Fault-tolerance thresholds for the surface code with fabrication errors

Understand

The construction of topological error correction codes requires the ability to fabricate a lattice of physical qubits embedded on a manifold with a non-trivial topology such that the quantum information is encoded in the global degrees of freedom (i.e.

• the topology) of the manifold.
• However, the manufacturing of large-scale topological devices will undoubtedly suffer from fabrication errors---permanent faulty components such as missing physical qubits or failed entangling gates---introducing permanent defects into the topology of the lattice and hence significantly reducing the distance of the code and the quality of the encoded logical qubits.
• In this work we investigate how fabrication errors affect the performance of topological codes, using the surface code as the testbed.