  Reliable entangling gates for qubits encoded in single-photon states
represent a major challenge on the road to scalable quantum computing
architectures based on linear optics. In this work, we present two approaches
to develop high-fidelity, near-deterministic controlled-sign-shift gates based
on the techniques of quantum gate teleportation. On the one hand, teleportation
in a discrete-variable setting, i.e., for qubits, offers unit-fidelity
operations but suffers from low success probabilities. Here, we apply recent
results on advanced linear optical Bell measurements to reach a
near-deterministic regime. On the other hand, in the setting of continuous
variables, associated with coherent states, squeezing, and, typically, Gaussian
states, teleportation can be performed in a deterministic fashion, but the
finite amount of squeezing implies an inevitable deformation of a teleported
single-mode state. Using a new generalized form of the nonlinear-sign-shift
gate for gate teleportation, we are able to achieve fidelities of the resulting
CSIGN gate above 90%. A special focus is also put on a comparison of the two
approaches, not only with respect to fidelity and success probability, but also
in terms of resource consumption.
