Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping

Abstract

Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For instance, the measurement effort poses a critical bottleneck for variational quantum algorithms. We aim to find the optimal strategy with single-qubit measurements that yields the highest provable accuracy given a total measurement budget. As a central tool, we establish new tail bounds for empirical estimators of the energy. They are helpful for identifying measurement settings that improve the energy estimate the most. This task constitutes an NP-hard problem. However, we are able to circumvent this bottleneck and use the tail bounds to develop a practical, efficient estimation strategy, which we call ShadowGrouping. As the name indicates, it combines shadow estimation methods with grouping strategies for Pauli strings. In numerical experiments, we demonstrate that ShadowGrouping improves upon state-of-the-art methods in estimating the electronic ground-state energies of various small molecules, both in provable and practical accuracy benchmarks. Hence, this work provides a promising way, e.g., to tackle the measurement bottleneck associated with quantum many-body Hamiltonians.

16+9 pages, 5+4 figures. v3: extended numerical benchmarks. Presented at TQC 2023

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Cited by in corpus (10)

• A Simple and Efficient Joint Measurement Strategy for Estimating Fermionic Observables and Hamiltonians
• Sampling Groups of Pauli Operators to Enhance Direct Fidelity Estimation
• Biased Estimator Channels for Classical Shadows
• Shot-noise reduction for lattice Hamiltonians
• Reducing the sampling complexity of energy estimation in quantum many-body systems using empirical variance information
• Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables
• Resource-Optimized Grouping Shadow for Efficient Energy Estimation
• Improving shadow estimation with locally-optimal dual frames
• One, Two, Three: One empirical evaluation of a two-copy shadow tomography scheme with triple efficiency
• Accelerating Fermionic System Simulation on Quantum Computers