1] Let |ψ⟩=(2+i/3)|0>−(2/3)|1>. If we measure |ψ⟩ in the basis |u⟩=(1+i/2)|0>+(1−i/2)|1>, |u⊥>=1−i/2|0>−1+i/2|1>, what is the probability our outcome is |u>?
2]Suppose we are trying to solve Simon's problem with n=4. We ran 4 iterations of Simon's algorithm and obtained 0000, 1101, 1010, and 0110. What is the secret string s? (Assume that s is not the all-zero string 0000.)
3]What is the superposition that results if you apply the Hadamard transform H⊗n to the state 12√(|0n>+|1n>)? (Here, |0n⟩:=|00⋯0n⟩ and |1n⟩:=|11⋯1n⟩.)