Questions

1. How many qubits do we need to search for something in a list containing 1,000,000 entries? How many steps will the search take?
2. Write the matrix of the diffuser to search through an eight-value list.
3. Modify the code in this chapter’s Coding Grover’s algorithm with matrices section so that the target is a randomly chosen state between |000⟩ and |111⟩.
4. For what values of x, y, and z is the following expression true?

   (x | y | ~z) & (x | ~y | z) & (x | ~y | ~z) &
   (~x | y | z) & (~x | y | ~z) & (~x | ~y | z) &
   (~x | ~y | ~z)

Legend: | means or, ~ means not, and & means and.

5. Run the following code:

   from qiskit import QuantumCircuit, execute
   from qiskit import Aer
   from qiskit.visualization import array_to_latex
   circ = QuantumCircuit(3)
   circ.x(2)
   circ.h(2)
   circ.barrier()
   circ.toffoli(0, 1, 2)
   display(circ.draw('latex'))
   device = Aer.get_backend('unitary_simulator')
   job = execute...