  Performing entangling gates between physical qubits is necessary for building
a large-scale universal quantum computer, but in some physical implementations
- for example, those that are based on linear optics or networks of ion traps -
entangling gates can only be implemented probabilistically. In this work, we
study the fault-tolerant performance of a topological cluster state scheme with
local non-deterministic entanglement generation, where failed entangling gates
(which correspond to bonds on the lattice representation of the cluster state)
lead to a defective three-dimensional lattice with missing bonds. We present
two approaches for dealing with missing bonds; the first is a non-adaptive
scheme that requires no additional quantum processing, and the second is an
adaptive scheme in which qubits can be measured in an alternative basis to
effectively remove them from the lattice, hence eliminating their damaging
effect and leading to better threshold performance. We find that a
fault-tolerance threshold can still be observed with a bond-loss rate of 6.5%
for the non-adaptive scheme, and a bond-loss rate as high as 14.5% for the
adaptive scheme.
