More documentation on the various ways to construct Stab/Destab/MixedDestab objects

[Krastanov]

A friend asked me over email something that should probably be added to the documentation (after being polished)

A quick question, in quantumclifford.jl, how should I manually construct the (Mixed)Destabilizer tableau? Suppose I have a list of stabilizers and destabilizers as strings, for example s = ["XX","ZZ"] and d=["ZI","IX"].

My answer was

[Fe-r-oz]

I will be delighted to work in this issue!

[Krastanov]

That would be great! It is a pretty difficult balance to strike between too much information on a given page and too many separate pages -- this will need some pedagogical effort, maybe a separate page, maybe a lot of reference to that new page, maybe something else

[Fe-r-oz]

Indeed, I understand your point. Striking balance is important so that the reader is not overwhelmed by too much information in one page. I will give proper attention to it.

[Fe-r-oz]

On the page about choosing Data Structure, https://quantumsavory.github.io/QuantumClifford.jl/stable/datastructures/#Choosing-Appropriate-Data-Structure

Would you like to add a flowchart like this? I can modify it as per your requirements if needed.

[Fe-r-oz]

Another Representation:

[Krastanov]

These look promising! Are you using mermaid for them? I would prefer to keep the source for diagrams as part of the documentation, so that it is easy to modify. We already do something like that for QuantumSavory: https://quantumsavory.github.io/QuantumSavory.jl/stable/register_interface/

Using mermaid can also help with making the visualization a bit tighter -- there is a lot of empty space in this one.

I would suggest doing first the separation between (Mixed)Stabilizer and (Mixed)Destabilizer and only then dealing with the mixed-vs-nonmixed distinction.

MixedDestabilizer is probably the main and most useful datastructure, but it is not included here.

I think all of these datastructures support projective measurements, definitely including Stabilizer.

Some of the descriptions inside of the bottom rectangles does not make much sense to me right now -- "handles commuting operators" and "requires user to check for consistency" and "no canonicalization needed".

Explicit descriptions of what these datastructures are would be useful.

[Fe-r-oz]

Latest Improvements:

flowchart TD
    A["<code>Tableau Data Structure Selection</code>"]
    class A startEnd
    A --> B{"Is the state a stabilizer?"}
    class A,B startEnd
    B -->|Yes| C{"Pure state?"}
    B -->|No| D{"Pure state?"}
    class B,C,D decision
    C -->|Yes| E["<code>Stabilizer</code>"]
    E --> E_desc["<code>Pure stabilizer states<br/>Efficient 'project!' operations</code>"]
    class E_desc description
    C -->|No| F["<code>MixedStabilizer</code>"]
    F --> F_desc["<code>Tracks rank of mixed states<br/>'Project!' on non-Stabilizer commuting operators</code>"]
    class F_desc description
    D -->|Yes| G["<code>Destabilizer</code>"]
    G --> G_desc["<code>Pure stabilizer states<br/>Tracks destabilizers<br/>Efficient 'project!' operations</code>"]
    class G_desc description
    D -->|No| H["<code>MixedDestabilizer<code>"]
    H --> H_desc["<code>Tracks destabilizers<br/>Tracks 'logical' operators<br/>Efficient 'project!' operations</code>"]
    class H_desc description

Loading

[Fe-r-oz]

To be consistent with other member packages, I think it's better to use the default scheme instead of the ones presented.