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Role of Error Syndromes in Teleportation Scheduling

Aparimit Chandra, Filip Rozpędek, Don Towsley

TL;DR

This work addresses scheduling teleportation requests in quantum networks where memory decoherence and stochastic EPR generation limit fidelity. By incorporating error-syndrome information from repeated quantum error correction, the authors define Freshest Qubit First (FQF), a scheduling policy that selects the qubit with the lowest estimated logical-error probability, and prove its batch-optimality. They derive conditional error probabilities from a 3-qubit repetition code under dephasing noise and connect them to teleportation fidelity, enabling quantitative policy evaluation. Through simulations of batch and continuous arrivals, FQF consistently improves teleportation fidelity, with gains increasing for larger batches and higher system load, and interacting favorably with pushout buffer control. The results offer a practical route to higher-fidelity quantum communication in near-term networks and highlight directions for future work on larger codes and richer syndrome information.

Abstract

Quantum teleportation enables quantum information transmission, but requires distribution of entangled resource states. Unfortunately, decoherence, caused by environmental interference during quantum state storage, can degrade quantum states, leading to entanglement loss in the resource state and reduction of the fidelity of the teleported information. In this work, we investigate the use of error correction and error syndrome information in scheduling teleportation at a quantum network node in the presence of multiple teleportation requests and a finite rate of remote entanglement distribution. Specifically, we focus on the scenario where stored qubits undergo decoherence over time due to imperfect memories. To protect the qubits from the resulting errors, we employ quantum encodings, and the stored qubits undergo repeated error correction, generating error syndromes in each round. These error syndromes can provide additional benefits, as they can be used to calculate qubit-specific error likelihoods, which can then be utilized to make better scheduling decisions. By integrating error correction techniques into the scheduling process, our goal is to minimize errors and decoherence effects, thereby enhancing the fidelity and efficiency of teleportation in a quantum network setting.

Role of Error Syndromes in Teleportation Scheduling

TL;DR

This work addresses scheduling teleportation requests in quantum networks where memory decoherence and stochastic EPR generation limit fidelity. By incorporating error-syndrome information from repeated quantum error correction, the authors define Freshest Qubit First (FQF), a scheduling policy that selects the qubit with the lowest estimated logical-error probability, and prove its batch-optimality. They derive conditional error probabilities from a 3-qubit repetition code under dephasing noise and connect them to teleportation fidelity, enabling quantitative policy evaluation. Through simulations of batch and continuous arrivals, FQF consistently improves teleportation fidelity, with gains increasing for larger batches and higher system load, and interacting favorably with pushout buffer control. The results offer a practical route to higher-fidelity quantum communication in near-term networks and highlight directions for future work on larger codes and richer syndrome information.

Abstract

Quantum teleportation enables quantum information transmission, but requires distribution of entangled resource states. Unfortunately, decoherence, caused by environmental interference during quantum state storage, can degrade quantum states, leading to entanglement loss in the resource state and reduction of the fidelity of the teleported information. In this work, we investigate the use of error correction and error syndrome information in scheduling teleportation at a quantum network node in the presence of multiple teleportation requests and a finite rate of remote entanglement distribution. Specifically, we focus on the scenario where stored qubits undergo decoherence over time due to imperfect memories. To protect the qubits from the resulting errors, we employ quantum encodings, and the stored qubits undergo repeated error correction, generating error syndromes in each round. These error syndromes can provide additional benefits, as they can be used to calculate qubit-specific error likelihoods, which can then be utilized to make better scheduling decisions. By integrating error correction techniques into the scheduling process, our goal is to minimize errors and decoherence effects, thereby enhancing the fidelity and efficiency of teleportation in a quantum network setting.
Paper Structure (16 sections, 1 theorem, 23 equations, 3 figures)

This paper contains 16 sections, 1 theorem, 23 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Memory Noise and Error Correction
  4. Scheduling Choices
  5. Buffer Control
  6. Error Likelihood Analytics
  7. Teleportation Fidelity
  8. Batch Arrivals
  9. Evaluation through simulation
  10. Batch teleportation
  11. Continuous Arrivals
  12. Effects of Continuous Batch arrivals
  13. Conclusion
  14. Future Work
  15. Appendix
  16. ...and 1 more sections

Key Result

Theorem 1

Of all service policies, FQF minimizes probability of logical error for serving arrivals within a single batch.

Figures (3)

  • Figure 1: Average $Pr[e']$ for different batch sizes and $\tau = 0.003 s$ under YQF and FQF, dotted lines correspond to YQF.
  • Figure 2: CDF of $Pr[e']$ in an infinite buffer system with on demand EPR generation where $\tau = 0.003 s, \Gamma = (1/0.02) Hz = 50Hz, \lambda_r = 90 Hz, \lambda_e = 100 Hz$
  • Figure 3: Average fidelity of teleportation with changing load for different rates and buffer sizes. Solid lines are for performance under FQF and dotted lines are for YQF. The EPR generation rates and buffer sizes are scaled according to the batch size with $\lambda_r$ adjusted to keep the load on the system consistent with the x axis.

Theorems & Definitions (1)

  • Theorem 1