obtain a two-level quantum system (a.k.a. qubit). Note that some recent papers adopt a different notation, and define the charging energy as that of one electron: and then the corresponding Hamiltonian is: Benefits To-date, the realizations of qubits that have had the most success are ion traps and NMR, with Shor's algorithm even being implemented using NMR. However, it is hard to see these two methods being scaled to the hundreds, thousands, or millions of qubits necessary to create a quantum computer. Solid-state representations of qubits are much more easily scalable, but they themselves have their own problem: decoherence. Superconductors, however, have the advantage of being more easily scaled, and they are more coherent than normal solid-state systems. Experimental progresses The implementation of Superconducting charge qubits have been progressing quickly since 1996. Design was theoretically described in 1997 by Shnirman, while the evidence of quantum coherence of the charge in a Cooper pair box was published in February 1997 by Vincent Bouchiat et al. In 1999, coherent oscillations in the charge Qubit were first observed by Nakamura et al. Manipulation of the quantum states and full realization of the charge qubit was observed 2 years later. In 2007, a more advanced device known as Transmon showing enhanced coherence times due to its reduced sensitivity to charge noise was developed at Yale University by Robert J. Schoelkopf, Michel Devoret, Steven M. Girvin and their colleagues . References Quantum information science Quantum electronics Superconductivity