Hamiltonian complexity for bosonic systems

Develop a systematic Hamiltonian-complexity theory for bosonic systems, including the complexity of bosonic analogues of local-Hamiltonian and QMA-type problems and the complexity of approximating Gibbs states, partition functions, and thermodynamic observables for restricted bosonic Hamiltonians.

Background

The paper develops computational-complexity results for BEQC but emphasizes that the corresponding Hamiltonian-complexity landscape for infinite-dimensional bosonic systems remains incomplete. Important parameters include interaction degree, locality, number of modes, energy constraints, and temperature.

References

Basic questions include identifying the complexity of bosonic analogues of local-Hamiltonian and other \mathsf{QMA}-type problems, as well as understanding how these complexities depend on restrictions such as interaction degree, locality, number of modes, and energy. Closely related questions arise in the study of finite-temperature properties. What is the complexity of approximating Gibbs states, partition functions, or thermodynamic observables for restricted families of bosonic Hamiltonians?

— A physical and universal model of bosonic computations with Solovay-Kitaev theorem  (2609.40226 - Rudolph et al., 30 Sep 2026) in Section 1. Results, subsection “Open questions,” item “Bosonic Hamiltonian complexity”