Quantum Network Tomography for General Topology with SPAM Errors

2025-11-02

AI Summary

Quantum network tomography (QNT) aims to characterize internal quantum channels via peripheral operations, yet existing approaches are restricted to star-topology networks and simplistic noise models, with no established identifiability theory for general topologies. This work presents the first solution to QNT for arbitrary network topologies under general Pauli channels and state-preparation-and-measurement (SPAM) errors. We propose Mergecast—a novel protocol—and an asymptotic etching procedure to achieve unique identifiability of all internal channels. We further introduce the bypassable Pauli channel model and the BypassUnicast protocol for efficient estimation. Integrating SPAM error modeling, joint parameter estimation, and NetSquid-based simulation, we demonstrate high accuracy and robustness under realistic conditions, including photon loss and memory decoherence. Our framework establishes foundational identifiability guarantees and enables scalable, topology-agnostic QNT in practical quantum networks.

Technology Category

• Machine Learning: Quantum Machine Learning
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

The goal of quantum network tomography (QNT) is the characterization of internal quantum channels in a quantum network from external peripheral operations. Prior research has primarily focused on star networks featuring bit-flip and depolarizing channels, leaving the broader problem -- such as QNT for networks with arbitrary topologies and general Pauli channels -- largely unexplored. Moreover, establishing channel identifiability remains a significant challenge even in simplified quantum star networks. In the first part of this paper, we introduce a novel network tomography method, termed Mergecast, in quantum networks. We demonstrate that Mergecast, together with a progressive etching procedure, enables the unique identification of all internal quantum channels in networks characterized by arbitrary topologies and Pauli channels. As a side contribution, we introduce a subclass of Pauli channels, termed bypassable Pauli channels, and propose a more efficient unicast-based tomography method, called BypassUnicast, for networks exclusively comprising these channels. In the second part, we extend our investigation to a more realistic QNT scenario that incorporates state preparation and measurement (SPAM) errors. We rigorously formulate SPAM errors in QNT, propose estimation protocols for such errors within QNT, and subsequently adapt our Mergecast approaches to handle networks affected by SPAM errors. Lastly, we conduct NetSquid-based simulations to corroborate the effectiveness of our proposed protocols in identifying internal quantum channels and estimating SPAM errors in quantum networks. In particular, we demonstrate that Mergecast maintains good performance under realistic conditions, such as photon loss and quantum memory decoherence.

Problem

• Characterizing quantum network channels with arbitrary topologies and Pauli channels
• Addressing channel identifiability challenges in quantum network tomography
• Developing protocols for quantum networks with SPAM errors and realistic conditions

Innovation

• Mergecast enables unique identification of arbitrary topology networks
• BypassUnicast efficiently handles specific subclass of Pauli channels
• Protocols adapted to handle SPAM errors in quantum networks