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arXiv · 2504.01083

Fault-tolerant correction-ready encoding of the [[7,1,3]] Steane code on a 2D grid

Andrea Rodriguez-Blanco·Ho Nam Nguyen·K. Birgitta Whaley
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Abstract

Practical quantum computation heavily relies on the ability to perform quantum error correction in a fault-tolerant manner. Fault-tolerant encoding is a critical first step, and careful consideration of the error correction cycle that follows is essential for ensuring the encoding's effectiveness and compatibility. In this work, we investigate various correction-ready encoding methods to fault-tolerantly prepare the zero-logical state of the [[7,1,3]] Steane code on a 2D grid. Through numerical simulations, we demonstrate that parity-check encoding with a few Flag-Bridge qubits outperforms verification-based encoding by achieving lower error rates and allowing flexible tuning of the performance-efficiency trade-off. Additionally, parity-check approach enables a compact hybrid protocol that combines encoding and error correction, capable of matching the performance of a standalone error correction protocol with perfect encoding. Surprisingly, compared to the resource-intensive Steane error correction, this low-overhead method still offers a practical advantage in noisy settings. These findings highlight the approach with Flag-Bridge qubits as a robust and adaptable solution for noisy near-term quantum hardware.

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Andrea Rodriguez-Blanco, Ho Nam Nguyen, K. Birgitta Whaley. 2025-04-01. Fault-tolerant correction-ready encoding of the [[7,1,3]] Steane code on a 2D grid. https://arxiv.org/abs/2504.01083

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