Quantum Routing and Entanglement Dynamics Through Bottlenecks

Journal Article · Thu Jan 15 00:00:00 EST 2026 · PRX Quantum

DOI:https://doi.org/10.1103/7b1x-hjcy· OSTI ID:3025085

Devulapalli, Dhruv ^[1]; Yin, Chao ^[2]; Guo, Andrew Y. ^[3]; Schoute, Eddie ^[4]; Childs, Andrew M. ^[1]; Gorshkov, Alexey V. ^[1]; Lucas, Andrew ^[2]

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1. NIST/University of Maryland, College Park, MD (United States)
2. University of Colorado, Boulder, CO (United States)
3. Quantinuum, Broomfield, CO (United States)
4. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); MIT-IBM Watson AI Lab, Cambridge, MA (United States)

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 𝑁_𝐿,𝑁_𝑅 qubits, respectively, coupled only through an intermediate region 𝐶 with 𝑁_𝐶 qubits, for any 𝛿 > 0 we show a lower bound of Ω⁢(𝑁$$^{1−𝛿}_{𝑅}$$/√𝑁_𝐿⁢𝑁_𝐶) 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⁡(𝑁_𝐿⁢𝑡) to 𝑂⁡(√𝑁_𝐿⁢𝑡). As a special case, when applied to the star graph (i.e., one vertex connected to 𝑁 leaves), we obtain an Ω⁡(√𝑁^1−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).

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); University of Maryland, College Park, MD (United States)
• Sponsoring Organization: Defense Advanced Research Projects Agency (DARPA); LDRD; Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); National Science Foundation (NSF); National Science Foundation (NSF) GRFP; National Science Foundation (NSF) QLCI; U.S. Air Force; USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR) (SC-31)
• Grant/Contract Number: 89233218CNA000001; SC0019040; SC0024220; SC0024324
• Other Award/Contract Number: OMA-2120757
• OSTI ID: 3025085
• Alternate ID(s): OSTI ID: 3023360
• Report Number(s): LA-UR-25-21861
• Journal Information: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 1 Vol. 7; ISSN 2691-3399
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Quantum Computing
Quantum Routing