Title: Distilling perfect cluster states from imperfect ones

Matt Elliott

University of New Mexico

Abstract: We study how universal measurement based quantum computation can be achieved despite only having the ability to prepare faulty cluster states. The model we use is one where there are heralded qubit losses during the preparation of a two-dimensional cluster state. Above the percolation threshold we find a polynomial-time algorithm that concentrates a universal cluster state, using resources that scale optimally in the size of the original lattice. On the other hand, below the percolation threshold, the imperfections become severe enough that single qubit measurements on the faulty lattice can be efficiently simulated classically.