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Decoherence-Aware Entangling and Swapping Strategy Optimization for Entanglement Routing in Quantum Networks

Shao-Min Huang, Cheng-Yang Cheng, Ming-Huang Chien, Jian-Jhih Kuo, Chih-Yu Wang

TL;DR

The paper tackles end-to-end entanglement routing in quantum networks under decoherence, introducing a short time-slot protocol and the TETRIS optimization problem to choose entangling/swapping strategies (numerologies) per request. It develops two algorithms: FNPR, a bi-criteria approximation using LP separation and randomized rounding, and FLTO, a DP-driven greedy method balancing fidelity and load via the REI index. Theoretical results establish NP-hardness and a bi-criteria performance bound for FNPR, while extensive simulations show substantial gains over state-of-the-art baselines (up to 60–78% in fidelity/throughput) across varied network settings and parameters. The work provides practical, scalable approaches to decoherence-aware entanglement routing, with clear implications for quantum network reliability and quantum-secured communications.

Abstract

Quantum teleportation enables high-security communications through end-to-end quantum entangled pairs. End-to-end entangled pairs are created by using swapping processes to consume short entangled pairs and generate long pairs. However, due to environmental interference, entangled pairs decohere over time, resulting in low fidelity. Thus, generating entangled pairs at the right time is crucial. Moreover, the swapping process also causes additional fidelity loss. To this end, this paper presents a short time slot protocol, where a time slot can only accommodate a process. It has a more flexible arrangement of entangling and swapping processes than the traditional long time slot protocol. It raises a new optimization problem TETRIS for finding strategies of entangling and swapping for each request to maximize the fidelity sum of all accepted requests. To solve the TETRIS, we design two novel algorithms with different optimization techniques. Finally, the simulation results manifest that our algorithms can outperform the existing methods by up to 60 ~ 78% in general, and by 20 ~ 75% even under low entangling probabilities.

Decoherence-Aware Entangling and Swapping Strategy Optimization for Entanglement Routing in Quantum Networks

TL;DR

The paper tackles end-to-end entanglement routing in quantum networks under decoherence, introducing a short time-slot protocol and the TETRIS optimization problem to choose entangling/swapping strategies (numerologies) per request. It develops two algorithms: FNPR, a bi-criteria approximation using LP separation and randomized rounding, and FLTO, a DP-driven greedy method balancing fidelity and load via the REI index. Theoretical results establish NP-hardness and a bi-criteria performance bound for FNPR, while extensive simulations show substantial gains over state-of-the-art baselines (up to 60–78% in fidelity/throughput) across varied network settings and parameters. The work provides practical, scalable approaches to decoherence-aware entanglement routing, with clear implications for quantum network reliability and quantum-secured communications.

Abstract

Quantum teleportation enables high-security communications through end-to-end quantum entangled pairs. End-to-end entangled pairs are created by using swapping processes to consume short entangled pairs and generate long pairs. However, due to environmental interference, entangled pairs decohere over time, resulting in low fidelity. Thus, generating entangled pairs at the right time is crucial. Moreover, the swapping process also causes additional fidelity loss. To this end, this paper presents a short time slot protocol, where a time slot can only accommodate a process. It has a more flexible arrangement of entangling and swapping processes than the traditional long time slot protocol. It raises a new optimization problem TETRIS for finding strategies of entangling and swapping for each request to maximize the fidelity sum of all accepted requests. To solve the TETRIS, we design two novel algorithms with different optimization techniques. Finally, the simulation results manifest that our algorithms can outperform the existing methods by up to 60 ~ 78% in general, and by 20 ~ 75% even under low entangling probabilities.
Paper Structure (34 sections, 8 theorems, 22 equations, 13 figures, 1 table)

This paper contains 34 sections, 8 theorems, 22 equations, 13 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background and Assumptions
  4. Fidelity and Decoherence of Entangled Pairs
  5. Entanglement Swapping
  6. Assumptions
  7. System Model & Problem Formulation
  8. System Model
  9. Problem Formulation
  10. NP-hardness and Inapproximability
  11. The Design of Fractional Numerology Packing and Rounding Algorithm (FNPR)
  12. The Combinatorial Algorithm
  13. The Separation Oracle
  14. The Randomized Rounding
  15. Bi-Criteria Approximation Ratio and Time Complexity
  16. ...and 19 more sections

Key Result

Lemma 1

For any given path $p$, there exists a one-to-one and onto mapping $f$, which maps a feasible strategy tree $\gamma$ to a feasible numerology $m$, while $f^{-1}$ denotes the inverse mapping, i.e., $f(\gamma)=m$ and $f^{-1}(m)=\gamma$.

Figures (13)

  • Figure 1: Scheduling of entangling and swapping in QN.
  • Figure 2: Fidelity loss due to elapsed time and swapping.
  • Figure 3: Numerologies induced by different strategy trees.
  • Figure 4: An illustrating example of transforming a numerology into a strategy tree.
  • Figure 5: Overlapping numerologies for two accepted requests.
  • ...and 8 more figures

Theorems & Definitions (19)

  • Definition 1
  • Definition 2
  • Lemma 1
  • proof
  • Definition 3
  • Definition 4
  • Theorem 1
  • proof
  • Corollary 1
  • Definition 5
  • ...and 9 more