About
Gabe of the Jungle
About the Hamiltonian Jungle
The Hamiltonian Jungle was created as a way of unifying known results related to the local Hamiltonian problem in quantum complexity theory. There is a large class of results, the most notable being the $2$–local Hamiltonian problem is QMA–complete [KKR05]. This result has spurred numerous subsequent ideas and proofs. Explorations into geometrical restrictions [OT08] as well as specific many–body model types [SV09] have developed the jungle. Those new to the field can see this long array of results as extremely interesting, but also daunting. The effort needed, not only to understand the content but to have a grasp on many of the known results, is significant. The Hamiltonian Jungle was created to ease a few issues:
- Entry to the Field: Assist those new to and interested in the field in gaining a clear understanding of the current jungle of local Hamiltonian complexity classifications.
- Cohesive Analysis: Provide a unified and cohesive analysis of known results to hopefully eliminate any potential ambiguities.
- Reduction Clarity: Illustrate reductions between Hamiltonian instances, offering valuable insights into the relationships between different problems.
- Knowledge Gaps: Clarify where gaps in knowledge currently exist, highlighting areas that warrant further exploration and research.
- Technique Analysis: Shed light on the techniques employed in reduction proofs, making the intricacies of the proofs more accessible to a wider audience.
We have taken much inspiration from Complexity Zoo, Quantum Algorithm Zoo, Error Correction Zoo and Wolfram Mathworld. As it currently stands, the Hamiltonian Jungle is far from complete and there is much work to be done before we have a full library of known results. In its current form, the jungle conveys some of the more interesting results and open questions. As a final remark, we note that the supplementary analysis is also a work in progress. We are attempting to convey difficult concepts to a range of audiences; if some things are not clear, please contact us to discuss more on how the jungle can be improved.
@misc{TheHamiltonianJungle,
title = {The {H}amiltonian {J}ungle},
author = {Waite, Gabriel and Mann, Ryan L and Elman, Samuel J},
year = {2023}
}
Acknowledgements
- Jannis Ruh
- Karl Lin
Updates
Date Created: September 2023
Last Update: 18 April 2024