From aeacfca5aea5df7c107cf0c12e72ab5d496c96e1 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Tue, 3 Jan 2023 19:48:17 +0100
Subject: More improvements to knowledge base

---
 source/know/concept/toffoli-gate/index.md | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

(limited to 'source/know/concept/toffoli-gate/index.md')

diff --git a/source/know/concept/toffoli-gate/index.md b/source/know/concept/toffoli-gate/index.md
index 23dc81e..b8caba1 100644
--- a/source/know/concept/toffoli-gate/index.md
+++ b/source/know/concept/toffoli-gate/index.md
@@ -49,7 +49,7 @@ i.e. OR is NAND of NOT $$A$$ and NOT $$B$$:
 Thanks to its reversibility and universality,
 the Toffoli gate is interesting for quantum computing.
 Its [quantum gate](/know/concept/quantum-gate/) form is often called **CCNOT**.
-In the basis $$\Ket{A} \Ket{B} \Ket{C}$$, its matrix is:
+In the basis $$\ket{A} \ket{B} \ket{C}$$, its matrix is:
 
 $$\begin{aligned}
     \boxed{
@@ -67,16 +67,16 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-If we apply this gate to an arbitrary three-qubit state $$\Ket{\psi}$$,
+If we apply this gate to an arbitrary three-qubit state $$\ket{\psi}$$,
 it swaps the last two coefficients:
 
 $$\begin{aligned}
-    \mathrm{CCNOT} \Ket{\psi}
-    &= \mathrm{CCNOT} \big( c_{000} \Ket{000} + c_{001} \Ket{001} + c_{010} \Ket{010} + c_{011} \Ket{011} + \\
-    &\qquad\qquad\quad\:\; c_{100} \Ket{100} + c_{101} \Ket{101} + c_{110} \Ket{110} + c_{111} \Ket{111} \big)
+    \mathrm{CCNOT} \ket{\psi}
+    &= \mathrm{CCNOT} \big( c_{000} \ket{000} + c_{001} \ket{001} + c_{010} \ket{010} + c_{011} \ket{011} + \\
+    &\qquad\qquad\quad\:\; c_{100} \ket{100} + c_{101} \ket{101} + c_{110} \ket{110} + c_{111} \ket{111} \big)
     \\
-    &= c_{000} \Ket{000} + c_{001} \Ket{001} + c_{010} \Ket{010} + c_{011} \Ket{011} + \\
-    &\quad\,\, c_{100} \Ket{100} + c_{101} \Ket{101} + c_{111} \Ket{110} + c_{110} \Ket{111}
+    &= c_{000} \ket{000} + c_{001} \ket{001} + c_{010} \ket{010} + c_{011} \ket{011} + \\
+    &\quad\,\, c_{100} \ket{100} + c_{101} \ket{101} + c_{111} \ket{110} + c_{110} \ket{111}
 \end{aligned}$$
 
 
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