Strategies for graph state growth
Earl Campbell
University of Oxford
Abstract: We propose some strategies for the construction of graphs with hybrid matter/optical architectures. The strategies are designed remove the need for post-selection in the face of (i) probabilistic entangling operations; (ii) imperfect path erasure. Upon failure of a probabilistic gate, a graph state is typically damaged. However, if a some local resource (e.g. an additional local qubits) is available this can act as a broker for the logical, client, qubit. This broker/client strategy prevents failures from doing damage to a graph, and hence, eliminates the need to use one of numerous strategies for graph growth that have an overhead resource cost.
When photon source are not identical, there is imperfect path erasure in hybrid architectures. Consequently, successful entangling operations are not maximally entangling. However, if the distinguishibility is calibrated and the error is monitored, the state will be a pure state. We propose an extension of the graph state language to track these errors. Furthermore, we propose a series of protocol for distilling a proper graph state, which are shown to be significantly more efficient than post-selection strategies.