Things to do:

[ndattani]

1. Improve Introduction (including addition of a quadratic that has same ground state as the quantum cubic example)
2. Examples for:

• NTR-ABCG (should be called NTR-ABCG-1)
• NTR-ABCG-2
• PTR-BCR-1
• PTR-BCR-2
• PTR-BCR-3
• PTR-BCR-4
• PTR-KZ
• PTR-KZ (z version)
• SFR-ABCG-1

3. Asymmetric Cubic Reduction example is written in a slightly different format from the previous examples. (Same with the Alternative Forms subsection of this section). Please do not delete this comment until all examples and "alternative forms" are consistent throughout the book.
4. Add "reproduces the full spectrum" as a "pro" for all methods that do, which includes "Asymmetric Cubic Reduction"
5. RBL-2016,

• T should be t_a.
• There is no description of the transformation in the summary section
• There is no example given.
• Eq. 37 in https://github.com/k-local-quadratization/review/blob/6248e11ded86d514745d6f06f03ebfd1263a3ade/k-local-review.pdf has z on the left and b on the right.
• Needs to be verified
• Binomial squared has to be expanded

6. Alternative forms for all methods such that everything is in the "tableau"/matrix form

7. Asymmetric Reduction: Why is there 4 equations instead of 3, and why is the 3rd equation slightly indented?

8. Deduc-Reduc where we kill negative cubic terms (can even be generalized to higher order, and quadraitcs, and linear?)

9. Deduc-Reduc where we kill positive terms but require pre-/post-processing to rule out the artificially low ground states which do not satisfy the deducs.

10. Groebner bases method that Richard originally had, rather than this example which is from Emile's January 2015 work. 1-Qubit's paper was more similar to what Richard originally had.

11. Example of "application of ELM"

12. Method for using "strong quadratizations" for reducing multiple terms at once

13. z versions of all b methods, and b versions of all z methods

14. Feynman Hamiltonian would normally have many values of t, really it should say "The Feynman Hamiltonian contains 4-local Hamiltonians of the form:" (suggestion by Elizabeth Crosson was "Each term can be written in the form:" but really it's "each term plus its conjugate" so I have changed it to the sentence given here).

Add: FGBZ can be used for more than one term, it's a pro! Also add 2015 paper of FGBZ, we have cited 2011 one which is just the conference version 2-cover / pairwise-cover: ABCZ 2016 (one with the bounds), proof of upper bound: Remark 2, there is another quadratization method!!!

Add: YY gadget to 2 -> 2 gadgets.