add more contents

docs/Project.toml

@@ -1,5 +1,6 @@
 [deps]
 BitBasis = "50ba71b6-fa0f-514d-ae9a-0916efc90dcf"
+Compose = "a81c6b42-2e10-5240-aca2-a61377ecd94b"
 DocThemeIndigo = "8bac0ac5-51bf-41f9-885e-2bf1ac2bec5f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
@@ -14,4 +15,6 @@ Yao = "5872b779-8223-5990-8dd0-5abbb0748c8c"
 YaoAPI = "0843a435-28de-4971-9e8b-a9641b2983a8"
 YaoArrayRegister = "e600142f-9330-5003-8abb-0ebd767abc51"
 YaoBlocks = "418bc28f-b43b-5e0b-a6e7-61bbc1a2c1df"
+YaoPlots = "32cfe2d9-419e-45f2-8191-2267705d8dbc"
 YaoSym = "3b27209a-d3d6-11e9-3c0f-41eb92b2cb9d"
+ZXCalculus = "3525faa3-032d-4235-a8d4-8c2939a218dd"

docs/src/quick-start.md

@@ -3,12 +3,92 @@
 In this quick start, we list several common use cases for Yao before you
 go deeper into the manual.
 
-## Create a quantum register
+## Create a quantum register/state
+
+A register is an object that describes a device with an internal state. See [Registers](@ref registers)
+for more details. Yao use registers to represent quantum states. The most common register
+is the [`ArrayReg`](@ref), you can create it by feeding a state vector to it, e.g
+
+```@repl quick-start
+using Yao
+ArrayReg(rand(ComplexF64, 2^3))
+zero_state(5)
+rand_state(5)
+product_state(bit"10100")
+ghz_state(5)
+```
+
+the internal quantum state can be accessed via [`statevec`](@ref) method
+
+```@repl quick-start
+statevec(ghz_state(2))
+```
+
+for more functionalities about registers please refer to the manual of [`registers`](@ref).
+
 ## Create quantum circuit with Yao blocks
+
+Yao uses the quantum "block"s to describe quantum circuits, e.g
+the following code creates a 2-qubit circuit
+
+```@repl quick-start
+chain(2, put(1=>H), put(2=>X))
+```
+
+where `H` gate is at 1st qubit, `X` gate is at 2nd qubit.
+A more advanced example is the quantum Fourier transform circuit
+
+```@repl quick-start
+A(i, j) = control(i, j=>shift(2π/(1<<(i-j+1))))
+B(n, k) = chain(n, j==k ? put(k=>H) : A(j, k) for j in k:n)
+qft(n) = chain(B(n, k) for k in 1:n)
+qft(3)
+```
+
 ## Create Hamiltonian with Yao blocks
+
+the quantum "block"s are expressions on quantum operators, thus, it can
+also be used to represent a Hamiltonian, e.g we can create a simple Ising
+Hamiltonian on 1D chain as following
+
+```@repl quick-start
+sum(kron(5, i=>Z, mod1(i+1, 5)=>Z) for i in 1:5)
+```
+
 ## Automatic differentiate a Yao block
+
+Yao has its own automatic differentiation rule implemented, this allows one obtain
+gradients of a loss function by simply putting a `'` mark behind [`expect`](@ref)
+or [`fidelity`](@ref), e.g
+
+```@repl quick-start
+expect'(X, zero_state(1)=>Rx(0.2))
+```
+
+or for fiedlity
+
+```@repl quick-start
+fidelity'(zero_state(1)=>Rx(0.1), zero_state(1)=>Rx(0.2))
+```
+
 ## Combine Yao with ChainRules/Zygote
+
+
 ## Symbolic calculation with Yao block
+Yao supports symbolic calculation of quantum circuit via `SymEngine`. We can show
+
+
 ## Plot quantum circuits
+
+The [YaoPlots]() in Yao's ecosystem provides plotting for quantum circuits and ZX diagrams.
+
+```@example quick-start
+using Yao.EasyBuild, YaoPlots
+using Compose
+
+# show a qft circuit
+Compose.SVG(plot(qft_circuit(5)))
+```
+
 ## Convert quantum circuits to tensor network
 ## Simplify quantum circuit with ZX calculus