Improving Classical Shadows with Grouping Strategies

Abstract

Efficiently extracting information from quantum systems is a key challenge in quantum computing. This thesis explores the combination of two complementary techniques—classical shadows and grouping—to improve quantum measurement strategies under resource constraints. Classical shadows enable the prediction of many properties of a quantum state from a small number of measurements, while grouping strategies reduce the number of measurements needed by exploiting commutativity among observables. We implement a hybrid method, Shadow–Grouping, that unifies both approaches to enhance measurement efficiency on current quantum devices. We also demonstrate its effectiveness by estimating the ground state energies of H2 and LiH molecules: compared to standard classical shadows, our results show that Shadow–Grouping achieves up to 18-fold gains in accuracy and reaches chemical precision using orders of magnitude fewer measurements.