Welcome to the Hamiltonian Jungle — an online resource for categorising the complexity classifications of various Hamiltonian problems. Please note, this is a work in progress! If you have any suggestions please refer to the Contact page.

Models

Reading Guide

For those interested in learning more about Hamiltonian complexity, we recommend the following resources:

• [KSV02]: The $5$–local Hamiltonian problem is QMA–complete
• [KR03]: The $3$–local Hamiltonian problem is QMA–complete
• [KKR05]: The $2$–local Hamiltonian problem is QMA–complete
• [OT08]: The $2$–local Hamiltonian problem on a square lattice is QMA–complete
• [BBT06]: The $2$–local stoquastic Hamiltonian problem is StoqMA–complete
• [BL08]: $2$–local Hamiltonians with no $Y$ terms are QMA–complete
• [SV09]: The Fermi–Hubbard Hamiltonian is QMA–complete
• [BH16]: The complexity of the transverse field Ising model
• [CM16]: The complexity classification of local Hamiltonians
• [PM15]: The complexity classification of antiferromagnetic local Hamiltonians
• [MM24]: Algorithmic Cluster Expansions for Quantum Problems

New Paper!

We have a new paper looking at the complexity of stoquastic local Hamiltonians on square lattices. This will soon be available on the arXiv.