  Quantum walks are the quantum-mechanical analog of random walks, in which a
quantum `walker' evolves between initial and final states by traversing the
edges of a graph, either in discrete steps from node to node or via continuous
evolution under the Hamiltonian furnished by the adjacency matrix of the graph.
We present a hybrid scheme for universal quantum computation in which a quantum
walker takes discrete steps of continuous evolution. This `discontinuous'
quantum walk employs perfect quantum state transfer between two nodes of
specific subgraphs chosen to implement a universal gate set, thereby ensuring
unitary evolution without requiring the introduction of an ancillary coin
space. The run time is linear in the number of simulated qubits and gates. The
scheme allows multiple runs of the algorithm to be executed almost
simultaneously by starting walkers one timestep apart.
