The Dicke state |D n k is an equal-weight superposition of all n-qubit states with Hamming Weight k (i.e. all strings of length n with exactly k ones over a binary alphabet). Dicke states are an important class of entangled quantum states that among other things serve as starting states for combinatorial optimization quantum algorithms.We present a deterministic quantum algorithm for the preparation of Dicke states. Implemented as a quantum circuit, our scheme uses O(kn) gates, has depth O(n) and needs no ancilla qubits. The inductive nature of our approach allows for lineardepth preparation of arbitrary symmetric pure states and -used in reverse -yields a quasilinear-depth circuit for efficient compression of quantum information in the form of symmetric pure states, improving on existing work requiring quadratic depth. All of these properties even hold for Linear Nearest Neighbor architectures.

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With their blistering expansions in recent years, popular online social sites such as Twitter, Facebook and Bebo, have become some of the major news sources as well as the most effective channels for viral marketing nowadays. However, alongside these promising features comes the threat of misinformation propagation which can lead to undesirable effects, such as the widespread panic in the general public due to faulty swine flu tweets on Twitter in 2009. Due to the huge magnitude of online social network (OSN) users and the highly clustered structures commonly observed in these kinds of networks, it poses a substantial challenge to efficiently contain viral spread of misinformation in large-scale social networks.