51. Quadratic Speedup for Spatial Search by Continuous-Time Quantum Walk
- Author
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Apers, Simon, Chakraborty, Shantanav, Goncalves Novo, Leonardo Filipe, Roland, Jérémie, Apers, Simon, Chakraborty, Shantanav, Goncalves Novo, Leonardo Filipe, and Roland, Jérémie
- Abstract
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a quadratic advantage over classical random walks has been an outstanding problem. Thus far, this advantage is obtained only for specific graphs or when a single node of the underlying graph is marked. In this Letter, we provide a new continuous-time quantum walk search algorithm that completely resolves this: our algorithm can find a marked node in any graph with any number of marked nodes, in a time that is quadratically faster than classical random walks. The overall algorithm is quite simple, requiring time evolution of the quantum walk Hamiltonian followed by a projective measurement. A key component of our algorithm is a purely analogue procedure to perform operations on a state of the form e-tH2, SCOPUS: ar.j, info:eu-repo/semantics/published
- Published
- 2022