par Apers, Simon 
;Chakraborty, Shantanav ;Goncalves Novo, Leonardo Filipe ;Roland, Jérémie
Référence Physical review letters, 129, 16
Publication Publié, 2022-10
;Chakraborty, Shantanav ;Goncalves Novo, Leonardo Filipe ;Roland, Jérémie Référence Physical review letters, 129, 16
Publication Publié, 2022-10
Article révisé par les pairs
| Résumé : | 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 |
