Quantum complex networks

WHAT ARE THEY?
Networks are any systems amenable to being partitioned into pairwise related subsystems; in some cases it is quite natural to use a network representation, while in others it may lead to a compact presentation that helps identifying the key features of an otherwise complicated system. Complex networks combine features from both lattices, such as having a high number of triangles, and from random networks, such as having high navigability. In some cases, in particular with quantum networks, complexity can also simply refer to networks that are not lattices. A network is said to be quantum when it requires a quantum description, for example when it represents an entangled state of a set of qubits or the interaction pattern of a set of quantum systems. Yet another example is a network of quantum channels.
OUR RESEARCH
Our research has so far focused on the following two avenues.
  1. We consider quantum information processing tasks on graphs implemented by quantum walks. More specifically, we have considered quantum spatial search by continuous-time quantum walks and investigated how the presence of noise affects the optimality of the search.
  2. We consider networks of interacting quantum systems as structured tunable environments for an open quantum system or the open system as a probe for the properties of the network. More recently, we have also proposed an implementation of these networks on a multimode optical platform. Simulations of the implementation suggest that while the size of the networks is limited to some tens of nodes, the structure is not a limiting factor; even networks of genuine complexity are in principle possible to impement in this way.
REFERENCES
  • M. A. C. Rossi, M. Cattaneo, M. G. A. Paris, S. Maniscalco: Non-Markovianity is not a resource in noisy quantum spatial search. ​[arXiv].
  • M. Cattaneo, M. A. C. Rossi, M. G. A. Paris, S. Maniscalco: Quantum spatial search on graphs subject to dynamical noise. Phys. Rev. A 98, 052347 (2018) [arXiv].
  • J. Nokkala, S. Maniscalco, J. Piilo: Non-Markovianity over ensemble averages in quantum complex networks. Open Systems & Information Dynamics 24, 1740018 (2017) [arXiv]. 
  • J. Nokkala, F. Arzani, F. Galve, R. Zambrini, S. Maniscalco, J. Piilo, N. Treps, V. Parigi: Reconfigurable optical implementation of quantum complex networks. New J. Phys. 20, 053024 (2018) [arXiv].
COLLABORATIONS
  • Applied Quantum Mechanics group of the University of Milan (quantum walks on graphs)
  • Multimode Quantum Optics group of the University of Sorbonne (networks of quantum harmonic oscillators).