Charge qubit
In quantum computing, a charge qubit is a qubit whose basis states are charge states (e.g. states which represent the presence or absence of excess Cooper pairs in the island). In superconducting quantum computing, a charge qubit is formed by a tiny superconducting island (also known as a Cooper-pair box) coupled by a Josephson junction to a superconducting reservoir (see figure). The state of the qubit is determined by the number of Cooper pairs which have tunneled across the junction. In contrast with the charge state of an atomic or molecular ion, the charge states of such an "island" involve a macroscopic number of conduction electrons of the island. The quantum superposition of charge states can be achieved by tuning the gate voltage U that controls the chemical potential of the island. The charge qubit is typically read-out by electrostatically coupling the island to an extremely sensitive electrometer such as the radio-frequency single-electron transistor.
Superconducting quantum computing
where formula_23 is the shape of the microwave pulse in time, formula_24 is the resonance frequency of the second qubit, formula_25 are the Pauli matrices, formula_26 is the coupling coefficient between the two qubits via the resonator, formula_27 is the qubit detuning, formula_28 is the stray (unwanted) coupling between qubits and formula_29 is Planck constant divided by formula_30. The time integral over formula_23 determines the angle of rotation. Unwanted rotations due to the first and third terms of the Hamiltonian can be compensated with single qubit operations. The remaining part is exactly the controlled-X gate.