Subject: [Qirg] Architectural considerations for quantum networks

From: Alexander Pirker <[email-masked]>
Date: Wed, 13 Mar 2019 09:49:41 +0100

Dear all,

as I am also a member of the QIRG list, I've noticed the latest  
discussions regarding quantum network stacks, link layer, etc.

I wanted to point at two works which me and Wolfgang Dür here at  
Innsbruck (one of them together with Julius Wallnöfer) did recently,  
which might be of interest for you. Particularly, I mean the following  
two works:

"Modular architectures for quantum networks"
https://iopscience.iop.org/article/10.1088/1367-2630/aac2aa

"A quantum network stack and protocols for reliable entanglement-based  
networks"
https://iopscience.iop.org/article/10.1088/1367-2630/ab05f7

The first work presents network architectures for quantum networks  
which use multipartite entangled states to generate arbitrary graph  
states among clients (which is the ultimate goal in our quantum  
networks as we define them, since this also includes the sending of  
states by means of teleportation). Specifically, we introduce there  
the notion of switches and routers which connect either by GHZ states  
of decreasing size or m-partite, fully connected decorated graph  
states. Clients solely connect to these devices, which implies they  
need minimal functionality. In a request the clients ask the network  
to share a certain state, and the network devices shall generate that  
state. We provide a protocol which achieves this for both states (GHZ,  
decorated state).

The second work outlines how a quantum network stack for quantum  
networks (which use entanglement) could look like. Here we assume  
again that the ultimate goal of clients is to share arbitrary graph  
states (as this is the most general scenario). We have identified four  
different layers which allow for this in a coordinated and  
straightforward manner:

1. Physical layer: Quantum channels connecting network devices.  
Responsible for establishing short-link entanglement. Possible  
protocols are sender-receiver, midpoint etc.

2. Connectivity layer: Quantum repeaters. Responsible for establishing  
long-distance entanglement. Possible protocols are repeater protocols  
(EPP recurrence based, EPP hashing based, encoded, etc).

3. Link layer: Quantum switches. Responsible for defining the boundary  
of a network, which network devices connect in the same network, and  
generating arbitrary graph states among clients in a network. Devices  
here connect via the network states which we identified in the first  
work. For this layer we also identified so-called reliable protocols.  
Protocols in general are the protocols of the first work.

4. Network layer: Quantum routers. Responsible for enabling for  
inter-network graph state generation among clients. In order to do so,  
we proposed a routing protocol for GHZ states which allows for the  
generation of a virtual network state among requesting devices. Since  
in that case, the requesting devices just have to run the protocols of  
layer 3 to complete a graph state request of clients.

In addition to this we provide a full example how the elements and  
layers in that stack combine. Specifically, we show how they work  
together in a concrete inter-network graph state request, including  
routing and graph state generation. Finally, we also discuss  
reachability in quantum networks (which is more or less the counter  
part to a classical ping). We believe that this closely relates to  
checking for entanglement across network devices.

Best regards
Alexander Pirker