add distance to vidal gauge

Author: ArrogantGao

src/BPGauge.jl

@@ -12,6 +12,7 @@ export absorb!
 export apply_gauge!, gauge!
 
 export square_lattice
+export dist_to_vidal
 
 include("utils.jl")
 

src/gauge.jl

@@ -84,4 +84,26 @@ function apply_gauge!(ansatz::TensorNetworkAnsatz{TA, TB}, s::Int, d::Int, M_sd:
     einsum!(eincode_d.ixs, eincode_d.iy, d_xs, ansatz.site_tensors[d], 1, 0, sdd)
 
     nothing
+end
+
+# check the distance from a gauged state to the vidal gauge
+function dist_to_vidal(tn::TensorNetworkAnsatz, bp_path::BPPath)
+    Ts = tn.site_tensors
+    Tcs = conj.(Ts)
+
+    err = 0.0
+    for step in bp_path.bp_steps
+        eincode = step.eincode
+        Tid = step.Tid
+        inputs = step.inputs
+        output = step.output
+
+        T = Ts[Tid]
+        Tc = Tcs[Tid]
+        Λs2 = [tn.gauge_tensors[tn.gauge_tensors_map[(min(i, j), max(i, j))]] for (i, j) in inputs].^2
+
+        output_tensor = eincode(T, Tc, Λs2...)
+        err = max(err, maximum(abs.(output_tensor - output_tensor[1, 1] * I(size(output_tensor, 1)))))
+    end
+    return err
 end

test/gauge.jl

@@ -104,11 +104,21 @@ end
     gauge!(tn, bp_state)
     @test inner_product(tn, adjoint(tn)) ≈ 1.0
 
-    for i in 1:nv(g) - 2
-        j = i == nv(g) ? 1 : i + 1
-        G = tn.gauge_tensors[tn.gauge_tensors_map[(min(i, j), max(i, j))]]
-        T = tn.site_tensors[j]
-        L = ein"ij, jk, jln, kmn -> lm"(G, G, T, conj(T))
-        @test maximum(abs.(L ./ L[1, 1] - I(size(L, 1)))) < 2 * 1e-6
-    end
+    @test dist_to_vidal(tn, bp_path) < 1e-5
+end
+
+@testset "rr3 graph gauge" begin
+    g = random_regular_graph(20, 3)
+    tn = random_state(g, d_virtual = 4)
+    normalize_state!(tn)
+    @test inner_product(tn, adjoint(tn)) ≈ 1.0
+
+    bp_state = BPState(tn)
+    bp_path = BPPath(tn)
+    bp!(bp_state, bp_path, tn, atol = 1e-8)
+
+    gauge!(tn, bp_state)
+    @test inner_product(tn, adjoint(tn)) ≈ 1.0
+
+    @test dist_to_vidal(tn, bp_path) < 1e-5
 end