noncliff: Documentation for overview of Generalized Stabilizer Representation

[Fe-r-oz]

Basic documentation for Genstab is added.

This is the Browser display of what the timeline will look like.

In markdown,

timeline
    title Related Work in Generalization of the Gottesman-Knill Theorem
    1997 : Gottesman [3] introduces stabilizer formalism and the Gottesman-Knill theorem.
    2002 : Bartlett et al. [4] expand to continuous variable quantum computation.
    2004 : Aaronson and Gottesman [5] improve measurement time complexity to 𝒪(n²).
    2006 : Anders and Briegel [6] achieve 𝒪(n log n) speedup in time complexity with graph states.
    2012 : Bermejo-Vega and Van den Nest [7] generalize to any finite Abelian group from n-qubits ℤ₂ⁿ.
    2012 : Yoder [2] presents the Generalized Stabilizer with a novel state representation.

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[Fe-r-oz]

The second schematic detail:

Yoder investigated the classical simulation of quantum circuits in the context of strong simulation, which focuses on calculating exact probabilities for specific measurement outcomes.

mindmap
  root((Classical Simulation of Quantum Circuits))
    Strong Simulation
      Goal: Exact probability of specific outcome
      Example: Calculate probability of outcome 01
      Precision: High, requires precise probabilities
      Complexity:: Can be #P-complete
    Weak Simulation
      Goal: Sample outcome close to quantum distribution
      Example: Sample outcomes like 00, 01, 10, 11
      Precision: Lower, approximate sampling
      Complexity: Generally in BPP

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[Fe-r-oz]

The PR is ready for review, Thank you!

[Fe-r-oz]

@Krastanov, please find the schematic that provides the summary of Ted's work. Thanks to your feedback, I have implemented Algorithm 2 in #427. I think we should have brief documentation about each of these algorithms along with their doctests in the documentation as well.

graph TD
    A[GeneralizedStabilizer <br> by Ted Yoder] --> B[Clifford Gates]
    B --> C1[Algorithm 𝟏]
    C1 --> D1[apply!❨sm, 𝐂❩]
    
    A --> E[Pauli Measurements]
    E --> C2[Algorithm 𝟐]
    C2 --> D2[projectrand!❨sm, 𝐏❩]
    
    A --> F[Pauli Channels]
    F --> C3[Algorithm 𝟑]
    C3 --> D3[apply!❨sm, 𝛏❩]

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