added toffoli as an example

Author: sotashimozono

docs/make.jl

@@ -34,7 +34,10 @@ makedocs(;
     modules=[GroverAlgorithm],
     pages=[
         "Home" => "index.md",
-        "Getting Started" => "getting_started.md",
+        "Getting Started" => "example/getting_started.md",
+        "example" => [
+            "toffoli" => "example/toffoli.md"
+        ],
         #"Core Concepts" => [
         #    "Quantum Gates and Circuits" => "structures.md",
         #    "Initial States" => "initialstates.md",

docs/src/example/toffoli.md

@@ -0,0 +1,91 @@
+```@meta
+EditURL = "../../../example/toffoli.jl"
+```
+
+# Toffoli Gate Example
+Here we define the Toffoli gate (CCNOT) using the GroverAlgorithm package
+This is an example of how to use the package.
+Toffoli gate is available in ITensorMPS.jl as a built-in gate.
+Let's create a Toffoli gate and check its action on the basis states.
+
+## Using the built-in Toffoli gate
+In ITensorMPS.jl, the Toffoli gate is available as a built-in three-qubit gate. We can simply add it to our quantum circuit and execute it.
+
+````@example toffoli
+using Printf
+using GroverAlgorithm
+using ITensors, ITensorMPS
+
+circuit = QuantumCircuit(3)
+add_gate!(circuit, ThreeQubitGate(1, 2, 3, :Toffoli))
+
+sites = siteinds("Qubit", 3)
+psi = execute_circuit(circuit, sites)
+counts = measure(psi, Sampling(100))
+println("結果: ", counts)
+````
+
+Toffoli gate acts as follows for the basis states:
+
+````@example toffoli
+function test_actions(circuit)
+    println("Test of Toffoli Gate")
+    println("=" ^ 50)
+    println("Input  |  Output")
+    println("-" ^ 50)
+    for a in 0:1, b in 0:1, c in 0:1
+        initial = AbstractInitialState[ProductState([string(a), string(b), string(c)])]
+        set_state!(circuit, initial)
+
+        sites = siteinds("Qubit", 3)
+        psi = execute_circuit(circuit, sites)
+
+        counts = measure(psi, Sampling(1))
+        output = collect(keys(counts))[1]
+        @printf("|%d%d%d⟩ → |%s⟩\n", a, b, c, output)
+    end
+end
+
+test_actions(circuit)
+````
+
+## Toffoli gate decomposition
+Then, Lets's construct the Toffoli gate using the standard decomposition into CNOT and single-qubit gates,
+and verify that it produces the same results as the built-in Toffoli gate.
+
+````@example toffoli
+function toffoli_decomposed(circuit)
+    add_gate!(circuit, SingleQubitGate(3, :H))
+    add_gate!(circuit, ControlledGate(2, 3, :CX))
+    add_gate!(circuit, SingleQubitGate(3, :Tdag))
+    add_gate!(circuit, ControlledGate(1, 3, :CX))
+    add_gate!(circuit, SingleQubitGate(3, :T))
+    add_gate!(circuit, ControlledGate(2, 3, :CX))
+    add_gate!(circuit, SingleQubitGate(2, :Tdag))
+    add_gate!(circuit, SingleQubitGate(3, :Tdag))
+    add_gate!(circuit, ControlledGate(1, 3, :CX))
+    add_gate!(circuit, ControlledGate(1, 2, :CX))
+    add_gate!(circuit, SingleQubitGate(1, :T))
+    add_gate!(circuit, SingleQubitGate(2, :Tdag))
+    add_gate!(circuit, SingleQubitGate(3, :T))
+    add_gate!(circuit, ControlledGate(1, 2, :CX))
+    add_gate!(circuit, SingleQubitGate(2, :S))
+    add_gate!(circuit, SingleQubitGate(3, :H))
+    return circuit
+end
+circuit_decomposed = QuantumCircuit(3)
+toffoli_decomposed(circuit_decomposed)
+
+tp = to_tikz_picture(circuit_decomposed)
+````
+
+Let's test the action of the decomposed Toffoli gate on the basis states to verify that it behaves the same as the built-in Toffoli gate.
+
+````@example toffoli
+test_actions(circuit_decomposed)
+````
+
+---
+
+*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*
+