english tutorials of state

doc/en/source/guide/2.0_python_advanced.ipynb

@@ -783,6 +783,7 @@
    ]
   },
   {
+   "attachments": {},
    "cell_type": "markdown",
    "metadata": {},
    "source": [
@@ -792,8 +793,10 @@
     "\n",
     "**It is fundamentally different in behavior from the operation of the same name in `QuantumState`, which corresponds to the quantum state**\n",
     "\n",
-    "-- `add_state` of `QuantumState` creates superpositon, but `add_state` of `DensityMatrix` create mixed state\n",
-    "-- The operation corresponding to `multiply_coef(z)` of `QuantumState` is `multiply_coef(abs(z)**2)` for `DensityMatrix`"
+    "- `add_state` of `QuantumState` creates superpositon, but `add_state` of `DensityMatrix` create mixed state\n",
+    "- The operation corresponding to `multiply_coef(z)` of `QuantumState` is `multiply_coef(abs(z)**2)` for `DensityMatrix`\n",
+    "\n",
+    "Using `state.make_superposition()` `state.make_mixture()` is recommended since `add_state()` `multiply_coef()` make users confused with those generated by `QuantumState`."
    ]
   },
   {
@@ -885,6 +888,46 @@
     "print(obtained)"
    ]
   },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Creating superposition states and mixture states\n",
+    "\n",
+    "You can create superposition states and mixture states by using `make_superposition()` `make_mixture()` in `state` module.\n",
+    "These states can also be creaated by applying `add_state()` `multiply_coef()` to `QuantumState` `DensityMatrix`, but is deprecated due to low readability."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from qulacs import QuantumState, DensityMatrix\n",
+    "from qulacs.state import make_superposition, make_mixture\n",
+    "# from QuantumState |a> and |b>, create a superposition state p|a> + q|b>\n",
+    "a = QuantumState(2)\n",
+    "a.set_computational_basis(0b00)\n",
+    "b = QuantumState(2)\n",
+    "b.set_computational_basis(0b11)\n",
+    "p = 1 / 2\n",
+    "q = 1 / 2\n",
+    "c = make_superposition(p, a, q, b)\n",
+    "print(c.get_vector())\n",
+    "# from QuantumState |a> and DensityMatrix |b><b|, create a mixture state p|a><a| + q|b><b|\n",
+    "# You can also create a mixture states from two QuantumState or two DensitMatrix\n",
+    "a = QuantumState(2)\n",
+    "a.set_computational_basis(0b00)\n",
+    "b = DensityMatrix(2)\n",
+    "b.set_computational_basis(0b11)\n",
+    "p = 1 / 2\n",
+    "q = 1 / 2\n",
+    "c = make_mixture(p, a, q, b)\n",
+    "print(c.get_matrix())"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},