Physical Implementation of a Majorana Fermion Surface Code for Fault-Tolerant Quantum Computation

Understand

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.