Cluster states can be used to perform measurement-based quantum computation.
The cluster state is a useful resource, because once it has been generated only
local operations and measurements are needed to perform universal quantum
computation. In this paper, we explore techniques for quickly and
deterministically building a cluster state. In particular we consider
generating cluster states on a qubus quantum computer, a computational
architecture which uses a continuous variable ancilla to generate interactions
between qubits. We explore several techniques for building the cluster, with
the number of operations required depending on whether we allow the ability to
destroy previously created controlled-phase links between qubits. In the case
where we can not destroy these links, we show how to create an n x m cluster
using just 3nm -2n -3m/2 + 3 operations. This gives more than a factor of 2
saving over a naive method. Further savings can be obtained if we include the
ability to destroy links, in which case we only need (8nm-4n-4m-8)/3
operations. Unfortunately the latter scheme is more complicated so choosing the
correct order to interact the qubits is considerably more difficult. A half way
scheme, that keeps a modular generation but saves additional operations over
never destroying links requires only 3nm-2n-2m+4 operations. The first scheme
and the last scheme are the most practical for building a cluster state because
they split up the generation into the repetition of simple sections.Comment: 16 pages, 11 figure
