A local and scalable lattice renormalization method for ballistic quantum computation

A recent proposal has shown that it is possible to perform linear-optics quantum computation using a ballistic generation of the lattice. Yet, due to the probabilistic generation of its cluster state, it is not possible to use the fault-tolerant Raussendorf lattice, which requires a lower failure rate during the entanglement-generation process. Previous work in this area showed proof-of-principle linear-optics quantum computation, while this paper presents an approach to it which is more practical, satisfying several key constraints. We develop a classical measurement scheme, that purifies a large faulty lattice to a smaller lattice with entanglement faults below threshold. A single application of this method can reduce the entanglement error rate to $7\%$ for an input failure rate of $25\%$. Thus, we can show that it is possible to achieve fault tolerance for ballistic methods.