  We propose a physical realization of a commuting Hamiltonian of interacting
Majorana fermions realizing $Z_{2}$ topological order, using an array of
Josephson-coupled topological superconductor islands. The required multi-body
interaction Hamiltonian is naturally generated by a combination of charging
energy induced quantum phase-slips on the superconducting islands and electron
tunneling. Our setup improves on a recent proposal for implementing a Majorana
fermion surface code [1], a 'hybrid' approach to fault-tolerant quantum
computation that combines (1) the engineering of a stabilizer Hamiltonian with
a topologically ordered ground state with (2) projective stabilizer
measurements to implement error correction and a universal set of logical
gates. Our hybrid strategy has advantages over the traditional surface code
architecture in error suppression and single-step stabilizer measurements, and
is widely applicable to implementing stabilizer codes for quantum computation.
