diff --git a/src/register.jl b/src/register.jl
index ef539dc73..6beba94e6 100644
--- a/src/register.jl
+++ b/src/register.jl
@@ -68,7 +68,7 @@ explicitly. The batch size will be `size(raw, 2)` by default.
 """
 function ArrayReg{B}(raw::MT) where {B,T,MT<:AbstractMatrix{T}}
     ispow2(size(raw, 1)) ||
-    throw(DimensionMismatch("Expect first dimension size to be power of 2"))
+        throw(DimensionMismatch("Expect first dimension size to be power of 2"))
     if !(ispow2(size(raw, 2) ÷ B) && size(raw, 2) % B == 0)
         throw(DimensionMismatch("Expect second dimension size to be an integral multiple of batch size $B"))
     end
@@ -235,7 +235,7 @@ function YaoBase.fidelity(r1::ArrayReg{B1}, r2::ArrayReg{B2}) where {B1,B2}
     return B == 1 ? res[] : res
 end
 
-function YaoBase.fidelity(r1::ArrayReg{B}, r2::ArrayReg{1}) where B
+function YaoBase.fidelity(r1::ArrayReg{B}, r2::ArrayReg{1}) where {B}
     state1 = rank3(r1)
     state2 = rank3(r2)
     nqubits(r1) == nqubits(r2) || throw(DimensionMismatch("Register size not match!"))
@@ -247,7 +247,7 @@ function YaoBase.fidelity(r1::ArrayReg{B}, r2::ArrayReg{1}) where B
     return B == 1 ? res[] : res
 end
 
-YaoBase.fidelity(r1::ArrayReg{1}, r2::ArrayReg{B}) where B = YaoBase.fidelity(r2, r1)
+YaoBase.fidelity(r1::ArrayReg{1}, r2::ArrayReg{B}) where {B} = YaoBase.fidelity(r2, r1)
 
 function YaoBase.fidelity(r1::ArrayReg{1}, r2::ArrayReg{1})
     state1 = state(r1)
diff --git a/test/density_matrix.jl b/test/density_matrix.jl
index c521525ac..3fef1356f 100644
--- a/test/density_matrix.jl
+++ b/test/density_matrix.jl
@@ -15,15 +15,19 @@ using Test, YaoArrayRegister
     focus!(reg5, 1:3)
     @test isapprox(fidelity(reg, reg_), fidelity(reg4, reg5), atol = 1e-5)
 
-    @test isapprox.(fidelity(reg, reg_), fidelity(repeat(reg4, 3), repeat(reg5, 3)), atol = 1e-5) |>
-          all
+    @test isapprox.(
+        fidelity(reg, reg_),
+        fidelity(repeat(reg4, 3), repeat(reg5, 3)),
+        atol = 1e-5,
+    ) |> all
 
     # batch
     st = rand(ComplexF64, 8, 2)
     reg1 = ArrayReg(st)
     reg2 = rand_state(3)
 
-    @test fidelity(reg1, reg2) ≈ [fidelity(ArrayReg(st[:, 1]), reg2), fidelity(ArrayReg(st[:, 2]), reg2)]
+    @test fidelity(reg1, reg2) ≈
+          [fidelity(ArrayReg(st[:, 1]), reg2), fidelity(ArrayReg(st[:, 2]), reg2)]
 
     @test isapprox.(
         fidelity(reg, reg_),