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Abstract We investigate the ground states of spin models defined on networks that we imprint (e.g., non-complex random networks like Erdos–Renyi, or complex networks like Watts–Strogatz, and Barabasi–Albert), and their response to decohering processes which we model with network attacks. We quantify the complexity of these ground states, and their response to the attacks, by calculating distributions of network measures of an emergent network whose link weights are the pairwise mutual information between spins. We focus on attacks which projectively measure spins. We find that the emergent networks in the ground state do not satisfy the usual criteria for complexity, and their average properties are captured well by a single dimensionless parameter in the Hamiltonian. While the response of classical networks to attacks is well-studied, where classical complex networks are known to be more robust to random attacks than random networks, we find counter-intuitive results for our quantum networks. We find that the ground states for Hamiltonians defined on different classes of imprinted networks respond similarly to all our attacks, and the attacks rescale the average properties of the emergent network by a constant factor. Mean field theory explains these results for relatively dense networks, but we also find the simple rescaling behavior away from the regime of validity of mean field theory. Our calculations indicate that complex spin networks are not more robust to projective measurement attacks, and presumably also other quantum attacks, than non-complex spin networks, in contrast to the classical case. Understanding the response of the spin networks to decoherence and attacks will have applications in understanding the physics of open quantum systems, and in designing robust complex quantum systems—possibly even a robust quantum internet in the long run—that is maximally resistant to decoherence.
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Complex quantum network models from spin clusters
Abstract In the emerging quantum internet, complex network topology could lead to efficient quantum communication and robustness against failures. However, there are concerns about complexity in quantum communication networks, such as potentially limited end-to-end transmission capacity. These challenges call for model systems in which the impact of complex topology on quantum communication protocols can be explored. Here, we present a theoretical model for complex quantum communication networks on a lattice of spins, wherein entangled spin clusters in interacting quantum spin systems serve as communication links between appropriately selected regions of spins. Specifically, we show that ground state Greenberger-Horne-Zeilinger clusters of the two-dimensional random transverse-field Ising model can be used as communication links between regions of spins. Further, the resulting quantum networks can have complexity comparable to that of the classical internet. Our work provides a generative model for further studies towards determining the network characteristics of the emerging quantum internet.
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- Award ID(s):
- 2310706
- PAR ID:
- 10524399
- Publisher / Repository:
- Communications Physics
- Date Published:
- Journal Name:
- Communications Physics
- Volume:
- 6
- Issue:
- 1
- ISSN:
- 2399-3650
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1038/s42005-023-01394-8
