Implementation of decoherence-protected logical qubits in medium-size Josephson junction arrays

摘要

We outline the physical principles underlying the design of finite size superconducting arrays that may serve as protected qubits. These systems are built from fully frustrated rhombi consisting of four Josephson junctions; their low energy spectrum is composed of localized Z_2 charge excitations and r phase vortices. Protection from both the phase and flip errors requires a balance between charging and Josephson energies; optimization of the array size results in the hierarchical construction of these arrays. We have developed computational methods, based on a combination of perturbation theory and numerical diagonalization, which allow us to compute the global phase stiffness and the energy of localized charge excitations in various geometries. We present the most promising designs, which are currently under experimental investigation.