ComputerScience - QuantumComputing

Question 1: Which of the following is a valid Quantum State Vector?

$\frac{i}{2}|00\rangle + \frac{i}{2}|11\rangle$ $\frac{2}{\sqrt{2}}|00\rangle + \frac{2}{\sqrt{2}}|11\rangle$ $\frac{1}{\sqrt{2}}|00\rangle + \frac{1}{\sqrt{2}}|11\rangle$ $\frac{1}{2}|00\rangle + \frac{1}{2}|11\rangle$

Question 2: What are the measurement probabilities associated with the state in Question 1?

00 with probability 1, 11 with probability 0 00 with probability 1/2, 11 with probability 1/2 00 with probability 1/4, 11 with probability 1/4, other with probability 1/2 00 with probability 1/4, 11 with probability 1/4

Question 3: Which of the following is a valid Quantum State Vector?

$\frac{i}{3}|00\rangle + \frac{i}{3}|10\rangle + \frac{i}{3}|11\rangle$ $\frac{i}{\sqrt{2}}|00\rangle + \frac{i}{2}|10\rangle + \frac{i}{2}|11\rangle$ $\frac{i}{\sqrt{2}}|00\rangle + \frac{i}{\sqrt{2}}|10\rangle + \frac{i}{2}|11\rangle$ $\frac{i}{4}|00\rangle + \frac{i}{4}|10\rangle + \frac{i}{2}|11\rangle$

Question 4: What are the measurement probabilities associated with the state in Question 3?

00 with probability 1/2, 10 with probability 1/3, 11 with probability 1/2 00 with probability 1/4, 10 with probability 1/4, 11 with probability 1/2 00 with probability 1/3, 10 with probability 1/3, 11 with probability 1/3 00 with probability 1/2, 10 with probability 1/4, 11 with probability 1/4

Question 5: Which of the following is a valid Quantum State Vector?

$\frac{i}{2}|00\rangle + \frac{i}{2}|10\rangle + \frac{i}{2}|11\rangle$ $\frac{1}{\sqrt{3}}|00\rangle + \frac{1}{\sqrt{3}}|10\rangle + \frac{1}{\sqrt{3}}|11\rangle$ $\frac{3i}{\sqrt{3}}|00\rangle + \frac{3i}{\sqrt{3}}|10\rangle + \frac{3i}{\sqrt{3}}|11\rangle$ $\frac{1}{2}|00\rangle + \frac{1}{2}|10\rangle + \frac{1}{2}|11\rangle$

Question 6: What are the measurement probabilities associated with the state in Question 5?

00 with probability 1/2, 10 with probability 1/4, 11 with probability 1/4 00 with probability 1/2, 10 with probability 1/2, 11 with probability 0 00 with probability 1/3, 10 with probability 1/3, 11 with probability 1/3 00 with probability 1/4, 10 with probability 1/4, 11 with probability 1/2

Question 7: Which of the following is a valid Quantum State Vector?

$\frac{1}{\sqrt{6}}|00\rangle + \frac{i}{\sqrt{3}}|01\rangle + \frac{1}{4}|10\rangle + \frac{i}{4}|11\rangle$ $\frac{i}{4}|00\rangle + \frac{i}{4}|01\rangle + \frac{i}{4}|10\rangle + \frac{i}{4}|11\rangle$ $\frac{i}{\sqrt{6}}|00\rangle + \frac{1}{\sqrt{3}}|01\rangle + \frac{1}{2}|10\rangle + \frac{i}{2}|11\rangle$ $\frac{1}{6}|00\rangle + \frac{i}{3}|01\rangle + \frac{1}{4}|10\rangle + \frac{i}{4}|11\rangle$

Question 8: What are the measurement probabilities associated with the state in Question 7?

00 with probability 1/6, 01 with probability 1/3, 10 with probability 1/4, 11 with probability 1/4 00 with probability 1/6, 01 with probability 1/3, 10 with probability 1/2, 11 with probability 1/2 00 with probability 1/4, 01 with probability 1/4, 10 with probability 1/4, 11 with probability 1/4 00 with probability 1/2, 01 with probability 1/4, 10 with probability 1/4, 11 with probability 0

Question 9: Which expression represents a valid uniform Quantum State Vector over $n$ states?

$\sum_{i=1}^{n} \frac{1}{n}|i\rangle$ $\sum_{i=1}^{n} \frac{1}{n^2}|i\rangle$ $\sum_{i=1}^{n} \frac{1}{\sqrt{n}}|i\rangle$ $\sum_{i=1}^{n} \frac{1}{2n}|i\rangle$

Question 10: For the state vector in question 9, what is the measurement probability for each basis state $|i\rangle$?

Each state |i⟩ with probability 1/2n Each state |i⟩ with probability 1/√n Each state |i⟩ with probability 1/n^2 Each state |i⟩ with probability 1/n

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