new trace operator

Author: GiggleLiu

README.md

@@ -22,7 +22,6 @@ Disclaimer: **this package is still under development and needs further polish.*
 ## Contents
 
 - [x] [QFT](https://github.com/QuantumBFS/YaoExtensions.jl)
-- [x] Grover search
 - [x] Phase Estimation
 - [x] Imaginary Time Evolution Quantum Eigensolver
 - [x] Variational Quantum Eigensolver
@@ -37,6 +36,7 @@ In examples folder, you will find
 - [x] Quantum Circuit Born Machine
 - [x] QuGAN
 - [x] Shor
+- [x] Grover search
 
 - [x] [QuODE](https://github.com/QuantumBFS/QuDiffEq.jl)
 - [x] [TensorNetwork Inspired Circuits](https://github.com/GiggleLiu/QuantumPEPS.jl)

docs/make.jl

@@ -58,4 +58,4 @@ function generate(islocal::Bool="local" in ARGS)
     )
 end
 
-generate(true)
+generate(false)

docs/src/index.md

@@ -9,13 +9,19 @@ A curated implementation of quantum algorithms with [Yao.jl](https://github.com/
 ## Tutorial
 ```@contents
 Pages = [
+    "tutorial/Grover.md",
     "tutorial/VQE.md",
     "tutorial/Shor.md",
 ]
 Depth = 1
 ```
 
+Some examples are not yet documented, please refer the [README](https://github.com/QuantumBFS/QuAlgorithmZoo.jl) for a full list of algorithms.
+
 ## Manual
+
+The manual is a references of utilities defined in QuAlgorithmZoo,
+like `Adam` optimizer and `NumberTheory` submodule.
 ```@contents
 Pages = [
     "man/zoo.md",

examples/TraceOperator/README.md

@@ -0,0 +1,8 @@
+# Tracing an operator
+
+To compute $\Re[{\rm Tr}(Ue^{-i\theta})]$, we utilize the Hadamard test.
+
+The circuit is
+![trace circuit](traceop.png)
+
+This result can be proved from its tensor network representation.

examples/TraceOperator/TraceOperator.jl

@@ -0,0 +1,17 @@
+using Yao
+using QuAlgorithmZoo
+using YaoBlocks.ConstGate
+using Test
+using LinearAlgebra
+
+@testset "hadamard test" begin
+    n = 2
+    U = chain(put(n, 2=>Rx(0.2)), put(n, 1=>Rz(1.2)), put(n, 1=>phase(0.4)))
+    US = chain(2n, put(2n, (3,4)=>U),
+            chain(2n, [swap(2n,i,i+n) for i=1:n]))
+    reg = zero_state(2n)
+    reg |> repeat(2n, H, 1:n) |> chain(2n, [cnot(2n,i,i+n) for i=1:n])
+    @show real(tr(mat(U)))/(1<<n)
+    @test hadamard_test(US, reg, 0.0) ≈ real(tr(mat(U)))/(1<<n)
+    @test hadamard_test(US, reg, -π/2) ≈ imag(tr(mat(U)))/(1<<n)
+end