Optimizing quantum repeater placement in terrestrial and non-terrestrial quantum networks

Abstract

Quantum networks rely on repeaters to distribute entangled qubit pairs for applications such as quantum key distribution and distributed quantum computing. Minimizing the number of repeaters—while meeting connectivity and range constraints—is central to making deployments practical at scale. This thesis unifies three complementary lines of work toward that goal for terrestrial and non-terrestrial quantum networks.

Two-Step Linear Programming (TSLP) is a scalable optimization framework that decomposes complex problems into two sequential linear programming steps to reduce computational complexity. First, a TSLP approach for repeater placement on existing infrastructure (terrestrial networks) is presented. Integer Linear Programming (ILP) is a mathematical modeling technique where variables are restricted to be integers to find the best possible outcome in a set of requirements. This work contributes a scalable optimization framework that addresses the computational limitations of traditional ILP models. While existing ILP solutions face O(n2) complexity, the proposed TSLP approach reduces this to O(n) variables. Simulation results on synthetic and real-world topologies show that TSLP dramatically decreases running time while achieving higher node connectivity through a strategic, slight increase in the number of repeaters. This advances research by enabling the design of large-scale fiber-based quantum networks that were previously computationally inaccessible.

Second, a drone-based (non-terrestrial) repeater network for serving ground stations is studied. A key contribution of this work is the development of a polynomial-time, two- stage algorithm that decouples coverage and connectivity requirements. Stage 1 optimizes the coverage of ground terminals, while Stage 2 ensures the network backbone is fully connected.

Third, the thesis addresses the need for fault tolerance in error-prone quantum networks by extending the 1-connected drone model to achieve 2-connectedness. The Delaunay Triangulation with pruning, Steiner points, and pruning again (DT-PSP) is a geometry-aware heuristic that minimizes the number of required drone-based repeaters by leveraging geometric properties. The major contribution here is the introduction of the DT-PSP approach based on Delaunay Triangulation and Steiner node placement.

Collectively, the proposed algorithms improve network connectivity and reduce deployment cost across diverse quantum-network settings. By bridging the gap between theoretical optimality and practical scalability, this PhD work provides a comprehensive toolkit for the real-world deployment of future large-scale quantum networks.

Date of Thesis submission	2026
Original language	English
Awarding Institution	Western Sydney University
Sponsors	Australian Government Research Training Program Scholarship
Supervisor	Weisheng Si (Supervisor) & Rodrigo Neves Calheiros (Supervisor)