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Suppose we have a qubit in the state ψ⟩=120⟩+3√21⟩. If we measure this qubit in u⟩=3√20⟩+121⟩,u⊥⟩=−120⟩+3√21⟩ basis, what is … 
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Let ϕ⟩=a0⟩+b1⟩ where a and b are nonnegative real numbers. We know that if we measure ϕ⟩ in the standard basis, the probability of getting a 0 is 925. What is ϕ⟩? 
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We have a qubit in the state ϕ⟩=3√20⟩+121⟩, which we want to measure in the {cosθ0⟩+sinθ1⟩,sinθ0⟩−cosθ1⟩} basis. In order for the two possible … 
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Suppose we have a onequbit unitary U that maps 0⟩ to 130⟩+2−2i31⟩ and 1⟩ to 2+2i30⟩−131⟩. What is U? 
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Suppose we have a onequbit unitary U that maps 0⟩ to 120⟩+3√i21⟩ and +⟩ to 1−3√i22√0⟩+3√i−122√1⟩. What is U? 
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Suppose we have two qubits in the state (a0⟩+b1⟩)0⟩, to which we apply the following circuit. (a) Is the resulting state entangled? 
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Consider the Hamiltonian H=Z⊗3 acting on 3 qubits. What is the ground energy of the system? 
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et ϕ⟩=a0⟩+b1⟩ where a and b are nonnegative real numbers. We know that if we measure ϕ⟩ in the standard basis, the probability of getting a 0 is 925. What is ϕ⟩? 
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The following circuit is designed for testing whether u⟩=v⟩. The threequbit gate in the middle is called the controlled SWAP gate, which swaps the last two qubits if and only if the first qubit is 1 (a) If u⟩=v⟩=+⟩, …