Transfer and routing of Gaussian states through quantum complex networks with and without community structure

Markku Hahto; Johannes Nokkala; Guillermo García-Pérez; Sabrina Maniscalco; Jyrki Piilo

doi:10.22331/q-2025-05-20-1751

Transfer and routing of Gaussian states through quantum complex networks with and without community structure

Markku Hahto¹, Johannes Nokkala¹, Guillermo García-Pérez², Sabrina Maniscalco^2,3, and Jyrki Piilo¹

¹Department of Physics and Astronomy, University of Turku, FI-20014, Turun Yliopisto, Finland
²Algorithmiq Ltd, Kanavakatu 3 C, FI-00160, Helsinki, Finland
³Department of Physics, University of Helsinki, FI-00014 Helsinki, Finland

Published:	2025-05-20, volume 9, page 1751
Editor:	Roohollah Ghobadi
Eprint:	arXiv:2403.05623v2
Doi:	https://doi.org/10.22331/q-2025-05-20-1751
Citation:	Quantum 9, 1751 (2025).

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Abstract

The goal in quantum state transfer is to avoid the need to physically transport carriers of quantum information. This is achieved by using a suitably engineered Hamiltonian that induces the transfer of the state of one subsystem to another. A less known generalization of state transfer considers multiple systems such that any pair can exchange quantum information and transfers can take place at any time, starting and stopping independently. This is sometimes called routing of quantum states. State transfer in particular has received a great deal of attention, however the vast majority of results in both state transfer and routing concern qubits transferred in a network of restricted structure. Here we consider routing of single-mode Gaussian states and entanglement through complex networks of quantum harmonic oscillators. We compare a protocol where the transfer is completed in a single step but the effective Hamiltonian only approximately transfers the state with one where the transfer can in principle be perfect but the transfer is done in two steps, and also illustrate the state-dependency of the transfer fidelity. We find that even in a random and homogeneous network, the transfer fidelity still depends on the degree of the nodes for any link density, and that in both random and complex networks it is the community structure that controls the appearance of higher frequency normal modes useful for transfer. Finally, we find that networks of sufficient complexity may have superior routing performance over superficially similar random networks. Our results pave the way for further exploration of the role of community structure in state transfer and related tasks.

Popular summary

A key part of future quantum technologies is moving quantum information from one quantum system to another. Quantum state transfer achieves this by having the communicating parties couple to an intermediate system which acts as an information bus. The intermediate system is generally a network of interacting quantum systems which are similar to the communicating systems; this avoids the need to interface between systems of different nature, such as stationary oscillators and flying photons.

In this work, we investigate the role of the structure of the intermediate network on the quality of the transfer when Gaussian states are transferred over a network of quantum harmonic oscillators. Our focus is on finding networks in which multiple simultaneous transfers can happen, which is known as quantum state routing. We also consider how selected network properties, such as the degree distribution, affect the transfers.

Our main result is that networks with community structure are a suitable platform for routing. This may be of interest in quantum computing, since distributed computing potentially leads to modular architectures. The result can also serve as a basis for quantum-inspired community detection algorithms. We also present some tentative results about quantifying the suitability of a network for the routing task.

► BibTeX data

@article{Hahto2025transferroutingof,
  doi = {10.22331/q-2025-05-20-1751},
  url = {https://doi.org/10.22331/q-2025-05-20-1751},
  title = {Transfer and routing of {G}aussian states through quantum complex networks with and without community structure},
  author = {Hahto, Markku and Nokkala, Johannes and Garc{\'{i}}a-P{\'{e}}rez, Guillermo and Maniscalco, Sabrina and Piilo, Jyrki},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1751},
  month = may,
  year = {2025}
}

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Cited by

[1] Markku Hahto, Jyrki Piilo, and Johannes Nokkala, "State Transfer in Noisy Modular Quantum Networks", arXiv:2407.02145, (2024).

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