[Paper Review] Optimising graph codes for measurement-based loss tolerance

Tom J. Bell, Love A. Pettersson+1 more|arXiv (Cornell University)|Dec 9, 2022

Optical Network Technologies4 citations

TL;DR

This paper develops analytical and optimization methods to enhance measurement-based loss tolerance in graph codes for photonic quantum technologies. By systematically analyzing and optimizing graph states, the authors identify codes with up to 12 qubits and modular large-scale constructions that achieve a 10.5% photon loss threshold in fault-tolerant fusion-based quantum computing, significantly improving over prior benchmarks and enabling practical near-term photonic quantum applications.

ABSTRACT

Graph codes play an important role in photonic quantum technologies as they provide significant protection against qubit loss, a dominant noise mechanism. Here, we develop methods to analyse and optimise measurement-based tolerance to qubit loss and computational errors for arbitrary graph codes. Using these tools we identify optimised codes with up to 12 qubits and asymptotically-large modular constructions. The developed methods enable significant benefits for various photonic quantum technologies, as we illustrate with novel all-photonic quantum repeater states for quantum communication and high-threshold fusion-based schemes for fault-tolerant quantum computing.

Motivation & Objective

• Address the challenge of photon loss as the dominant noise source in photonic quantum technologies.
• Develop general methods to analyze and optimize measurement-based loss tolerance in arbitrary graph codes.
• Design resource-efficient graph codes that minimize physical qubit overhead while maximizing loss and error tolerance.
• Enable practical improvements in photonic quantum communication and fault-tolerant quantum computing through optimized modular graph states.
• Provide open-source tools for researchers to adapt the framework to specific hardware constraints and error models.

Proposed method

• Formalize the loss tolerance of graph codes using stabilizer formalism and graph state properties, with stabilizer generators defined as $ K_i = X_i \prod_{k \in \mathcal{N}_i} Z_k $.
• Model measurement-based error correction via sequential destructive measurements on resource states, preserving unmeasured logical qubits.
• Implement a parallelized optimization framework using the BlueCrystal high-performance computing cluster to search for optimal graph structures up to 11 qubits.
• Analyze both transversal and adaptive fusion strategies for logical operations, evaluating their resilience to photon loss and fusion failure.
• Use a logical error suppression framework that tracks the probability of logical $ X $ and $ Z $ errors under loss, enabling threshold analysis.
• Integrate modular graph constructions to extrapolate performance to asymptotically large systems, identifying scalable loss-tolerant architectures.

Experimental results

Research questions

• RQ1 What is the maximum photon loss threshold achievable by measurement-based graph codes in fault-tolerant photonic quantum computing?
• RQ2 How can graph code structures be systematically optimized to maximize loss tolerance while minimizing physical qubit overhead?
• RQ3 To what extent do modular graph designs improve loss tolerance compared to standard tree or beacon codes?
• RQ4 How does the choice between transversal and adaptive fusion strategies affect the achievable loss threshold in fusion-based quantum computing?
• RQ5 Can optimized graph codes significantly improve performance in all-photonic quantum repeater schemes and other photonic quantum technologies?

Key findings

• The authors identify graph codes with up to 12 physical qubits that achieve a 10.5% photon loss threshold in fault-tolerant fusion-based quantum computing using standard non-boosted linear optical fusion gates.
• For transversal fusion schemes, the loss threshold is 4.9%, demonstrating a trade-off between implementation simplicity and noise resilience.
• Optimized modular graph constructions show asymptotic improvements in loss tolerance, suggesting orders-of-magnitude gains over conventional tree graph codes.
• The developed optimization framework identifies suboptimal use of existing codes—such as tree graphs and Shor-Beacon codes—in current photonic quantum applications.
• The study reveals that the loss threshold is sensitive to physical fusion gate performance, with concave trade-offs between success rate and ancilla photon loss.
• The authors make their full optimization and analysis code publicly available, enabling adaptation to diverse hardware platforms and error models.