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feat: Add expansion of Pauli matrices as basis vect

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This commit is contained in:
jstoobysmith 2024-10-23 06:50:55 +00:00
parent 1148234929
commit 74d4b2c2c0
4 changed files with 162 additions and 4 deletions
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8
HepLean/Tensors/Tree/Basic.lean
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@ -652,6 +652,14 @@ lemma constTwoNode_tensor {c1 c2 : S.C}
(OverColor.Discrete.pairIsoSep S.FDiscrete).hom.hom (v.hom (1 : S.k)) :=
rfl
@[simp]
lemma constThreeNode_tensor {c1 c2 c3 : S.C}
(v : 𝟙_ (Rep S.k S.G) ⟶ S.FDiscrete.obj (Discrete.mk c1) ⊗ S.FDiscrete.obj (Discrete.mk c2) ⊗
S.FDiscrete.obj (Discrete.mk c3)) :
(constThreeNode v).tensor =
(OverColor.Discrete.tripleIsoSep S.FDiscrete).hom.hom (v.hom (1 : S.k)) :=
rfl
lemma prod_tensor {c1 : Fin n → S.C} {c2 : Fin m → S.C} (t1 : TensorTree S c1)
(t2 : TensorTree S c2) :
(prod t1 t2).tensor = (S.F.map (OverColor.equivToIso finSumFinEquiv).hom).hom