Questions

1. Using a pencil and paper or a hand calculator, find the factors of 14 using 3 as a coprime. (Use only the technique shown in the section entitled The role of a period in factoring a number. Don’t try applying the QFT.)
2. Using a pencil and paper or a hand calculator, find the factors of 35 using 2 as a coprime. (Again, use only the technique shown in the section entitled The role of a period in factoring a number.)
3. Write the value of using a + bi notation.
4. Write down the entries of a 4 × 4 QFT matrix. Use the notation for complex numbers that’s shown in Figure 9.8. Then, use the 4 × 4 QFT matrix to find the entries in the QFT† matrix.
5. Write down the entries of a 2 × 2 QFT matrix. Does this matrix look familiar?
6. Fill in the missing values in Figure 9.20.
7. Why isn’t 3 useful as a coprime when you try to factor 22?
8. Starting with the powers of 7 shown in the How Shor’s algorithm works section, use...