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Entanglement Distribution Delay Optimization in Quantum Networks with Distillation

Mahdi Chehimi, Kenneth Goodenough, Walid Saad, Don Towsley, Tony X. Zhou

TL;DR

This work tackles entanglement distribution delay in star-shaped quantum networks by introducing a joint QS resource allocation framework that optimizes end-to-end delay $T_{\mathrm{e2e}}$ while applying distillation to meet heterogeneous rate and fidelity requirements. It leverages NV-center based SPSs and memory with region- and isotopic-identity controls ($x_i,y_i$) and seven distillation schemes ($z_i$), deriving analytical expressions for average memory decoherence $\langle \lambda_{\mathrm{d,avg}} \rangle$ and resulting e2e fidelity, and solving a nonconvex optimization problem $\mathcal{P}1$ via simulated annealing. The approach demonstrates substantial gains over distillation-agnostic, minimal-distillation, and physics-agnostic baselines, achieving 30-50% delay reductions and modest fidelity trade-offs in simulations. This framework offers practical guidance for deploying quantum networks with NV centers, by balancing memory coherence, gate noise, and distillation overhead to meet diverse application needs. The results underscore the value of physics-aware resource control and distillation scheduling in reducing entanglement distribution delays in quantum networks.

Abstract

Quantum networks (QNs) distribute entangled states to enable distributed quantum computing and sensing applications. However, in such QNs, quantum switches (QSs) have limited resources that are highly sensitive to noise and losses and must be carefully allocated to minimize entanglement distribution delay. In this paper, a QS resource allocation framework is proposed, which jointly optimizes the average entanglement distribution delay and entanglement distillation operations, to enhance the end-to-end (e2e) fidelity and satisfy minimum rate and fidelity requirements. The proposed framework considers realistic QN noise and includes the derivation of the analytical expressions for the average quantum memory decoherence noise parameter, and the resulting e2e fidelity after distillation. Finally, practical QN deployment aspects are considered, where QSs can control 1) nitrogen-vacancy (NV) center SPS types based on their isotopic decomposition, and 2) nuclear spin regions based on their distance and coupling strength with the electron spin of NV centers. A simulated annealing metaheuristic algorithm is proposed to solve the QS resource allocation optimization problem. Simulation results show that the proposed framework manages to satisfy all users rate and fidelity requirements, unlike existing distillation-agnostic (DA), minimal distillation (MD), and physics-agnostic (PA) frameworks which do not perform distillation, perform minimal distillation, and does not control the physics-based NV center characteristics, respectively. Furthermore, the proposed framework results in around 30% and 50% reductions in the average e2e entanglement distribution delay compared to existing PA and MD frameworks, respectively. Moreover, the proposed framework results in around 5%, 7%, and 11% reductions in the average e2e fidelity compared to existing DA, PA, and MD frameworks, respectively.

Entanglement Distribution Delay Optimization in Quantum Networks with Distillation

TL;DR

This work tackles entanglement distribution delay in star-shaped quantum networks by introducing a joint QS resource allocation framework that optimizes end-to-end delay while applying distillation to meet heterogeneous rate and fidelity requirements. It leverages NV-center based SPSs and memory with region- and isotopic-identity controls () and seven distillation schemes (), deriving analytical expressions for average memory decoherence and resulting e2e fidelity, and solving a nonconvex optimization problem via simulated annealing. The approach demonstrates substantial gains over distillation-agnostic, minimal-distillation, and physics-agnostic baselines, achieving 30-50% delay reductions and modest fidelity trade-offs in simulations. This framework offers practical guidance for deploying quantum networks with NV centers, by balancing memory coherence, gate noise, and distillation overhead to meet diverse application needs. The results underscore the value of physics-aware resource control and distillation scheduling in reducing entanglement distribution delays in quantum networks.

Abstract

Quantum networks (QNs) distribute entangled states to enable distributed quantum computing and sensing applications. However, in such QNs, quantum switches (QSs) have limited resources that are highly sensitive to noise and losses and must be carefully allocated to minimize entanglement distribution delay. In this paper, a QS resource allocation framework is proposed, which jointly optimizes the average entanglement distribution delay and entanglement distillation operations, to enhance the end-to-end (e2e) fidelity and satisfy minimum rate and fidelity requirements. The proposed framework considers realistic QN noise and includes the derivation of the analytical expressions for the average quantum memory decoherence noise parameter, and the resulting e2e fidelity after distillation. Finally, practical QN deployment aspects are considered, where QSs can control 1) nitrogen-vacancy (NV) center SPS types based on their isotopic decomposition, and 2) nuclear spin regions based on their distance and coupling strength with the electron spin of NV centers. A simulated annealing metaheuristic algorithm is proposed to solve the QS resource allocation optimization problem. Simulation results show that the proposed framework manages to satisfy all users rate and fidelity requirements, unlike existing distillation-agnostic (DA), minimal distillation (MD), and physics-agnostic (PA) frameworks which do not perform distillation, perform minimal distillation, and does not control the physics-based NV center characteristics, respectively. Furthermore, the proposed framework results in around 30% and 50% reductions in the average e2e entanglement distribution delay compared to existing PA and MD frameworks, respectively. Moreover, the proposed framework results in around 5%, 7%, and 11% reductions in the average e2e fidelity compared to existing DA, PA, and MD frameworks, respectively.
Paper Structure (19 sections, 1 theorem, 34 equations, 6 figures, 1 table, 1 algorithm)

This paper contains 19 sections, 1 theorem, 34 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. System Model
  5. NV Centers and Entanglement Generation
  6. Quantum Channel Losses and Noise
  7. QS Quantum Memory Selection
  8. QS Entanglement Distillation Protocols
  9. Average E2E Noise and Entanglement Fidelity
  10. Average Quantum Memory Decoherence Noise
  11. E2E Entangled State Fidelity
  12. Delay-Minimizing QS Resource Allocation Optimization Formulation
  13. Average Entanglement Distribution Delay
  14. QS Resource Allocation Optimization Problem
  15. Proposed Solution
  16. ...and 4 more sections

Key Result

Theorem 1

The QS average quantum memory decoherence depolarizing noise parameter affecting $z_i$ entangled qubits stored in nuclear spins in region $y_i$ in a type-$x_i$ NV center in diamond for serving user $i\in\mathcal{U}$ averaged over all possible SISs is: where $R_i \equiv e^{-\frac{1}{T_{\mathrm{c}}(x_i,y_i)}}$ and $q_i \equiv 1 - P_{\mathrm{in}}(\theta_i,x_i)$. Here, $P_{\mathrm{in}}(\theta_i,x_i)$

Figures (6)

  • Figure 1: The proposed QN system model.
  • Figure 2: Average achieved e2e entanglement distribution delay, $T_{\mathrm{e2e}}$, for the different QN users.
  • Figure 3: Average achieved e2e fidelity, $F_{\mathrm{e2e}}$, for the different QN users.
  • Figure 4: Average achieved e2e fidelity, $F_{\mathrm{e2e}}$, for a user $i=4$ with an average distance of $d_4 = 1$ km from the QS vs $\theta_4$, in a 4-user QN.
  • Figure 5: Average achieved e2e entanglement generation rate, $R_{\mathrm{e2e}}$, for a user $4$ with an average distance of $d_4 = 1$ km from the QS vs $\theta_4$, in a 4-user QN.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof