Quantum Circuit Switching with One-Way Repeaters in Star Networks

TL;DR

This work analyzes quantum circuit switching as a protocol to distribute quantum states in one-way quantum networks, and shows that requests are met at a higher rate when packets are distributed in parallel, although sequential distribution can generally provide service to a larger number of users simultaneously.

Abstract

Distributing quantum states reliably among distant locations is a key challenge in the field of quantum networks. One-way quantum networks address this by using one-way communication and quantum error correction. Here, we analyze quantum circuit switching as a protocol to distribute quantum states in one-way quantum networks. In quantum circuit switching, pairs of users can request the delivery of multiple quantum states from one user to the other. After waiting for approval from the network, the states can be distributed either sequentially, forwarding one at a time along a path of quantum repeaters, or in parallel, sending batches of quantum states from repeater to repeater. Since repeaters can only forward a finite number of quantum states at a time, a pivotal question arises: is it advantageous to send them sequentially (allowing for multiple requests simultaneously) or in parallel (reducing processing time but handling only one request at a time)? We compare both approaches in a quantum network with a star topology. Using tools from queuing theory, we show that requests are met at a higher rate when packets are distributed in parallel, although sequential distribution can generally provide service to a larger number of users simultaneously. We also show that using a large number of quantum repeaters to combat channel losses limits the maximum distance between users, as each repeater introduces additional processing delays. These findings provide insight into the design of protocols for distributing quantum states in one-way quantum networks.

Figures (12)

• Figure 1: In QCS, packets can be distributed (a) sequentially or (b) in parallel. Illustration of a QCS scheme with (a) sequential and (b) parallel distribution of packets, in a star network with five users and a single central repeater (big circle). The repeater contains $k=3$ forwarding stations (squares), therefore it can forward at most $k=3$ quantum data packets (triangles and pentagons) at a time. In sequential distribution of packets, a single forwarding station is reserved to meet each of the requests submitted by the pairs of users in orange and blue. In parallel distribution, all three stations are used in parallel to meet a single request at a time.
• Figure 2: Illustration of a star quantum network.$u$ users are at distance $L$ from a central repeater. There are $N$ repeaters between each user and the central repeater ($N=2$ in the figure), and each of them has $k$ forwarding stations (squares). The spacing between adjacent nodes is $L_0 = L/(N+1)$.
• Figure 3: A network with more forwarding stations $k$ can support more users, but only when distribution of packets is sequential. Critical number of users, $u_\mathrm{crit}$, vs number of forwarding stations, $k$, for QCS with sequential (blue dots) and parallel (orange crosses) distribution of packets, in the small budget use case (see (\ref{['eq.ucrit']}) and (\ref{['eq.Tservice_p1']})). The critical number of users is the maximum number of users the system can support before the sojourn time goes to infinity. In sequential distribution, $u_\mathrm{crit}(k)$ scales as $\sqrt{k}$. In parallel distribution, $u_\mathrm{crit}(k) = \mathrm{constant}$, $\forall k>n$. Parameters used in this figure: $N=0$, $p=1$, $n=7$, $w=10$, $\lambda_0 = 10^{-4}$$\mu$s$^{-1}$, $c=0.2$ km/$\mu$s, $t_\mathrm{fwd} = 100$$\mu$s.
• Figure 4: Parallel distribution of packets is generally faster. Relative difference in mean sojourn time (MST) between sequential and parallel packet distribution, for different numbers of users $u$ and forwarding stations $k$. (a) Small-budget use case ($p=1$; $w\geq n$; $N=0$, $L=1$ km) and (b) large-budget use case ($p\approx0.7$) with $N=0$, $L=7.5$ km, and $w=8$. Sequential/parallel distribution provides lower MST in blue/red regions. In regions with an 's'/'p', only sequential/parallel distribution can provide service (i.e., yield finite MST). In dark regions with an 'x', no service is possible. Parameters used in this figure: $n=7$, $\lambda_0 = 10^{-4}$$\mu$s$^{-1}$, $c=0.2$ km/$\mu$s, $t_\mathrm{fwd} = 100$$\mu$s. MSTs in (a) calculated with (\ref{['eq.Tservice_p1']}). MSTs in (b) calculated with Monte Carlo sampling with $10^4$ samples (the standard error in the relative difference in MST was below 0.5 for every combination of parameters).
• Figure 5: Networks with many users cannot cover long distances. Critical distance $L_\mathrm{crit}$ vs number of users $u$, for different numbers of repeaters $N$. Parameters used in this figure: sequential distribution, $n=7$, $w\rightarrow\infty$, $k=12$, $\lambda_0 = 10^{-4}$$\mu$s$^{-1}$, $c=0.2$ km/$\mu$s, $t_\mathrm{fwd} = 100$$\mu$s.