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

TL;DR

This paper presents a physical implementation of a Majorana fermion surface code using Josephson-coupled topological superconductors, enhancing fault-tolerant quantum computation with improved error suppression and measurement strategies.

Contribution

It introduces a novel hybrid approach combining stabilizer Hamiltonian engineering with projective measurements for Majorana-based quantum error correction.

Findings

Realizes a commuting Hamiltonian with $Z_{2}$ topological order using Majorana fermions.

Demonstrates improved error suppression over traditional surface codes.

Provides a scalable method for implementing stabilizer codes in quantum computing.

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.