In this work we propose a quantum-walk model, named controlled intermittent quantum walks (CIQWs), where one performs a continuous quantum walk for a period of time under a certain control signal and then adjusts the control signal and performs a continuous quantum walk for another period of time under the new control signal, repeating the operation in this way. We apply the model to tackle the fundamental problem of finding an unknown marked vertex on a graph, known as spatial search, obtaining a universal quantum search algorithm. For any graph with any number of marked vertices, our CIQW-based algorithm achieves a quadratic speedup in query complexity over classical random-walk-based algorithms. Compared to state-of-the-art results in quantum spatial search, our algorithm achieves significantly lower query complexity in certain cases. Furthermore, by using the simpler Laplacian matrix as the Hamiltonian for our continuous-time quantum walk, we facilitate a more concrete and concise search algorithm. These features distinguish our work and add a fresh perspective to the growing body of quantum spatial search algorithms.

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• Quantum algorithms & computation