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Quantum Entanglement Path Selection and Qubit Allocation via Adversarial Group Neural Bandits

Yin Huang, Lei Wang, Jie Xu

TL;DR

This paper addresses the online challenge of optimal path selection and qubit allocation, aiming to learn the best strategy for achieving the highest success rate of entanglement connections between two chosen quantum computers without prior knowledge of the success rate and in the presence of a QDN attacker.

Abstract

Quantum Data Networks (QDNs) have emerged as a promising framework in the field of information processing and transmission, harnessing the principles of quantum mechanics. QDNs utilize a quantum teleportation technique through long-distance entanglement connections, encoding data information in quantum bits (qubits). Despite being a cornerstone in various quantum applications, quantum entanglement encounters challenges in establishing connections over extended distances due to probabilistic processes influenced by factors like optical fiber losses. The creation of long-distance entanglement connections between quantum computers involves multiple entanglement links and entanglement swapping techniques through successive quantum nodes, including quantum computers and quantum repeaters, necessitating optimal path selection and qubit allocation. Current research predominantly assumes known success rates of entanglement links between neighboring quantum nodes and overlooks potential network attackers. This paper addresses the online challenge of optimal path selection and qubit allocation, aiming to learn the best strategy for achieving the highest success rate of entanglement connections between two chosen quantum computers without prior knowledge of the success rate and in the presence of a QDN attacker. The proposed approach is based on multi-armed bandits, specifically adversarial group neural bandits, which treat each path as a group and view qubit allocation as arm selection. Our contributions encompass formulating an online adversarial optimization problem, introducing the EXPNeuralUCB bandits algorithm with theoretical performance guarantees, and conducting comprehensive simulations to showcase its superiority over established advanced algorithms.

Quantum Entanglement Path Selection and Qubit Allocation via Adversarial Group Neural Bandits

TL;DR

This paper addresses the online challenge of optimal path selection and qubit allocation, aiming to learn the best strategy for achieving the highest success rate of entanglement connections between two chosen quantum computers without prior knowledge of the success rate and in the presence of a QDN attacker.

Abstract

Quantum Data Networks (QDNs) have emerged as a promising framework in the field of information processing and transmission, harnessing the principles of quantum mechanics. QDNs utilize a quantum teleportation technique through long-distance entanglement connections, encoding data information in quantum bits (qubits). Despite being a cornerstone in various quantum applications, quantum entanglement encounters challenges in establishing connections over extended distances due to probabilistic processes influenced by factors like optical fiber losses. The creation of long-distance entanglement connections between quantum computers involves multiple entanglement links and entanglement swapping techniques through successive quantum nodes, including quantum computers and quantum repeaters, necessitating optimal path selection and qubit allocation. Current research predominantly assumes known success rates of entanglement links between neighboring quantum nodes and overlooks potential network attackers. This paper addresses the online challenge of optimal path selection and qubit allocation, aiming to learn the best strategy for achieving the highest success rate of entanglement connections between two chosen quantum computers without prior knowledge of the success rate and in the presence of a QDN attacker. The proposed approach is based on multi-armed bandits, specifically adversarial group neural bandits, which treat each path as a group and view qubit allocation as arm selection. Our contributions encompass formulating an online adversarial optimization problem, introducing the EXPNeuralUCB bandits algorithm with theoretical performance guarantees, and conducting comprehensive simulations to showcase its superiority over established advanced algorithms.

Paper Structure

This paper contains 28 sections, 5 theorems, 21 equations, 9 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background
  4. Quantum Teleportation
  5. Entanglement Swapping
  6. Quantum Data Network
  7. System Model
  8. Network Architecture
  9. Problem Formulation
  10. Algorithm Design
  11. Adversarial Group Neural Bandits
  12. Function Approximation via Neural Network
  13. EXPNeuralUCB
  14. Regret Analysis
  15. Simulation Results
  16. ...and 13 more sections

Key Result

Lemma 1

For a sufficiently large network width $m$, $\forall r \in \mathcal{R}, \forall x \in \mathcal{X}_r^t$, there exists a $\theta_r^*$ at round $t$ such that with probability at least $1-\delta$, we have where $H_r$ is the neural tangent kernel (NTK) matrix for $h_r$ defined in zhou2020neural.

Figures (9)

  • Figure 1: Quantum Data Network. There exist four possible paths between Alice and Bob and one attacker aims to disrupt one of them. Note that different possible paths can have different success rates of establishing entanglement connections
  • Figure 2: Quantum Teleportation and Entanglement Swapping.
  • Figure 3: The topology of the QDN used in the simulation.
  • Figure 4: Regret achieved by EXPNeuralUCB and baselines.
  • Figure 5: Total reward achieved by EXPNeuralUCB and baselines.
  • ...and 4 more figures

Theorems & Definitions (9)

  • Lemma 1: Lemma 5.1 in zhou2020neural
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Theorem 1
  • proof
  • proof
  • proof
  • proof