diff --git a/python/taichi/lang/matrix.py b/python/taichi/lang/matrix.py
index 70288029dde42..f52bfff75a6f3 100644
--- a/python/taichi/lang/matrix.py
+++ b/python/taichi/lang/matrix.py
@@ -300,8 +300,7 @@ def subscript(self, *indices):
             # ptr.is_global_ptr() will check whether it's an element in the field (which is different from ptr.is_global_var()).
             if isinstance(
                     self.entries[0],
-                    ti.Expr) and self.entries[0].ptr.is_global_ptr() and (
-                        ti.cfg.arch == ti.cpu or ti.cfg.arch == ti.gpu):
+                    ti.Expr) and self.entries[0].ptr.is_global_ptr() and ti.is_extension_supported(ti.cfg.arch, ti.extension.dynamic_index):
                 return ti.subscript_with_offset(self.entries[0], (i, j),
                                                 self.m, True)
             else:
diff --git a/taichi/inc/extensions.inc.h b/taichi/inc/extensions.inc.h
index 5c0ba10343346..0dc106864c8a0 100644
--- a/taichi/inc/extensions.inc.h
+++ b/taichi/inc/extensions.inc.h
@@ -9,3 +9,4 @@ PER_EXTENSION(bls)        // Block-local storage
 PER_EXTENSION(assertion)  // Run-time asserts in Taichi kernels
 PER_EXTENSION(extfunc)    // Invoke external functions or backend source
 PER_EXTENSION(packed)     // Shape will not be padded to a power of two
+PER_EXTENSION(dynamic_index)     // Dynamic index support for both global and local tensors
diff --git a/taichi/ir/statements.h b/taichi/ir/statements.h
index fd0d1c48cb31a..dfa04f51b24d0 100644
--- a/taichi/ir/statements.h
+++ b/taichi/ir/statements.h
@@ -318,6 +318,9 @@ class GlobalTensorElementStmt : public Stmt {
   }
 
   bool has_global_side_effect() const override {
+    // After access lowered, activate info will be recorded in SNodeLookupStmt's
+    // activate for AOS sparse data structure. We don't support SOA sparse data
+    // structure for now.
     return false;
   }
 
diff --git a/taichi/program/extension.cpp b/taichi/program/extension.cpp
index 7dbae325f3067..a33b098d3a701 100644
--- a/taichi/program/extension.cpp
+++ b/taichi/program/extension.cpp
@@ -11,15 +11,17 @@ bool is_extension_supported(Arch arch, Extension ext) {
       {Arch::x64,
        {Extension::sparse, Extension::async_mode, Extension::quant,
         Extension::quant_basic, Extension::data64, Extension::adstack,
-        Extension::assertion, Extension::extfunc, Extension::packed}},
+        Extension::assertion, Extension::extfunc, Extension::packed,
+        Extension::dynamic_index}},
       {Arch::arm64,
        {Extension::sparse, Extension::async_mode, Extension::quant,
         Extension::quant_basic, Extension::data64, Extension::adstack,
-        Extension::assertion, Extension::packed}},
+        Extension::assertion, Extension::packed, Extension::dynamic_index}},
       {Arch::cuda,
        {Extension::sparse, Extension::async_mode, Extension::quant,
         Extension::quant_basic, Extension::data64, Extension::adstack,
-        Extension::bls, Extension::assertion, Extension::packed}},
+        Extension::bls, Extension::assertion, Extension::packed,
+        Extension::dynamic_index}},
       {Arch::metal,
        {Extension::adstack, Extension::assertion, Extension::quant_basic,
         Extension::async_mode, Extension::sparse}},
diff --git a/tests/python/test_matrix.py b/tests/python/test_matrix.py
index 74572077e78b0..c8257cd2a5076 100644
--- a/tests/python/test_matrix.py
+++ b/tests/python/test_matrix.py
@@ -161,18 +161,32 @@ def run():
     assert np.allclose(r2[None].value.to_numpy(), ops(a, c))
 
 
-@ti.test(arch=[ti.cpu, ti.gpu])
+@ti.test(require=ti.extension.dynamic_index)
 def test_matrix_non_constant_index():
     m = ti.Matrix.field(2, 2, ti.i32, 5)
+    v = ti.Vector.field(10, ti.i32, 5)
 
     @ti.kernel
-    def func():
+    def func1():
         for i in range(5):
             for j, k in ti.ndrange(2, 2):
-                m[i][j, k] = 12
-
-    func()
+                m[i][j, k] = j * j + k * k
+        assert m[1][0, 1] == 1
+        assert m[2][1, 0] == 1
+        assert m[3][1, 1] == 2
+    func1()
+    assert m[4][0, 1] == 1
 
+    @ti.kernel
+    def func2():
+        for i in range(5):
+            for j in range(4):
+                v[i][j * j] = j * j
+        assert v[1][0] == 0
+        assert v[1][1] == 1
+        assert v[1][4] == 4
+    func2()
+    assert v[1][9] == 9
 
 @ti.test(arch=ti.cpu)
 def test_matrix_constant_index():