chargequbit

Chargequbit is a type of quantum bit in which quantum information is encoded in the number of charges on a superconducting island or quantum dot. In superconducting implementations, the logical states are two charge states differing by a Cooper pair on the island. The system is typically formed by a small superconducting island connected to a reservoir via a Josephson junction and controlled by a gate electrode that sets the offset charge n_g. The effective Hamiltonian is H = 4 E_C (n - n_g)^2 - E_J cos(phi), where E_C is the charging energy and E_J the Josephson energy. At the charge degeneracy point n_g ~ 1/2, the two charge states hybridize to form qubit states with an energy splitting determined by E_J and E_C, enabling coherent manipulation by microwave pulses.

Realizations include superconducting charge qubits, such as the Cooper-pair box, and semiconductor quantum dots where qubit states differ by electron number. In quantum dot systems, tunneling between closely spaced dots provides the coupling, and gates tune the energy detuning and tunnel rates.

Charge qubits are highly sensitive to charge noise in the environment, leading to dephasing and short coherence times. This sensitivity motivated designs that reduce charge dispersion, notably the transmon, which operates with a large ratio of E_J to E_C to suppress sensitivity to offset charge. Other approaches include improved materials, shielding, and circuit geometries, as well as alternative readout schemes.

Readout is typically performed with charge sensors such as a single-electron transistor or via dispersive coupling to a microwave resonator, enabling readout of the charge configuration. Although modern superconducting qubits have surpassed early charge qubits in coherence, the charge qubit concept remains relevant in discussions of superconducting circuits and quantum-dot qubits.