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A Framework for Distributed Resource Allocation in Quantum Networks

Nitish K. Panigrahy, Leonardo Bacciottini, C. V. Hollot, Emily A. Van Milligen, Matheus Guedes de Andrade, Nageswara S. V. Rao, Gayane Vardoyan, Don Towsley

TL;DR

The paper introduces a distributed framework for allocating quantum network resources using Quantum Network Utility Maximization (QNUM) and a primal–dual algorithm (QPrimalDual) that operates with local information and modest classical messaging. It formalizes a sequential-quantum-network implementation with q-datagrams and ACKs, and provides stability guarantees (global for concave utilities, local for some non-concave cases) along with practical extensions to mitigate decoherence and reduce control overhead. Through simulations on dumbbell and NSFNet topologies, the approach outperforms baselines, remains scalable, and demonstrates resilience to latency and memory decoherence. The work offers a practical foundation for fully distributed resource allocation in evolving quantum networks and points to future work on delays, alternative swapping architectures, and broader utility classes.

Abstract

We introduce a distributed resource allocation framework for the Quantum Internet that relies on feedback-based, fully decentralized coordination to serve multiple co-existing applications. We develop quantum network control algorithms under the mathematical framework of Quantum Network Utility Maximization (QNUM), where utility functions quantify network performance by mapping entanglement rate and quality into a joint optimization objective. We then introduce QPrimal-Dual, a decentralized, scalable algorithm that solves QNUM by strategically placing network controllers that operate using local state information and limited classical message exchange. We prove global asymptotic stability for concave, separable utility functions, and provide sufficient conditions for local stability for broader non-concave cases. To reduce control overhead and account for quantum memory decoherence, we also propose schemes that locally approximate global quantities and prevent congestion in the network. We evaluate the performance of our approach via simulations in realistic quantum network architectures. Results show that QPrimalDual significantly outperforms baseline allocation strategies, scales with network size, and is robust to latency and decoherence. Our observations suggest that QPrimalDual could be a practical, high-performance foundation for fully distributed resource allocation in quantum networks.

A Framework for Distributed Resource Allocation in Quantum Networks

TL;DR

The paper introduces a distributed framework for allocating quantum network resources using Quantum Network Utility Maximization (QNUM) and a primal–dual algorithm (QPrimalDual) that operates with local information and modest classical messaging. It formalizes a sequential-quantum-network implementation with q-datagrams and ACKs, and provides stability guarantees (global for concave utilities, local for some non-concave cases) along with practical extensions to mitigate decoherence and reduce control overhead. Through simulations on dumbbell and NSFNet topologies, the approach outperforms baselines, remains scalable, and demonstrates resilience to latency and memory decoherence. The work offers a practical foundation for fully distributed resource allocation in evolving quantum networks and points to future work on delays, alternative swapping architectures, and broader utility classes.

Abstract

We introduce a distributed resource allocation framework for the Quantum Internet that relies on feedback-based, fully decentralized coordination to serve multiple co-existing applications. We develop quantum network control algorithms under the mathematical framework of Quantum Network Utility Maximization (QNUM), where utility functions quantify network performance by mapping entanglement rate and quality into a joint optimization objective. We then introduce QPrimal-Dual, a decentralized, scalable algorithm that solves QNUM by strategically placing network controllers that operate using local state information and limited classical message exchange. We prove global asymptotic stability for concave, separable utility functions, and provide sufficient conditions for local stability for broader non-concave cases. To reduce control overhead and account for quantum memory decoherence, we also propose schemes that locally approximate global quantities and prevent congestion in the network. We evaluate the performance of our approach via simulations in realistic quantum network architectures. Results show that QPrimalDual significantly outperforms baseline allocation strategies, scales with network size, and is robust to latency and decoherence. Our observations suggest that QPrimalDual could be a practical, high-performance foundation for fully distributed resource allocation in quantum networks.

Paper Structure

This paper contains 28 sections, 2 theorems, 32 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. Quantum Network Model
  3. A Distributed Algorithm for Resource Allocation
  4. Distributed solution to QNUM via primal-dual approach
  5. Stability analysis of primal-dual
  6. An efficient bi-level implementation
  7. Implementation in Sequential Quantum Networks
  8. q-datagrams and ACKs
  9. Controller state
  10. Roles of the session and link controllers, and the sink
  11. QPrimalDual extensions
  12. QPrimalDual-approx
  13. QPrimalDual-DA
  14. QPrimalDual-PI
  15. Handling q-datagram losses
  16. ...and 13 more sections

Key Result

Theorem 3.1

Concave Utilities: Assume that $U_r(R_r,\vec{w_r})$ is concave and separable over $(R_r,\overrightarrow{w_r}).$ Under this condition and other previously mentioned assumptions, the equilibrium point $(\vec{R}^*, \vec{w}^*, \vec{\lambda}^*, \vec{\mu}^*)$ is globally asymptotically stable.

Figures (15)

  • Figure 1:
  • Figure 2:
  • Figure 4:
  • Figure 5:
  • Figure 7: q-datagram header (classical) fields for QPrimalDual implementation in sequential quantum networks.
  • ...and 10 more figures

Theorems & Definitions (5)

  • Definition 1
  • Definition 2
  • Theorem 3.1
  • Theorem 3.2
  • Remark 1