Experimental Work: Conjugate destabs

[Fe-r-oz]

Hi, Stefan!

I would like to ask you a question about conjugate destabs. Please let me know if this is plausible: so we have apply! for CliffordOperator, but it's only conjugating the .stab parts and nothing is happening to the destabs. You have commented # TODO conjugate also the destabs . In light of this, I think a function should be callled inside apply! after this line(apply!(state.stab, gate)), so that we can conjugate destabs.

Currently, without conjugate destabs, we have the following output:

julia> sm = GeneralizedStabilizer(S"-Y")
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
+ Z
𝒮𝓉𝒶𝒷
- Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | + _ | + _

julia> apply!(sm, CliffordOperator(sZ))
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
+ Z
𝒮𝓉𝒶𝒷
+ Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | + _ | + _

julia> sm = GeneralizedStabilizer(S"-Y")
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
+ Z
𝒮𝓉𝒶𝒷
- Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | + _ | + _

julia> apply!(sm, CliffordOperator(sY))
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
- Z
𝒮𝓉𝒶𝒷
- Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | + _ | + _

julia> sm = GeneralizedStabilizer(S"-Y")
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
+ Z
𝒮𝓉𝒶𝒷
- Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | + _ | + _

julia> apply!(sm, CliffordOperator(sHadamard))
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
+ X
𝒮𝓉𝒶𝒷
+ Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | + _ | + _

Please let me know that after implementing conjugate destabs, are these plausible? I hope this is not so bad.

julia> sm = GeneralizedStabilizer(S"-Y")
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
+ Z
𝒮𝓉𝒶𝒷
- Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | + _ | + _

julia> apply!(sm, CliffordOperator(sZ))
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
+ Z
𝒮𝓉𝒶𝒷
+ Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | + Z | + Z

julia> sm = GeneralizedStabilizer(S"-Y")
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
+ Z
𝒮𝓉𝒶𝒷
- Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | + _ | + _

julia> apply!(sm, CliffordOperator(sY))
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
- Z
𝒮𝓉𝒶𝒷
- Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | - Z | - Z

julia> sm = GeneralizedStabilizer(S"-Y")
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
+ Z
𝒮𝓉𝒶𝒷
- Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | + _ | + _

julia> apply!(sm, CliffordOperator(sHadamard))
A mixture ∑ ϕᵢⱼ Pᵢ ρ Pⱼ† where ρ is
𝒟ℯ𝓈𝓉𝒶𝒷
+ X
𝒮𝓉𝒶𝒷
+ Y
with ϕᵢⱼ | Pᵢ | Pⱼ:
 1.0+0.0im | + X | + X

Thank you for your time.

[Fe-r-oz]

@Krastanov, please let me know that whether these outputs showing expected behaviour (2nd shaded block) of conj_destabs! ? Thank you.

[Fe-r-oz]

Hm, I think it's possible this might not make sense. It's an experimental work from a while back when I was trying some stuff.