From 71b9e1aa3050dd492761973ad4be73c6d65e7eb1 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sat, 10 Apr 2021 19:58:09 +0200
Subject: Expand knowledge base
---
content/know/concept/quantum-gate/index.pdc | 16 +++++++++++++++-
1 file changed, 15 insertions(+), 1 deletion(-)
(limited to 'content/know/concept/quantum-gate/index.pdc')
diff --git a/content/know/concept/quantum-gate/index.pdc b/content/know/concept/quantum-gate/index.pdc
index cd09094..189145f 100644
--- a/content/know/concept/quantum-gate/index.pdc
+++ b/content/know/concept/quantum-gate/index.pdc
@@ -208,6 +208,10 @@ but not always in the basis of $\ket{0}_1$, $\ket{1}_1$, $\ket{0}_2$ and $\ket{1
With that said, the first two-qubit gate is $\mathrm{SWAP}$,
which simply swaps $\ket{\psi_1}$ and $\ket{\psi_2}$:
+
+
+
+
$$\begin{aligned}
\boxed{
\mathrm{SWAP} =
@@ -233,6 +237,10 @@ $$\begin{aligned}
Next, there is the **controlled NOT gate** $\mathrm{CNOT}$,
which "flips" (applies $X$ to) $\ket{\psi_2}$ if $\ket{\psi_1}$ is true:
+
+
+
+
$$\begin{aligned}
\boxed{
\mathrm{CNOT} =
@@ -252,7 +260,13 @@ $$\begin{aligned}
&= c_{00} \ket{00} + c_{01} \ket{01} + c_{11} \ket{10} + c_{10} \ket{11}
\end{aligned}$$
-More generally, each one-qubit gate $U$ can be turned into a **controlled** $U$ **gate**:
+More generally, from every one-qubit gate $U$,
+we can define a two-qubit **controlled U gate** $\mathrm{CU}$,
+which applies $U$ to $\ket{\psi_2}$ if $\ket{\psi_1}$ is true:
+
+
+
+
$$\begin{aligned}
\boxed{
--
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