learning (QML)models train a parametrized quantum circuit to solve a given learning task. Thesuccess of these algorithms greatly hinges on appropriately choosing an ansatzfor the quantum circuit. Perhaps one of the most famous ansatzes is theone-dimensional layered Hardware Efficient Ansatz (HEA), which seeks tominimize the effect of hardware noise by using native gates and connectives.The use of this HEA has generated a certain ambivalence arising from the factthat while it suffers from barren plateaus at long depths, it can also avoidthem 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 HEAsshould likely be avoided (e.g., VQA or QML tasks with data satisfying a volumelaw of entanglement). More importantly, we identify a Goldilocks scenario whereshallow HEAs could achieve a quantum speedup: QML tasks with data satisfying anarea law of entanglement. We provide examples for such scenario (such asGaussian diagonal ensemble random Hamiltonian discrimination), and we show thatin these cases a shallow HEA is always trainable and that there exists ananti-concentration of loss function values. Our work highlights the crucialrole that input states play in the trainability of a parametrized quantumcircuit, a phenomenon that is verified in our numerics.

On the practical usefulness of the Hardware Efficient Ansatz