Convert argument of log to complex for proper loginner via BP.

src/abstractitensornetwork.jl

@@ -723,6 +723,17 @@ end
 
 function contract_with_BP(
   itn::AbstractITensorNetwork; outputlevel=1, partitioning=group(v -> v, vertices(itn))
+)
+  return contract_with_BP(
+    ComplexF64, itn::AbstractITensorNetwork; outputlevel, partitioning
+  )
+end
+
+function contract_with_BP(
+  T::Type,
+  itn::AbstractITensorNetwork;
+  outputlevel=1,
+  partitioning=group(v -> v, vertices(itn)),
 )
   @assert isempty(externalinds(itn))
   bp_cache = BeliefPropagationCache(copy(itn), partitioning)
@@ -739,15 +750,17 @@ function contract_with_BP(
   for pv in partitionvertices(pg)
     incoming_mts = incoming_messages(bp_cache, [pv])
     local_state = ITensor[itn[v] for v in vertices(pg, pv)]
-    log_numerator += log(ITensors.contract(vcat(incoming_mts, local_state))[])
+    log_numerator += log(complex(ITensors.contract(vcat(incoming_mts, local_state))[]))
   end
   for pe in partitionedges(pg)
     log_denominator += log(
-      ITensors.contract(vcat(message(bp_cache, pe), message(bp_cache, reverse(pe))))[]
+      complex(
+        ITensors.contract(vcat(message(bp_cache, pe), message(bp_cache, reverse(pe))))[]
+      ),
     )
   end
-
-  return exp(log_numerator - log_denominator)
+  res = exp(log_numerator - log_denominator)
+  return T(res)
 end
 
 # TODO: rename `sqnorm` to match https://github.com/JuliaStats/Distances.jl,