Physics of Single Qubit Gates
Daniel D. Stancil, Gregory T. Byrd · 2022
As one might expect, having some way to represent and manipulate qubits is a basic requirement of any quantum computer. For a single qubit the state vector is represented by a 2 × 1 matrix (or vector), and in other areas of quantum mechanics such state vectors are referred to as spinors. Before we move to more complex qubit interactions, it is useful to introduce another representation of a quantum state, known as a density matrix or density operator. The density matrix is a generalization of the state vector representation. Since in quantum computing we actually take measurements, we obtain estimates of the state vector components by taking the averages of large numbers of measurements, rather than doing calculations involving the Pauli matrices.