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# # [Prepare Greenberger–Horne–Zeilinger state with Quantum Circuit](@id example-ghz)
# First, you have to use this package in Julia.
using Yao
# Now, we just define the circuit according to the circuit image below:
# ![ghz](assets/ghz4.png)
circuit = chain(
4,
put(1=>X),
repeat(H, 2:4),
control(2, 1=>X),
control(4, 3=>X),
control(3, 1=>X),
control(4, 3=>X),
repeat(H, 1:4),
)
# Let me explain what happens here.
# ## Put single qubit gate X to location 1
# we have an `X` gate applied to the first qubit.
# We need to tell `Yao` to put this gate on the first qubit by
put(4, 1=>X)
# We use Julia's `Pair` to denote the gate and its location in the circuit,
# for two-qubit gate, you could also use a tuple of locations:
put(4, (1, 2)=>swap(2, 1, 2))
# But, wait, why there's no `4` in the definition above? This is because
# all the functions in `Yao` that requires to input the number of qubits as its
# first arguement could be lazy (curried), and let other constructors to infer the total
# number of qubits later, e.g
put(1=>X)
# which will return a lambda that ask for a single arguement `n`.
put(1=>X)(4)
# ## Apply the same gate on different locations
# next we should put Hadmard gates on all locations except the 1st qubits.
# We provide `repeat` to apply the same block repeatly, repeat can take an
# iterator of desired locations, and like `put`, we can also leave the total number
# of qubits there.
repeat(H, 2:4)
# ## Define control gates
# In Yao, we could define controlled gates by feeding a gate to `control`
control(4, 2, 1=>X)
# Like many others, you could leave the number of total qubits there, and infer it
# later.
control(2, 1=>X)
# ## Composite each part together
# This will create a `ControlBlock`, the concept of block in Yao basically
# just means quantum operators, since the quantum circuit itself is a quantum operator,
# we could create a quantum circuit by composite each part of.
# Here, we use `chain` to chain each part together, a chain of quantum operators
# means to apply each operators one by one in the chain. This will create a `ChainBlock`.
circuit = chain(
4,
put(1=>X),
repeat(H, 2:4),
control(2, 1=>X),
control(4, 3=>X),
control(3, 1=>X),
control(4, 3=>X),
repeat(H, 1:4),
)
# You can check the type of it with `typeof`
typeof(circuit)
# ## Construct GHZ state from 00...00
# For simulation, we provide a builtin register type called `ArrayReg`,
# we will use the simulated register in this example.
# First, let's create ``|00⋯00⟩``, you can create it with `zero_state`
zero_state(4)
# Or we also provide bit string literals to create arbitrary eigen state
ArrayReg(bit"0000")
# They will both create a register with Julia's builtin `Array` as storage.
# ## Feed Registers to Circuits
# Circuits can be applied to registers with `apply!`
apply!(zero_state(4), circuit)
# or you can use pipe operator `|>`, when you want to chain several operations
# together, here we measure the state right after the circuit for `1000` times
results = zero_state(4) |> circuit |> r->measure(r, nshots=1000)
using StatsBase, Plots
hist = fit(Histogram, Int.(results), 0:16)
bar(hist.edges[1] .- 0.5, hist.weights, legend=:none)
# GHZ state will collapse to ``|0000⟩`` or ``|1111⟩``.
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