improvements to `GeneralizedStabilizer` API

[Krastanov]

There are a few interfaces not yet supported for GeneralizedStabilizer but which are easy to add. Here are operations which we can and can not do -- the goal is to have all of them implemented.

• [X] sm = GeneralizedStabilizer(S"-X")
• [ ] sm⊗sm
• [ ] sm⊗S"X"
• [ ] pcT*sm
• [ ] tHadamard*sm
• [ ] pcT⊗tId1
• [ ] pcT⊗P"X"
• [ ] embed(..., sm)
• [ ] copy(sm)

[Krastanov]

@hongyehu pinging just for reference as this is related to #259

[Fe-r-oz]

For documentation of Generalized Stabilizer, the paper by ted yoder can be helpful. I will be to work on this documentation as well.

''" The generalized stabilizer representation of an arbitrary state τ is a two-tuple (χ, B(S, D)). Here χ is a density matrix and B(S, D) = B(T ) is the basis in which χ is expressed. A generalized stabilizer (χ, B(T )), in some sense, separates the “classical” part of the quantum state from the quantum. The quasi-classical tableau T updates through Clifford gates and measurements, while the the χ-matrix is updated by non-Clifford operations.""

Is implementation inspired from this paper (A generalization of the stabilizer formalism for simulating arbitrary quantum circuits) while building generalized stabilizer ?

Non-clifford and non-stabilizer/non-stabilizerness mean the same thing right?

[hongyehu]

Hi Feroz,  Yes, it is largely inspired by Ted’s paper.Hong-Ye Hu, Ph.D.Department of Physics,Harvard University, Cambridge, MAOn Jun 21, 2024, at 9:55 AM, Feroz @.***> wrote: For documentation of Generalized Stabilizer, the paper by ted yoder can be helpful. I will be to work on this documentation as well. ''" The generalized stabilizer representation of an arbitrary state τ is a two-tuple (χ, B(S, D)). Here χ is a density matrix and B(S, D) = B(T ) is the basis in which χ is expressed. A generalized stabilizer (χ, B(T )), in some sense, separates the “classical” part of the quantum state from the quantum. The quasi-classical tableau T updates through Clifford gates and measurements, while the the χ-matrix is updated by non-Clifford operations."" Is implementation inspired from this paper (A generalization of the stabilizer formalism for simulating arbitrary quantum circuits) while building generalized stabilizer ? Non-clifford and non-stabilizer/non-stabilizerness mean the same thing right?

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