In this module, our main objective will be
to discover the secret combination that opens a lock. Suppose that such combination
is described by bits. The naive method would be to try all combinations
one by one. Would a quantum computer make this task easier? Naively, it looks as if we could create a uniform
superposition over all -bit strings and immediately determine the
correct combination. After all, the uniform superposition encodes all possible combinations in a single state!
To create a uniform superposition over all possible -qubit basis states, we can apply
where we use bold letters
for strings of bits, In
particular, the string of zeros will be denoted by .
Thus, we can write the uniform superposition , where is the -fold tensor product of Hadamard gates. As a circuit:
This will prepare a state that includes the correct combination (or "solution") , so
if we measure, we should find it.
Fill in the following code to create the
uniform superposition over qubits. It will also plot the probability
of observing different outcomes. Does putting the circuit in a
uniform superposition help us break the lock?
Note. The pass is a placeholder you will replace with your code.
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Learning Objectives:
Explain why quantum superposition does not automatically imply exponential speedups.
Write a uniform superposition over multiple qubits as a tensor product.