A simple notebook showing how to build a quantum randum number generator. We're going to use Float32 for all calculations to save memory.

We define some well known constants. The 2x2 identity matrix and the 2x2 zero matrix:

In [9]:

using Test, LinearAlgebra

eye = Matrix{Float32}(I, 2, 2)
ZEROS = zeros(Float32, 2, 2)

@test eye*eye ≈ eye && eye * ZEROS == ZEROS

Out[9]:

Test Passed

We'll define the starting state for qubits as |0>.

In [2]:

UP = [1f0, 0]
DOWN = [0f0, 1f0]

Out[2]:

2-element Array{Float32,1}:
 0.0
 1.0

Now we can define some basic gates:

In [3]:

X = [0f0 1; 1 0]
H = Float32(1/sqrt(2)) * [1f0 1; 1 -1]
halfX = Float32(0.5) * [1f0+im 1-im; 1-im 1+im]

@test halfX*halfX ≈ X && H*H ≈ X*X && X*X ≈ eye

Out[3]:

Test Passed

In [4]:

qubits(n) = foldr(kron, fill(UP, n))

Out[4]:

qubits (generic function with 1 method)

$$\frac{x}{y}$$

In [4]:

circuit(n) = foldr(kron, fill(H, n))

Out[4]:

circuit (generic function with 1 method)

In [6]:

register = circuit(8)*qubits(8)

Out[6]:

256-element Array{Float32,1}:
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 ⋮          
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993
 0.062499993

In [7]:

M0 = FALSE * transpose(FALSE)

Out[7]:

2×2 Array{Float32,2}:
 1.0  0.0
 0.0  0.0

In [8]:

rand() > 0.5

Out[8]:

false

In [9]:

measure(i, n) = transpose(register)*foldr(kron, map(k -> k==i ? M0 : eye, [1:8]...))*register

Out[9]:

measure (generic function with 1 method)

In [10]:

measureAll(n) = map(v -> measure(v, n), collect(1:8))

Out[10]:

measureAll (generic function with 1 method)

In [11]:

measureAll(8)

Out[11]:

8-element Array{Float32,1}:
 0.49999988
 0.49999988
 0.49999988
 0.49999994
 0.49999994
 0.49999994
 0.49999994
 0.49999994

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