Optimal Quantum Spatial Search on Random Temporal Networks
Abstract
To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a timeordered sequence of ErdösRényi random graphs G (n ,p ), where p is the probability that any two given nodes are connected: After every time interval τ , a new graph G (n ,p ) replaces the previous one. We prove analytically that, for any given p , there is always a range of values of τ for which the running time of the algorithm is optimal, i.e., O (√{n }), even when search on the individual static graphs constituting the temporal network is suboptimal. On the other hand, there are regimes of τ where the algorithm is suboptimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a timedependent network, it emerges that the nontrivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish highfidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.
 Publication:

Physical Review Letters
 Pub Date:
 December 2017
 DOI:
 10.1103/PhysRevLett.119.220503
 arXiv:
 arXiv:1701.04392
 Bibcode:
 2017PhRvL.119v0503C
 Keywords:

 Quantum Physics
 EPrint:
 Published version. Keywords: temporal networks, random graphs, quantum spatial search, quantum walks, quantum state transfer