Regensburg 2022 – scientific programme

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QI: Fachverband Quanteninformation

QI 4: Poster: Quantum Information

QI 4.30: Poster

Monday, September 5, 2022, 18:00–20:00, P2

Efficient energy estimation for variational quantum algorithms using ShadowGrouping — •Alexander Gresch and Martin Kliesch — Quantum Technology Research Group, Heinrich Heine University, Düsseldorf

Hybrid variational quantum algorithms (VQAs) are one of the main candidates for relevant applications of quantum computation in the near future. However, due to the hybrid quantum-classical nature of VQAs, a large number of repeated energy measurements for various trial states is needed. Each of these states requires an estimate Ê of the target energy E.

In our work, we aim to find the optimal strategy with single-qubit measurements that yields the highest provable accuracy given a total measurement budget. To this end, we derive a new upper bound to the failure probability P[|Ê−E]> є] for a given tolerable accuracy є, which improves upon previous bounds obtained in the context of derandomized classical shadows. Moreover, we combine strategies that measure groups of commuting Hamiltonian terms with that framework. This combination results in a measurement allocation scheme which we call ShadowGrouping. Numerically, we demonstrate that ShadowGrouping outperforms state-of-the-art methods in estimating the electronic ground-state energies of various small molecules. Hence, this work provides a promising way to approach the measurement bottleneck of VQAs.