construct variance ZXWDiagram test

src/ZXCalculus.jl

@@ -24,7 +24,7 @@ export push_gate!, pushfirst_gate!, tcount, insert_wtrig!
 export convert_to_chain, convert_to_zxd
 export rewrite!, simplify!, clifford_simplification, full_reduction, 
     circuit_extraction, phase_teleportation
-export substitute_variables!
+export substitute_variables!, expval_circ!, diff_diagram!
 
 include("parameter.jl")
 include("phase.jl")

src/diff.jl

@@ -5,7 +5,7 @@ Take derivative of ZXWDiagram with respect to a parameter
 
 Assuming Spiders have Parameter of type PiUnit which is parameterized purely by θ
 """
-function diff_diagram(zxwd::ZXWDiagram{T,P}, θ::Symbol) where {T,P}
+function diff_diagram!(zxwd::ZXWDiagram{T,P}, θ::Symbol) where {T,P}
     vs_pos = symbol_vertices(zxwd, θ)
     vs_neg = symbol_vertices(zxwd, θ; neg = true)
 
@@ -29,7 +29,7 @@ function diff_diagram(zxwd::ZXWDiagram{T,P}, θ::Symbol) where {T,P}
         x_v = add_spider!(zxwd, X(Parameter(Val(:PiUnit), 1.0)), [v])
         w_v = add_spider!(zxwd, D, [x_v])
         frac_v = @match spider_type(zxwd, v).p begin
-            PiUnit(pu, _) => add_spider!(zxwd, Z(Parameter(Val(:Factor), π)), [w_v])
+            PiUnit(pu, _) => add_spider!(zxwd, Z(Parameter(Val(:PiUnit), 1.0)), [w_v])
             Factor(f, _) => error("Only supports PiUnit differentiation")
             _ => error("not a valid parameter")
         end
@@ -44,9 +44,9 @@ function diff_diagram(zxwd::ZXWDiagram{T,P}, θ::Symbol) where {T,P}
 end
 
 """
-Take derivative with of Circuit with expectation of Hamiltonian H.
+Construct ZXW Diagram for representing the expectation value circuit
 """
-function diff_expval!(zxwd::ZXWDiagram{T,P}, H::String, θ::Symbol) where {T,P}
+function expval_circ!(zxwd::ZXWDiagram{T,P}, H::String) where {T,P}
     # convert U to U H U^\dagger
     zxwd_dag = dagger(zxwd)
     for (i, h) in enumerate(H)
@@ -63,7 +63,7 @@ function diff_expval!(zxwd::ZXWDiagram{T,P}, H::String, θ::Symbol) where {T,P}
         end
     end
     concat!(zxwd, zxwd_dag)
-    return diff_diagram(zxwd, θ)
+    return zxwd
 end
 
 """
@@ -151,7 +151,7 @@ function integrate4!(zxwd::ZXWDiagram{T,P}, loca::T, locb::T, locc::T, locd::T)
 
     locm = add_spider!(zxwd, X(Parameter(Val(:PiUnit), 0)), [loca, locb])
     locm = add_spider!(zxwd, D, [locm])
-    locm = add_spider!(zxwd, X(Parameter(Val(:PiUnit), π)), [locm])
+    locm = add_spider!(zxwd, X(Parameter(Val(:PiUnit), 1.0)), [locm])
     add_spider!(zxwd, X(Parameter(Val(:PiUnit), 0)), [locm, locc, locd])
     return zxwd
 end

test/diff.jl

@@ -1,53 +1,16 @@
 using ZXCalculus: insert_spider!
-using ZXCalculus: symbol_vertices, diff_diagram, dagger, concat!, diff_expval!, integrate!
+using ZXCalculus: symbol_vertices, diff_diagram!, dagger, concat!, expval_circ!, integrate!
 
-# @testset "diff" begin
-#     zxwd = ZXWDiagram(3)
-#     insert_spider!(zxwd, 1, 2, Z(Parameter(Val(:PiUnit), :a)))
-#     insert_spider!(zxwd, 7, 2, Z(Parameter(Val(:PiUnit), :a)))
-#     insert_spider!(zxwd, 3, 4, X(Parameter(Val(:PiUnit), :b)))
-#     insert_spider!(zxwd, 5, 6, Z(Parameter(Val(:PiUnit), 0.3)))
-#     insert_spider!(zxwd, 8, 2, Z(Parameter(Val(:PiUnit), Expr(:call, :-, :a))))
-
-#     @test sort!(symbol_vertices(zxwd, :a)) == [7, 8]
-#     @test symbol_vertices(zxwd, :a; neg = true) == [11]
-#     @test symbol_vertices(zxwd, :b) == [9]
-#     @test symbol_vertices(zxwd, :c) == []
-
-#     diff_expval!(copy(zxwd), "ZZZ", :a)
-
-#     diff_zxwd = diff_diagram(copy(zxwd), :a)
-#     # originally 11 spiders, plus 12 spiders from differentiation
-#     @test length(vertices(diff_zxwd.mg)) == 23
-
-#     zxwd_dg = dagger(zxwd)
-#     @test spider_type(zxwd_dg, 7).p.pu == Expr(:call, :-, :a)
-#     @test sort!(symbol_vertices(zxwd_dg, :a; neg = true)) == [7, 8]
-
-#     concat!(zxwd, zxwd_dg)
-
-#     @test length(vertices(zxwd.mg)) == 16
-
-#     integrate!(zxwd, [7, 11])
-#     @test length(vertices(zxwd.mg)) == 16
-
-#     # abuse, cann't actually integrate like this
-#     integrate!(zxwd, [7, 8, 11, 9])
-#     @test length(vertices(zxwd.mg)) == 25
-
-# end
-
-@testset "Example 27 - 30" begin
+@testset "Example 28" begin
     zxwd = ZXWDiagram(2)
     push_gate!(zxwd, Val(:H), 1)
     push_gate!(zxwd, Val(:H), 2)
 
     push_gate!(zxwd, Val(:CZ), 1, 2)
-    push_gate!(zxwd, Val(:X), 1, :a; autoconvert = false)
-    push_gate!(zxwd, Val(:X), 2, :b; autoconvert = false)
+    push_gate!(zxwd, Val(:X), 1, :a; autoconvert=false)
+    push_gate!(zxwd, Val(:X), 2, :b; autoconvert=false)
 
-    # since :c is not in the circuit, this will return UHU^\dagger
-    exp_zxwd = diff_expval!(copy(zxwd), "ZZ", :c)
+    exp_zxwd = expval_circ!(copy(zxwd), "ZZ")
 
     exp_zxwd_sub = substitute_variables!(copy(exp_zxwd), Dict(:a => 0.3, :b => 0.4))
     exp_val = Matrix(exp_zxwd_sub)[1, 1]
@@ -80,3 +43,38 @@ using ZXCalculus: symbol_vertices, diff_diagram, dagger, concat!, diff_expval!,
     @test exp_val ≈ exp_yao
 
 end
+
+@testset "Lemma 30" begin
+    # to calculate variance, we double the circuit
+    zxwd = ZXWDiagram(4)
+
+    push_gate!(zxwd, Val(:H), 1)
+    push_gate!(zxwd, Val(:H), 2)
+    push_gate!(zxwd, Val(:H), 3)
+    push_gate!(zxwd, Val(:H), 4)
+    push_gate!(zxwd, Val(:CZ), 1, 2)
+    push_gate!(zxwd, Val(:CZ), 3, 4)
+    push_gate!(zxwd, Val(:X), 1, :a; autoconvert=false)
+    push_gate!(zxwd, Val(:X), 2, :b; autoconvert=false)
+    push_gate!(zxwd, Val(:X), 3, :a; autoconvert=false)
+    push_gate!(zxwd, Val(:X), 4, :c; autoconvert=false)
+
+    exp_zxwd = expval_circ!(copy(zxwd), "ZZZZ")
+    exp_zxwd = diff_diagram!(exp_zxwd, :b)
+    exp_zxwd = diff_diagram!(exp_zxwd, :c)
+
+
+    posb = ZXCalculus.symbol_vertices(exp_zxwd, :b; neg=false)[1]
+    posbminus = ZXCalculus.symbol_vertices(exp_zxwd, :b; neg=true)[1]
+
+    posc = ZXCalculus.symbol_vertices(exp_zxwd, :c; neg=false)[1]
+    poscminus = ZXCalculus.symbol_vertices(exp_zxwd, :c; neg=true)[1]
+
+    integrated_zxwd = ZXCalculus.integrate!(exp_zxwd, [posb, posbminus, posc, poscminus])
+
+
+    integrated_zxwd = substitute_variables!(integrated_zxwd, Dict(:a => 0.0))
+
+    integrated_mtx = Matrix(integrated_zxwd)
+
+end