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IEEE/ACM Symposium on Edge Computing (SEC)

Congestion-free Multiflow Quantum Tree Network with Logarithmic Overhead

Hyeongrak Choi, Marc Grau Davis, Dirk Englund

Published Dec 1, 2022• 1 citation
Publisher

Abstract

We propose quantum tree network (QTN) designs that are 1) free from congestion in multiflow communications, 2) optimal routing with only local information (self-information) and 3) completely covers 2D surface, 4) with only logarithmic overhead. If the channel is dominated by the insertion loss and the communication is limited by the local gates, as in current state-of-the-art technologies, the overhead is log(N), while this is relaxed to the general cases with poly-log overhead by engaging repeater chains in the long range communication.

DOI
10.1109/sec54971.2022.00061

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We propose quantum tree network (QTN) designs that are 1) free from congestion in multiflow communications, 2) optimal routing with only local information (self-information) and 3) completely covers 2D surface, 4) with only logarithmic overhead. If the channel is dominated by the insertion loss and the communication is limited by the local gates, as in current state-of-the-art technologies, the overhead is log(N), while this is relaxed to the general cases with poly-log overhead by engaging repeater chains in the long range communication.
We introduce Quantum Tree Networks (QTN), an architecture for hierarchical multi-flow entanglement routing. The network design is a kkk-ary tree where end nodes are situated on the leaves and routers at the internal nodes, with each node connected to kkk nodes in the child layer. The channel length between nodes grows with a rate aka_kak​, increasing as one ascends from the leaf to the root node. This construction allows for congestion-free and error-corrected operation with qubit-per-node overhead to scale sublinearly with the number of end nodes, NNN. The overhead for a kkk-ary QTN scales as O(Nlog⁡kak⋅log⁡kN)\mathcal{O}(N^{\log_k a_k} \cdot \log_k N)O(Nlogk​ak​⋅logk​N) and is sublinear for all kkk with minimal surface-covering end nodes. More specifically, the overhead of quarternary (k=4k=4k=4) QTN is ∼O(N0.25⋅log⁡4N)\sim \mathcal{O}(N^{0.25}\cdot\log_4 N)∼O(N0.25⋅log4​N). Alternatively, when end nodes are distributed over a square lattice, the quaternary tree routing gives the overhead ∼O(N⋅log⁡4N)\sim \mathcal{O}(\sqrt{N}\cdot\log_4 N)∼O(N​⋅log4​N). Our network-level simulations demonstrate a size-independent threshold behavior of QTNs. Moreover, tree network routing avoids the necessity for intricate multi-path finding algorithms, streamlining the network operation. With these properties, the QTN architecture satisfies crucial requirements for scalable quantum networks.
Long-range quantum communication and its associated repeater network are a necessity for any future quantum Internet. The performance of such networks is currently limited by the time it takes to establish entangled links between the appropriate parties on the network. Typically this scales as the round trip time for a signal to be transmitted between those parties. We present in this talk the design of a communications network for the direct transfer of quantum information where the rate at which quantum data can be transmitted is not limited by the distance the information needs to be sent but instead by the time to perform efficient local gate operations. Our scheme requires neither the establishment of entanglement between communication nodes nor the use of long-lived quantum memories. Our scheme thus provides a much higher communications rate than in standard teleportation based schemes.
Limited connectivity makes nonlocal quantum gates expensive on near-neighbor hardware, where compilation typically relies on SWAP transport, inheriting both depth overhead and path congestion. We present a swap-free routing framework in which higher levels of a qudit act as orthogonal spectral buses that transport control information without moving the computational state. We show that exact congestion relief in nearest-neighbor architectures requires local Hilbert-space expansion. In this model, a nonlocal operation over a path of length LLL requires 2L+12L+12L+1 logical routing primitives, compared to the 3L3L3L baseline. Overlapping routes remain distinguishable through bus labels encoded in the same physical qudits. This routing algebra extends to Boolean fan-in at a common target: multiple controls arriving on distinct buses trigger a local unitary based on an arbitrary Boolean function of bus digits, yielding multi-control operations of depth 2L+Dg+O(1)2L + D_g + O(1)2L+Dg​+O(1) for fan-in size KKK and target-synthesis cost DgD_gDg​. We prove decodability, reversibility, and correctness for CNOT and Boolean fan-in, along with a state-count lower bound d≥2K+1d \geq 2^{K+1}d≥2K+1 for exact overlap routing. Cirq simulations confirm single-control correctness and zero crosstalk. Compiler-level benchmarks on QFT, QAOA, and mirror-interaction circuits verify the predicted congestion law and transport reduction. Noisy QuTiP simulations show that the architectural advantage depends on higher-level coherence and speed. These results identify spectral qudit routing as a congestion-relief architecture that separates nonlocal control delivery from local target-side aggregation, providing a minimal mechanism for overcoming qubit routing limitations.
Long-range quantum communication and its associated repeater network are a necessity for any future quantum Internet. The performance of such networks is currently limited by the time it takes to establish entangled links between the appropriate parties on the network. Typically this scales as the round trip time for a signal to be transmitted between those parties. We present in this talk the design of a communications network for the direct transfer of quantum information where the rate at which quantum data can be transmitted is not limited by the distance the information needs to be sent but instead by the time to perform efficient local gate operations. Our scheme requires neither the establishment of entanglement between communication nodes nor the use of long-lived quantum memories. Our scheme thus provides a much higher communications rate than in standard teleportation based schemes.
Quantum network coding with classical assistance can transmit quantum information with fidelity one in error-free quantum channels. However, the dependency on classical network solutions leads to higher communication complexity and transmission congestion over a large-scale network with bottleneck channels. We find that certain types of quantum operation are sufficient to support multiple unicast sessions over the extended butterfly network. Furthermore, this construction decouples classical communication (assisting decoding information) from classical network solution. Based on this design, we propose an optimal protocol for this specific network, which significantly reduces the communication cost.