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

Abstract

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.

7 pages, 5 figures

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• Majorana Zero-Modes in a Two-Dimensional $p$-Wave Superconductor
• Optimal noise-canceling shortcuts to adiabaticity: application to noisy Majorana-based gates
• Scalable Fermionic Error Correction in Majorana Surface Codes
• Topological ordering in the Majorana Toric Code
• Edge Modes and Teleportation in a Topologically Insulating Quantum Wire
• Room-temperature superconductivity in an artificial 2D Mott-insulating square lattice and its advanced condensed phase that generates a low-loss current in the atmosphere: A possible perpetual motion machine