diff --git a/tutorials/phase_kickback/phase_kickback.ipynb b/tutorials/phase_kickback/phase_kickback.ipynb
index a37d4842..19eb5c6d 100644
--- a/tutorials/phase_kickback/phase_kickback.ipynb
+++ b/tutorials/phase_kickback/phase_kickback.ipynb
@@ -374,12 +374,12 @@
     "Therefore:\n",
     "\n",
     "$\\begin{equation}\n",
-    "O_f (| x \\rangle| - \\rangle) = | x \\rangle\\frac{1}{\\sqrt{2}}(|f(x)\\rangle - | x \\rangle |\\overline{f(x)}\\rangle)\n",
+    "O_f (| x \\rangle| - \\rangle) = | x \\rangle\\frac{1}{\\sqrt{2}}(|f(x)\\rangle - |\\overline{f(x)}\\rangle)\n",
     "\\end{equation}$\n",
     "\n",
-    "If $f(x)=0$ the target state is $\\frac{1}{\\sqrt{2}}(|0\\rangle - | x \\rangle|1\\rangle) = | - \\rangle = (-1)^{f(x)}| - \\rangle$.\n",
+    "If $f(x)=0$ the target state is $\\frac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle) = | - \\rangle = (-1)^{f(x)}| - \\rangle$.\n",
     "\n",
-    "If $f(x)=1$ the target state is $\\frac{1}{\\sqrt{2}}(|1\\rangle - | x \\rangle|0\\rangle) = -| - \\rangle = = (-1)^{f(x)}| - \\rangle$.\n",
+    "If $f(x)=1$ the target state is $\\frac{1}{\\sqrt{2}}(|1\\rangle - |0\\rangle) = -| - \\rangle = = (-1)^{f(x)}| - \\rangle$.\n",
     "\n",
     "Therefore:\n",
     "\n",
@@ -552,7 +552,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.9"
+   "version": "3.11.4"
   },
   "vscode": {
    "interpreter": {