- Single Qubit (18 pts.) For the following questions, assume that the qubit will start in the \(|\uparrow\rangle\) state:
- Draw a circuit for a single qubit where:
- (3 pt.) you measure the state of the qubit.
- (4 pts.) you apply a NOT gate and then measure the state of the qubit.
- (4 pts.) you apply a Z gate followed by a Hadamard gate and then you measure the state of the qubit.
- (7 pts.) What state (or states) did you create with each of the above circuits? Justify your results.
- Two Qubits (20 pts.)
- (8 pts.) Draw the circuits needed to create all four Bell states.
- (12 pts.) Draw a two qubit circuit where both qubits start in the \(|\downarrow\rangle\) state. First, there is a Hadamard gate applied to the first qubit, then there is a controlled CNOT gate where the second qubit is the control and the first qubit is the target. Finally there is a controlled Z gate where the first qubit is the control and the second qubit is the target. What state did you create?
- Three Qubits (12 pts.)
- (4 pts.) Draw a three qubit quantum circuit where you apply one one-qubit gate, one two-qubit gate, and one-three qubit gate. Add a measurement to all three qubits at the end.
- (8 pts.) Assume that all three qubits in the previous circuit started in the \(|\uparrow\rangle\) state. What state will you measure?