add pi rule for ZXW Calculus

src/ZXW/zxw_rules.jl

@@ -76,6 +76,21 @@ function Base.match(::Rule{:b1}, zxwd::ZXWDiagram{T,P}) where {T,P}
     return matches
 end
 
+function Base.match(::Rule{:pi}, zxwd::ZXWDiagram{T, P}) where {T, P}
+    matches = Match{T}[]
+    for v1 in spiders(zxwd)
+        degree(zxwd, v1) != 2 && continue
+        for v2 in neighbors(zxwd, v1)
+            res = @match (spider_type(zxwd,v1), spider_type(zxwd,v2)) begin
+                (X(p1), Z(p2)) && if p1 == one(P) end => Match{T}([v1, v2])
+                _ => nothing
+            end
+            isnothing(res) || push!(matches, res)
+        end
+    end
+    return matches
+end
+
 struct CalcRule{L} <: AbstractRule
     var::Symbol
 end
@@ -152,6 +167,22 @@ function rewrite!(::Rule{:b1}, zxwd::ZXWDiagram{T,P}, vs::Vector{T}) where {T,P}
     return zxwd
 end
 
+function rewrite!(r::Rule{:pi}, zxwd::ZXWDiagram{T, P}, vs::Vector{T}) where {T, P}
+    v1, v2 = vs
+    add_global_phase!(zxwd, parameter(zxwd, v2))
+    set_phase!(zxwd, v2, -parameter(zxwd, v2))
+    nb = neighbors(zxwd, v2, count_mul = true)
+    for v3 in nb
+        # TODO
+        v3 != v1 && insert_spider!(zxwd, v2, v3, X(parameter(zxwd, v1)))
+    end
+    if neighbors(zxwd, v1) != [v2]
+        add_edge!(zxwd, neighbors(zxwd, v1))
+        rem_spider!(zxwd, v1)
+    end
+    return zxwd
+end
+
 function rewrite!(::CalcRule{:diff}, zxwd::ZXWDiagram{T,P}, vs::Vector{T}) where {T,P}
     zero_loc = findfirst(x -> x == zero(T), vs)
 
@@ -392,3 +423,14 @@ function check_rule(r::CalcRule{:int}, zxwd::ZXWDiagram{T,P}, vs::Vector{T}) whe
     end
     return true
 end
+
+function check_rule(r::Rule{:pi}, zxwd::ZXWDiagram{T, P}, vs::Vector{T}) where {T, P}
+    v1, v2 = vs
+    (has_vertex(zxwd.mg, v1) && has_vertex(zxwd.mg, v2)) || return false
+    (degree(zxwd, v1)) == 2 || return false
+
+    return @match (spider_type(zxwd, v1), spider_type(zxwd, v2)) begin
+        (X(p1), Z(p2)) && if p1 == one(P) end => true
+        _ => false
+    end
+end