  Measurement-based quantum computation with continuous variables in an optical
setup shows the great promise towards implementation of large-scale quantum
computation, where the time-domain multiplexing approach enables us to generate
the large-scale cluster state used to perform measurement-based quantum
computation. To make effective use of the advantage of the time-domain
multiplexing approach, in this paper, we propose the method to generate the
large-scale 3-dimensional cluster state which is a platform for topologically
protected measurement-based quantum computation. Our method combines a
time-domain multiplexing approach with a divide-and-conquer approach, and has
the two advantages for implementing large-scale quantum computation. First, the
squeezing level for verification of the entanglement of the 3-dimensional
cluster states is experimentally feasible. The second advantage is the
robustness against analog errors derived from the finite squeezing of
continuous variables during topologically-protected measurement-based quantum
computation. Therefore, our method is a promising approach to implement
large-scale quantum computation with continuous variables.

Quantum Physics