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

• URL: http://arxiv.org/abs/2504.01083v1
• Date: Tue, 01 Apr 2025 18:00:30 GMT
• Title: Fault-tolerant correction-ready encoding of the [[7,1,3]] Steane code on a 2D grid
• Authors: Andrea Rodriguez-Blanco, Ho Nam Nguyen, K. Birgitta Whaley,
• Abstract summary: We investigate various correction-ready encoding methods to fault-tolerantly prepare the zero-logical state of the Steane code on a 2D grid.<n>We show that parity-check encoding with a few Flag-Bridge qubits outperforms verification-based encoding by achieving lower error rates.<n>Surprisingly, compared to the resource-intensive Steane error correction, this low-overhead method still offers a practical advantage in noisy settings.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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