The idea behind Grover’s algorithm

The strategy underlying Grover’s algorithm is quite clever. Instead of thinking about 64 boxes the way we did in the previous section, let’s imagine that you have only four boxes. This set of four boxes is called the search space.

You’re a quantum computing enthusiast, so you’ve electronically coded the contents of these boxes and labeled the boxes |00⟩, |01⟩, |10⟩, and |11⟩. Now your search space consists of the four values |00⟩, |01⟩, |10⟩, and |11⟩. In your quantum computing circuit, you represent these values with two qubits, both of which are in the state. When you take the tensor product, you get . Remember that each of the numbers in this vector is an amplitude. The square of each amplitude is the probability of getting a certain outcome when you measure the two qubits. (See Figure 8.1.)

Figure 8.1 – A state vector...