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

Area of Science:

• Quantum Computing
• Computational Physics
• Quantum Chemistry

Background:

• Accurate energy estimation of quantum many-body systems is vital for quantum advantage.
• Measurement effort is a significant bottleneck in variational quantum algorithms.
• Developing efficient strategies is crucial for practical quantum applications.

Purpose of the Study:

• To find an optimal single-qubit measurement strategy for accurate energy estimation within a given budget.
• To develop a practical and efficient method to overcome the measurement bottleneck.
• To improve the accuracy of energy estimation for quantum many-body systems.

Main Methods:

• Established tail bounds for empirical energy estimators.
• Developed ShadowGrouping, combining shadow estimation with Pauli string grouping.
• Circumvented the NP-hard problem of optimal measurement setting selection.

Main Results:

• ShadowGrouping demonstrates improved provable and practical accuracy over state-of-the-art methods.
• Numerical experiments show enhanced estimation of electronic ground-state energies for small molecules.
• The method effectively identifies measurement settings that maximize energy estimate improvement.

Conclusions:

• ShadowGrouping offers a promising solution to the measurement bottleneck in quantum many-body Hamiltonian simulations.
• This work provides a practical approach for achieving higher accuracy in quantum energy estimation.
• The developed strategy can accelerate the path towards quantum advantage in relevant problems.