transpose fix

BBN-Q · Dec 9, 2020 · 4738dca · 4738dca · JuliaRegistrator · Dec 10, 2020
1 parent 5bf9896
commit 4738dca
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diff --git a/src/open-systems.jl b/src/open-systems.jl
@@ -134,7 +134,7 @@ function liou2pauliliou{T}( m::Matrix{T} )
   n = round(Int,log(2,dsq)/2)
   for (i,pi) in enumerate(allpaulis(n))
     for (j,pj) in enumerate(allpaulis(n))
-      res[i,j] += trace( m * vec(complex(pi)) * vec(complex(pj))' / sqrt(dsq) )
+      res[j,i] = vec(complex(pj))' * m * vec(complex(pi)) / sqrt(dsq)
     end
   end
   res

diff --git a/test/runtests.jl b/test/runtests.jl
@@ -81,4 +81,16 @@ let
   @test isapprox(liou2pauliliou(eye(4)), eye(4))
   @test isapprox(pauliliou2liou(eye(4)), eye(4))
 
+  @testset "Pauli-Liouville" begin
+    # we expect an X90 to transform +X => +X, +Z => -Y, +Y => +Z
+    X90 = exp(-1im*π/4*[0 1;1 0])
+    @test liou2pauliliou(liou(X90)) ≈ [1 0 0 0;
+                                       0 1 0 0;
+                                       0 0 0 -1;
+                                       0 0 1 0]
+
+    # liou2pauliliou and pauliliou2liou should be inverses
+    @test pauliliou2liou(liou2pauliliou(liou(X90))) ≈ liou(X90)
+  end
+
 end