Protected qubits and quantum computation using Josephson junctions

Several schemes of topological protection have been proposed, in which qubits are realized as degenerate ground states of quantum many-body systems so that all likely perturbations are exponentially suppressed. In the realm of Josephson junction physics, this approach was pioneered by Doucot, Vidal, Ioffe, and Feigelman in 2002. I will report a variation of their scheme that offers greater robustness and flexibility. Its key element is a ``quantum transformer'', a superconducting current mirror operated in the quantum regime. This is a four-terminal device whose energy depends only on $\phi_1-\phi_2+\phi_3-\phi_4$, with exponentially small ``error terms'' like $\cos(\phi_1-\phi_4)$. The qubit is implemented by connecting terminal $1$ with $3$ and $2$ with $4$. I will describe a realization of the basic element, qubit measurements and unitary gates, and also discuss some parameter tradeoffs.