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A continuous-time quantum walk is a quantum walk on a given graph that is dictated by a time-varying unitary matrix that relies on the Hamiltonian of the quantum system and the adjacency matrix. The concept of a CTQW is believed to have been first considered for quantum computation by Edward Farhi and Sam Gutmann; since many classical algorithms are based on random walks, the concept of CTQWs were originally considered to see if there could be quantum analogues of these algorithms with e.g. better time-complexity than their classical counterparts. In recent times, problems such as deciding what graphs admit properties such as perfect state transfer with respect to their CTQWs have been of particular interest.
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