Merge branch 'master' of https://github.com/QuantumBFS/QuAlgorithmZoo.jl

README.md

@@ -32,6 +32,7 @@ In examples folder, you will find
 - [Grover search](examples/Grover)
 - [Learning a general two qubit unitary gate](examples/GateLearning)
 - [Bernstein-Vazirani algorithm](examples/BernsteinVazirani)
+- [Mermin Magic Square](examples/MerminMagic)
 
 Examples of using Yao in other projects
 - [QuODE](https://github.com/QuantumBFS/QuDiffEq.jl)

examples/MerminMagic/Project.toml

@@ -0,0 +1,7 @@
+[deps]
+Yao = "5872b779-8223-5990-8dd0-5abbb0748c8c"
+YaoPlots = "32cfe2d9-419e-45f2-8191-2267705d8dbc"
+
+[compat]
+Yao = "0.8"
+julia = "1.8"

examples/MerminMagic/main.jl

@@ -0,0 +1,97 @@
+# Mermin-Peres Magic Square Game Algorithm
+# https://www.gregegan.net/SCIENCE/MPMS/MPMS.html
+using Yao
+
+# measurement operator table
+# see Table S1 in https://arxiv.org/abs/2206.12042
+const magic_square = [kron(I2, Z) kron(Z, I2) kron(Z, Z)
+    kron(X, I2) kron(I2, X) kron(X, X)
+    kron(-X, Z) kron(-Z, X) kron(Y, Y)]
+
+"""
+    bell_state(which::Int) -> AbstractRegister
+
+Initialize bell state on a quantum register.
+
+# Arguments
+- `which::Int`: which of the four bell states to initialize
+  1 corresponds to ``(|00> + |11>)/√2``
+  2 corresponds to ``(|00> - |11>)/√2``
+  3 corresponds to ``(|01> + |10>)/√2``
+  4 corresponds to ``(|01> - |10>)/√2``
+
+# Returns
+- `AbstractRegister`: the register on which we have initialized the bell state
+"""
+function bell_state(which::Int)
+
+    @assert 1 <= which <= 4 "Input $(which) is not in range 1..4"
+    reg = zero_state(2)
+    apply!(reg, chain(put(2, 1 => H), cnot(2, 1, 2)))
+    (which == 2 || which == 4) && apply!(reg, put(2, 1 => Z))
+    (which == 3 || which == 4) && apply!(reg, put(2, 1 => X))
+    return reg
+end
+
+# Alice perform Measurement using Operator specified by row idx
+alice_measure!(reg::AbstractRegister, row::Int) = [real(measure!(op, reg, (1, 3))) for op in magic_square[row, :]]
+# Bob perform Measurement using Operator specified by row idx
+bob_measure!(reg::AbstractRegister, col::Int) = [real(measure!(op, reg, (2, 4))) for op in magic_square[:, col]]
+
+"""
+    input_idx(which::String) -> Int
+
+# Arguments
+- `which::String`: whether user is asked to provide the index for the row or column
+
+# Returns
+- `Int`: index determined by the user
+"""
+function input_idx(which::String)
+    idx = 0
+    while idx > 3 || idx < 1
+        println("Please provide a $which number in the range [1,3]")
+        try
+            idx = parse(Int64, readline())
+        catch e
+            showerror(stdout, e)
+            println(" Please enter a NUMBER!")
+        end
+    end
+    return idx
+end
+
+function main()
+    println("Dealer: Let's Play Mermin's Magic Square Game!")
+
+    # ask the user to input row and column index
+    i = input_idx("row")
+    j = input_idx("column")
+
+    println("Alice will provide three numbers to be written on row: $(i)")
+    println("Bob will provide three numbers to be written on column: $(j)")
+
+    # Initialize two pairs of bell state ``(|00> + |11>) ⊗ (|00> + |11>)/2``.
+    # First qubit of each bell state pair belongs to Alice and the others belong to Bob.
+    reg1 = join(bell_state(1), bell_state(1))
+
+    # do measurement and get answer string
+    a1, a2, a3 = alice_measure!(reg1, i)
+    b1, b2, b3 = bob_measure!(reg1, j)
+
+    println("Alice should give answer: $a1 , $a2 , $a3")
+    println("Bob should give answer: $b1 , $b2 , $b3")
+    #We should see j_th element  in [a1,a2,a3] is equal to i_th element in [b1,b2,b3]
+    @assert [a1, a2, a3][j] == [b1, b2, b3][i] ("Opps, something is wrong, the j_th item in
+       Alice's answer does not match the i_th item in Bob's answer")
+
+    # To reveal some magic behind the scenes, you may check that
+    # measurements on each row and each columns commute with
+    # each other and all are hermitian
+    @assert (all(k -> iscommute(magic_square[k, :]...), 1:3) &&
+             all(k -> iscommute(magic_square[:, k]...), 1:3) &&
+             all(ishermitian, magic_square))
+end
+
+
+main()

examples/run_examples.sh

@@ -1,6 +1,6 @@
 #! /bin/bash
 # run this file to make sure all examples work
-FILES="Grover QAOA HHL QCBM QuGAN Shor VQE GateLearning GroundStateSolvers BernsteinVazirani"
+FILES="Grover QAOA HHL QCBM QuGAN Shor VQE GateLearning GroundStateSolvers BernsteinVazirani MerminMagic"
 for folder in $FILES
 do
     echo "executing example: $folder"