Optimal Switching Networks for Paired-Egress Bell State Analyzer Pools

TL;DR

This work tackles scalable interconnects for distributed quantum computing by designing planar $N\times N$ switching networks that route entangled photon pairs to a shared pool of Bell state analyzers (BSAs). It introduces three recursive planar designs—Triangular, Chevron, and Brickwork—that realize rearrangeable non-blocking paired-egress switching with a lower bound of $N(N-2)/4$ switches, and provides efficient routing algorithms. The routing approaches have worst-case complexity $O(N^2)$ and feature detailed depth analyses to assess loss implications, showing improvements over full permutation networks. Importantly, the designs are reversible and applicable to shared EPPS pools, enabling scalable entanglement distribution and swapping for distributed quantum computing and the quantum Internet.

Abstract

To scale quantum computers to useful levels, we must build networks of quantum computational nodes that can share entanglement for use in distributed forms of quantum algorithms. In one proposed architecture, node-to-node entanglement is created when nodes emit photons entangled with stationary memories, with the photons routed through a switched interconnect to a shared pool of Bell state analyzers (BSAs). Designs that optimize switching circuits will reduce loss and crosstalk, raising entanglement rates and fidelity. We present optimal designs for switched interconnects constrained to planar layouts, appropriate for silicon waveguides and Mach-Zehnder interferometer (MZI) $2 \times 2$ switch points. The architectures for the optimal designs are scalable and algorithmically structured to pair any arbitrary inputs in a rearrangeable, non-blocking way. For pairing $N$ inputs, $N(N - 2)/4$ switches are required, which is less than half of number of switches required for full permutation switching networks. An efficient routing algorithm is also presented for each architecture. These designs can also be employed in reverse for entanglement generation using a shared pool of entangled paired photon sources.

Figures (8)

• Figure 1: Deployment of switches in quantum networks for two possible scenarios: Left: Entanglement generation using shared EPPSs for two nodes in the network. Right: Entanglement consumption for entanglement swapping using shared BSAs. As in the lower portion of the figure, a switch can be composed of sets of $2\times 2$ switching points. Because distributing Bell pairs via EPPS (left) or performing entanglement swapping via BSA (right) are not location-dependent operations, we are free to select any reachable EPPS or BSA, offering the opportunity to reduce switch complexity compared to classical full permutation switches.
• Figure 2: (a) 4$\times$4 non-blocking planar paired-egress switching interconnect. Changing the state of the 2$\times$2 switch points achieves all possible photon pairings. (b) A rearrangeable non-blocking $12\times 12$ planar paired-egress switching interconnect. Switch points of the same signify that they are added within the same network size and constitute a layer. Semicircles represent BSAs.
• Figure 3: A chevron shaped 12 $\times$ 12 non-blocking planar paired-egress switching design. For an $N \times N$ network with odd $N/2$, a chevron shaped set of switch points, without switch point on line $N/2-1$ and $N/2$, is added. The total number of switch points is $N(N-2)/4$.
• Figure 4: Recursively constructing larger chevron circuits (Sec. \ref{['sec:Chevron']} and Fig. \ref{['fig:chevron']}) requires handling five possible cases as two inputs are added, one at the top and one at the bottom. The same colored lines denote the location of photons to be paired. (a) represents the case pairing the top-most photon with the bottom-most photon. In this case all the other input ports are paired using previously-constructed internal non-blocking network. After applying the last chevron layer (not shown) the paired photons shift up or shift down to finally pair in the BSAs layer. (b), (c) represents the case that the photons at the top-most port and bottom-most port have to be paired with two other photons in upper half part of the switch configuration. In (b) the two pairs face each other. In (c) the two pairs face the opposite side. (d), (e) represents the case that the photons at the most top port and most bottom port have to be paired with two other photons in lower half part of the switch configuration. In (d) the two pairs face each other. In (e) the two pairs face the opposite side.
• Figure 5: Brickwork design for a $12\times12$ switching network.