Nick new

[nchancel]

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[ndattani]

It appears that the only change here is that you've added back the page on "Chained Three Body Parity Operators", but this page I already removed and replaced with a completely re-written section which comes directly after Kolmogorov-Zabih.

[ndattani]

Dear Nick,
You have two commits mentioning the addition of the Rocchetto-Benjamin-Li paper, but the only files changed in those commits are the PDFs, and the PDFs do not seem to have any mention on of their paper.

With best wishes,
Nike

[ndattani]

Dear Nick,
Can you put the year next to their names, in the title of the section?
See for example the section calleed: (Kempe, Kitaev, Regev, 2004)
or Kolmogorov & Zabih (2004).

Also, can you change trinary to ternary?

With best wishes,
Nike

[ndattani]

Dear Nick,
In addition to the comment below from 2 minutes ago, why does "Chained Three Body Parity Operators" keep re-appearing? I had commented it out, because it's already described in the page directly after Kolmogorov-Zabih.

With best wishes!
Nike

[ndattani]

Dear Nick,
Thank you for making the changes.
Regarding the RBL method you described, how is this a quadratization method?
You have said that a quadratic function is 0 if sum_i b_i is even, and > 0 if odd. Where is the k-local to 2-local?

[nchancel]

The quadratization comes from the fact that it reproduces the ground state manifold (but not the whole spectrum) of a 4 local operator out of a two local operator, for some applications, like LHZ this is sufficient, for others it is not.

[ndattani]

Dear Nick,
You have placed the RBL method under "negative term reduction", have you looked at some of the other examples in that section? Can you make your section look like Eq. 23, 28, 32, and 34, which are the opening equations for other methods? I'd like to keep the format consistent. That means k-local function on left side, and 2-local function on right side in the summary. Then the "example" is a full k-local function with some real numbers in there for the coefficients, where we apply this quadratization technique to quadratize it.

Now I understand that z1z2z3z4 = -1 if sum_i z_i = +/- 2, because it means either:

• we have one -1 and three +1, or:
• we have three -1 and one +1.

But you have placed this in "negative term reduction" which means we're quadratizing -z1z2z3z4, which = 1 only if sum_i z_i = 4 (all = 1), or -4 (all = -1) or 0 (two +1 and two -1). This does not seem to be what you've written. Shouldn't this be under "positive term reduction" ?

But for the case of b's, I don't see from what's currently in the section, what is being quadratized.
b1b2b3b4 only = 1 in the case where sum_i b_i = 4, and if sum_i b_i = anything else, we have 0.

With best wishes,
Nike

[nchancel]

Dear Nike,

You are right, the example I chose was a positive term reduction, although the paper contains both, negative and positive term reductions. Following what you have done in your sections I am actually going to split the RBL into two sections, one for positive and one for negative (even and odd sector selection respectively). This makes since since the methods in each case are different.

Note that the CZW symmetry based mapping can actually do both positive and negative terms, it is currently in the positive section, but should we include a note saying it can also do negative? I think dividing this into two sections would be unnecessary since the method for positive or negative is exactly the same.

Best,

Nick