# Grover's algorithm: a real life example?

I'm fairly confused about how Grover's algorithm could be used in practice and I'd like to ask help on clarification through an example.

Let's assume an $N=8$ element database that contains colors Red, Orange, Yellow, Green, Cyan, Blue, Indigo and Violet, and not necessarily in this order. My goal is to find Red in the database.

The input for Grover's algorithm is $n = \log_2(N=8) = 3$ qubits, where the 3 qubits encode the indices of the dataset. My confusion comes here (might be confused about the premises so rather say confusion strikes here) that, as I understand, the oracle actually searches for one of the indices of the dataset (represented by the superposition of the 3 qubits), and furthermore, the oracle is "hardcoded" for which index it should look for.

My questions are:

• What do I get wrong here?
• If the oracle is really looking for one of the indices of the database, that would mean we know already which index we are looking for, so why searching?
• Given the above conditions with the colors, could someone point it out if it is possible with Grover's to look for Red in an unstructured dataset?

There are implementations for Grover's algorithm with an oracle for $n=3$ searching for |111>, e.g. (or see an R implementation of the same oracle below): https://quantumcomputing.stackexchange.com/a/2205

Again, my confusion is, given I do not know the position of $N$ elements in a dataset, the algorithm requires me to search for a string that encodes the position of $N$ elements. How do I know which position I should look for when the dataset is unstructured?

R code:

#START
# 1st CNOT
a1= CNOT3_12(a)
# 2nd composite
# I x I x T1Gate
b = TensorProd(TensorProd(I2,I2),T1Gate(I2))
b1 = DotProduct(b,a1)
c = CNOT3_02(b1)
# 3rd composite
# I x I x TGate
d = TensorProd(TensorProd(I2,I2),TGate(I2))
d1 = DotProduct(d,c)
e = CNOT3_12(d1)
# 4th composite
# I x I x T1Gate
f = TensorProd(TensorProd(I2,I2),T1Gate(I2))
f1 = DotProduct(f,e)
g = CNOT3_02(f1)
#5th composite
# I x T x T
h = TensorProd(TensorProd(I2,TGate(I2)),TGate(I2))
h1 = DotProduct(h,g)
i = CNOT3_01(h1)
#6th composite
j = TensorProd(TensorProd(I2,T1Gate(I2)),I2)
j1 = DotProduct(j,i)
k = CNOT3_01(j1)
#7th composite
l = TensorProd(TensorProd(TGate(I2),I2),I2)
l1 = DotProduct(l,k)
#8th composite
n1 = DotProduct(n,l1)
n2 = TensorProd(TensorProd(PauliX(I2),PauliX(I2)),PauliX(I2))
a = DotProduct(n2,n1)
#repeat the same from 2st not gate
a1= CNOT3_12(a)
# 2nd composite
# I x I x T1Gate
b = TensorProd(TensorProd(I2,I2),T1Gate(I2))
b1 = DotProduct(b,a1)
c = CNOT3_02(b1)
# 3rd composite
# I x I x TGate
d = TensorProd(TensorProd(I2,I2),TGate(I2))
d1 = DotProduct(d,c)
e = CNOT3_12(d1)
# 4th composite
# I x I x T1Gate
f = TensorProd(TensorProd(I2,I2),T1Gate(I2))
f1 = DotProduct(f,e)
g = CNOT3_02(f1)
#5th composite
# I x T x T
h = TensorProd(TensorProd(I2,TGate(I2)),TGate(I2))
h1 = DotProduct(h,g)
i = CNOT3_01(h1)
#6th composite
j = TensorProd(TensorProd(I2,T1Gate(I2)),I2)
j1 = DotProduct(j,i)
k = CNOT3_01(j1)
#7th composite
l = TensorProd(TensorProd(TGate(I2),I2),I2)
l1 = DotProduct(l,k)
#8th composite
n = TensorProd(TensorProd(PauliX(I2),PauliX(I2)),PauliX(I2))
n1 = DotProduct(n,l1)