Majorana Fermion Surface Code for Universal Quantum Computation

TL;DR

This paper presents a solvable model of Majorana fermions forming a topological code suitable for universal quantum computation, with advantages over traditional bosonic qubit codes.

Contribution

It introduces a Majorana fermion surface code with a physical realization in solid state systems, enabling efficient quantum computation with improved error tolerance.

Findings

Model exhibits $Z_{2}$ topological order with fermion parity grading.

Proposes physical implementation using Josephson-coupled superconductors.

Achieves single-step stabilizer measurement without ancilla qubits.

Abstract

We introduce an exactly solvable model of interacting Majorana fermions realizing $Z_{2}$ topological order with a $Z_{2}$ fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid state systems, including topological insulators, nanowires or two-dimensional electron gases, proximitized by $s$-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.