Chapter 3, Math for Qubits and Quantum Gates

1. A. represents a qubit because .

B. doesn’t represent a qubit because .

C. doesn’t represent a qubit because it has three entries, not two.

2. Here is the result:

3. 
4. 
5. Here is the Qiskit code:

   qc = QuantumCircuit(1)
   qc.h(0)
   qc.z(0)

6. 
7. According to Figure 3.25, . So, we have .
   
8. Here is the matrix calculation:



9. Here’s the Hadamard gate acting on |+⟩:


Here’s the gate acting on |+⟩:


10.