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Quantum Computing Algorithms
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As we saw in the previous sections, each application of the Grover iterate has two parts:
Each part is a collection of quantum gates, and those gates apply a matrix to the circuit’s qubits. In this section, we’ll describe the matrix representations of the oracle and the diffuser.
Let’s assume that we have only two qubits. After these qubits go through Hadamard gates, we have a matrix representation of
. If we want to mark the |10⟩ amplitude, we must do the following:
In general, the oracle’s matrix is the identity matrix with one of the 1s along the diagonal changed to a -1. Simple as this is, it’s also somewhat disconcerting. To know which diagonal element becomes -1, you have to know which item is...