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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.
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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