diff --git a/src/gate_kernels.jl b/src/gate_kernels.jl
index 39ae323..4303533 100644
--- a/src/gate_kernels.jl
+++ b/src/gate_kernels.jl
@@ -110,8 +110,8 @@ matrix_rep(g::ZZ) = SMatrix{4,4}(
         exp(-im * g.angle[1] / 2.0),
     ]),
 )
-matrix_rep(g::ECR) =
-    SMatrix{4,4}(1/√2 * [0.0 0.0 1.0 im; 0.0 0.0 im 1.0; 1.0 -im 0.0 0.0; -im 1.0 0.0 0.0])
+# 1/√2 * (IX - XY)
+matrix_rep(g::ECR) = SMatrix{4,4}(1/√2 * [0 1 0 im; 1 0 -im 0; 0 im 0 1; -im 0 1 0])
 matrix_rep(g::Unitary) = g.matrix
 
 apply_gate!(::Val{false}, g::I, state_vec::StateVector{T}, qubits::Int...) where {T<:Complex} =
diff --git a/test/test_sv_simulator.jl b/test/test_sv_simulator.jl
index f68bc8c..111fd65 100644
--- a/test/test_sv_simulator.jl
+++ b/test/test_sv_simulator.jl
@@ -123,6 +123,47 @@ LARGE_TESTS = get(ENV, "BRAKET_SV_LARGE_TESTS", false)
             [0.70511898 - 0.0529833 * im, 0.70511898 + 0.0529833 * im],
             [0.5, 0.5],
         ),
+        (
+            [Instruction(H(), [0]), Instruction(GPi(0.15), [0])],
+            1,
+            [0.69916673 - 0.10566872im, 0.69916673 + 0.10566872im],
+            [0.5, 0.5],
+        ),
+        (
+            [Instruction(H(), [0]), Instruction(GPi2(0.15), [0])],
+            1,
+            [0.42528093 - 0.49438554im, 0.57471907 - 0.49438554im],
+            [0.42528093, 0.57471907],
+        ),
+        (
+            [Instruction(MS(π/2, -π/4, 0.3), [0, 1])],
+            2,
+            [0.98877108, 0, 0, 0.10566872 - 0.10566872im],
+            [0.97766824, 0, 0, 0.02233176],
+        ),
+        (
+            [Instruction(H(), [0]), Instruction(H(), [1]), Instruction(ECR(), [0, 1])],
+            2,
+            [
+                0.35355339 + 0.35355339im,
+                0.35355339 + 0.35355339im,
+                0.35355339 - 0.35355339im,
+                0.35355339 - 0.35355339im,
+            ],
+            [0.25, 0.25, 0.25, 0.25],
+        ),
+        (
+            [Instruction(H(), [0]), Instruction(U(0.15, 0.4, 0.7), [0])],
+            1,
+            [0.66459511 - 0.03413278im, 0.36864009 + 0.64903989im],
+            [0.44285171, 0.55714829],
+        ),
+        (
+            [Instruction(H(), [0]), Instruction(MultiQubitPhaseShift{1}(0.15), [0])],
+            1,
+            [0.69916673 + 0.10566872im, 0.69916673 + 0.10566872im],
+            [0.5, 0.5],
+        ),
         (
             [Instruction(X(), [0]), Instruction(PSwap(0.15), [0, 1])],
             2,