List of things to do

[ndattani]

• Do we have Eq. 4 and Proposition 1 and 2 of https://personal.lse.ac.uk/anthony/Quadratization_web.pdf in the book? Also same paper says " to quadratize in polynomial time any pseudo-Boolean function while only using O(n|F|) auxiliary variables" -- do we have that? Also check Remark 1 (Bucheim and Rinaldi)
• Example on opening page, b1b2 comes up twice: b1b2 - 4b1b2 = -3b1b2
• -4b1b2b3 -> -4(b1b2 + b1b3), is something like that possible? Think about example on Pg 1 more. Eq. 2 can be transformed from Eq. 1 very easily, how general can we do that?
• "approximate ELCs" which Andreas found to be like my "heuristic gadgets"
• change font of Pauli matrices. (not sure what I meant there, and don't have time to check what time that was written and compare it to when the last font change was made, but now in January 2021 I think perhaps the goal was to straighten up the letters so they take up less space? This is after they were already switched from "math font" to a straighter font, but they're still a bit tilted)
• example on page 1 for quantum case only has coefficients of 1. Some negatives and non-1 numbers would be nice.
• quantum example preserves entire spectrum, but I don't want people to think right from page 1 that the entire spectrum needs to be preserved. Perhaps an example that only preserves the round state would be better pedagogically.
• deduc-reduc. Con: only preserves ground state (and degeneracy?). Can we generalize it to a full-spectrum version?
• split-reduc: "At this point, we could split H0 again, ...." think about what this sentence means.
• NTR-ABCG: see comments in .tex.
• NTR-AC: example and alternative forms don't look right.
• NTR-RBL: alternative form is quartic not cubic? Also I have a note saying "Eq. 10. i+2 = j" for the bibliography section.
• PTR-RBL-(3->2): alternative form is quartic but should just be expanded version of 74. Eq. 74 shoudl be Eq. 11 of RBL i+2=j which is apparently not the case.
• PTR-RBL-(4->2): apprently Eq. 11, i+2 < j, whatever that means (this is just what it says in my rough notes). Example has -z1z2z3z4 but it should be positive.
• Follow PENCIL NOTES in Nike's printed version, for FGBZ.
• Describe strategies for choosing coeffs in pairwise covers and Rosenberg
• Add Rosenberg-like method from Gruber's thesis.
• KKR(3->2) needs bibliography section!
• added Alavi's paper but he told me it was an old idea so the original papers should also be added.
• Figure out what was meant by "Can reduce the connectivity of an objective function, as it breaks interactions between variables." for FGBZ
• 2017 ABCG paper appears twice in bibliography (probably one of them was meant to be a 2015 arXiv or something? ) figure out why and make sure all references to these are not erroneous.
• Add https://arxiv.org/abs/math/0103170