Importance of the spectral gap in estimating ground-state energies

Understand

The field of quantum Hamiltonian complexity lies at the intersection of quantum many-body physics and computational complexity theory, with deep implications to both fields.

• The main object of study is the LocalHamiltonian problem, which is concerned with estimating the ground-state energy of a local Hamiltonian and is complete for the class QMA, a quantum generalization of the class NP.
• A major challenge in the field is to understand the complexity of the LocalHamiltonian problem in more physically natural parameter regimes.
• One crucial parameter in understanding the ground space of any Hamiltonian in many-body physics is the spectral gap, which is the difference between the smallest two eigenvalues.