Vanderbilt University Quantum Computing Problems
1. Consider a quantum state | ⟩ = (2 |0⟩ + 1 + |1⟩). Find the value of . Compute the density matrix associated with this quantum state.
2. Calculate the output quantum state when the following series of single-qubit gates are applied on | ⟩ (from Question 1)
Z gate → Ry gate with = /2 →X gate
3. Consider two qubits, | 1⟩ = (1/13) (3|0⟩ + 2|1⟩) and | 2⟩ = (1/13) (2 |0⟩ + |1⟩)
- Apply the following gates on the first qubit: Z gate, H gate, X gate (ii) Apply the following gates on the second qubit: Ry gate with = 2 /3
- Apply the CNOT gate on the two qubits. Consider | 2⟩ as the control qubit and | 1⟩ as the target qubit.
- Now apply a second CNOT gate with | 1⟩ as the control qubit and | 2⟩ as the target qubit
4.Write down the complex conjugate transpose of the Y matrix.
5. Consider | 1⟩ = (1/13)(3|0⟩ + 2|1⟩) from Question 3. First, apply the Y gate on this qubit. Then apply the complex conjugate transpose of the Y gate (which you calculated in Question 4). Write down the output quantum state.
