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/cnot.png | Bin 0 -> 4584 bytes content/know/concept/quantum-gate/cu.png | Bin 0 -> 4625 bytes content/know/concept/quantum-gate/index.pdc | 16 +++++++++++++++- content/know/concept/quantum-gate/swap.png | Bin 0 -> 4061 bytes 4 files changed, 15 insertions(+), 1 deletion(-) create mode 100644 content/know/concept/quantum-gate/cnot.png create mode 100644 content/know/concept/quantum-gate/cu.png create mode 100644 content/know/concept/quantum-gate/swap.png (limited to 'content/know/concept/quantum-gate') diff --git a/content/know/concept/quantum-gate/cnot.png b/content/know/concept/quantum-gate/cnot.png new file mode 100644 index 0000000..9fae3ce Binary files /dev/null and b/content/know/concept/quantum-gate/cnot.png differ diff --git a/content/know/concept/quantum-gate/cu.png b/content/know/concept/quantum-gate/cu.png new file mode 100644 index 0000000..465f09c Binary files /dev/null and b/content/know/concept/quantum-gate/cu.png differ 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{ diff --git a/content/know/concept/quantum-gate/swap.png b/content/know/concept/quantum-gate/swap.png new file mode 100644 index 0000000..fa20442 Binary files /dev/null and b/content/know/concept/quantum-gate/swap.png differ -- cgit v1.2.3