1.1. The Problem of Implementing a Quantum Computer

Superconducting qubits are solid state electrical circuits fabricated using tech-niques borrowed from conventional integrated circuits. They are based on the Josephson tunnel junction, the only non-dissipative, strongly non-linear circuit ele-ment available at low temperature. In contrast to microscopic entities such as spins or atoms, they tend to be well coupled to other circuits, which make them appealling from the point of view of readout and gate implementation. Very recently, new designs of superconducting qubits based on multi-junction circuits have solved the problem of isolation from unwanted extrinsic electromagnetic per-turbations. We discuss in this review how qubit decoherence is affected by the intrinsic noise of the junction and what can be done to improve it