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  • Open Access

Quantum Routing and Entanglement Dynamics Through Bottlenecks

Dhruv Devulapalli1,2,*, Chao Yin3,†, Andrew Y. Guo4, Eddie Schoute5,6, Andrew M. Childs1,7,8, Alexey V. Gorshkov1,2, and Andrew Lucas3

  • *Contact author: devulapallidhruv@gmail.com
  • †Contact author: chao.yin@colorado.edu
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PRX Quantum 7, 010310 – Published 15 January, 2026

DOI: https://doi.org/10.1103/7b1x-hjcy

Abstract

To implement arbitrary quantum circuits in architectures with restricted interactions, one may effectively simulate all-to-all connectivity by routing quantum information. We consider the entanglement dynamics and routing between two regions only connected through an intermediate “bottleneck” region with few qubits. In such systems, where the entanglement rate is restricted by a vertex boundary rather than an edge boundary of the underlying interaction graph, existing results such as the small incremental entangling theorem give only a trivial constant lower bound on the routing time (the minimum time to perform an arbitrary permutation). We significantly improve the lower bound on the routing time in systems with a vertex bottleneck. Specifically, for any system with two regions L,R with NL,NR qubits, respectively, coupled only through an intermediate region C with NC qubits, for any δ>0 we show a lower bound of Ω(NR1−δ/NLNC) on the Hamiltonian quantum routing time when using piecewise time-independent Hamiltonians, or time-dependent Hamiltonians subject to a smoothness condition. We also prove an upper bound on the average amount of bipartite entanglement between L and C,R that can be generated in time t by such architecture-respecting Hamiltonians in systems constrained by vertex bottlenecks, improving the scaling in the system size from O(NLt) to O(NLt). As a special case, when applied to the star graph (i.e., one vertex connected to N leaves), we obtain an Ω(N1−δ) lower bound on the routing time and on the time to prepare N/2 Bell pairs between the vertices. We also show that, in systems of free particles, we can route optimally on the star graph in time Θ(N) using Hamiltonian quantum routing, obtaining a speedup over gate-based routing, which takes time Θ(N).

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Popular Summary

Quantum computers are expected to perform certain information-processing tasks far more efficiently than classical computers. However, implementing quantum algorithms in current architectures is challenging since only specific pairs of qubits can directly interact. One way to overcome this limitation is by routing or moving quantum information between parts of the device. In this work, we investigate fundamental limits on how quickly routing can be performed, especially in architectures where two large regions of qubits can communicate only through a small “bottleneck” region. We find that such bottlenecks strongly constrain the minimum time needed to perform routing.

We show that previous analysis of such systems underestimated the time required to perform routing. By combining ideas from entanglement dynamics theory with recent results on quantum simulation, we establish new lower bounds on the routing time that scale with the number of qubits in each region. We also derive bounds on how rapidly entanglement can be generated between the two regions. In systems of noninteracting identical particles (fermions or bosons), we discover a routing protocol that matches our lower bound and achieves a speedup for routing using a continuous-time evolution rather than conventional gate-based methods.

These results shed light on how bottlenecks may limit the performance of quantum computers. They may guide the design of scalable architectures and help characterize the overheads of implementing quantum algorithms. More broadly, our results on entanglement dynamics could also help understand which other quantum operations are slow on realistic architectures and quantum systems.

Article Text

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PRX Quantum 7, 010310– Published 15 January, 2026
  • Received 3 June 2025
  • Accepted 2 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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