Measurement based fault tolerance beyond foliation

Understand

In order to build a scalable quantum computer error correction will be required to reduce the impact of errors.

• Implementing error correction in the framework of measurement based computation manifests itself as the construction of fault tolerant cluster states (FTCSs).
• While any 2-dimensional stabilizer code can be used to construct a FTCS through the process of foliation, here we find FTCSs that cannot be constructed through foliation of a stabilizer code, and identify new examples of self-dual codes that can still be implemented in a 2-dimensional physical architecture.