A quantum computer is based on the notion ofaquantum bit (or qubit). A qubit has two fundamental vector states denoted by and . These states represent basis vectors in the complex two-dimensional vector space (equivalent to the Hilbert space ). A quantum computer manipulates these states by unitary matrix transformations. Two qubits are defined in the four-dimensional complex vector space associated with four basis vectors

More generally, quantum bits have basis states, defined by 〉, where or , .