SAMOP 2023 – wissenschaftliches Programm
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QI: Fachverband Quanteninformation
QI 30: Quantum Algorithms
QI 30.5: Vortrag
Donnerstag, 9. März 2023, 15:45–16:00, B305
Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping — •Alexander Gresch1 and Martin Kliesch1,2 — 1Institute for Theoretical Physics, Heinrich Heine University Düsseldorf — 2Institute for Quantum-Inspired and Quantum Optimization, Hamburg University of Technology
Energy estimation in quantum many-body Hamiltonians is a paradigmatic task in various research fields. In particular, an efficient estimation procedure may be crucial in achieving a quantum advantage for a practically relevant problem. Variational quantum algorithms (VQAs) are among the leading approaches for achieving this goal. However, the measurement effort due to the high required accuracy constitutes a crucial bottleneck.
In this work, we aim to find an optimal energy estimation strategy for single-qubit measurements with rigorous performance guarantees. Given any empirical estimator Ê of the energy E relying on different Pauli basis measurements, we derive a tail bound for the estimator Ê. Finding the optimal Pauli bases, we show to be NP-hard. Therefore, we develop a heuristic yet efficient estimation strategy based on our tail bound. It combines shadow estimation methods with grouping strategies for Pauli strings. Therefore, we call it 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, e.g., to tackle the measurement bottleneck of VQAs.