Smallest quantum codes for amplitude damping noise

• URL: http://arxiv.org/abs/2410.00155v1
• Date: Mon, 30 Sep 2024 18:55:09 GMT
• Title: Smallest quantum codes for amplitude damping noise
• Authors: Sourav Dutta, Aditya Jain, Prabha Mandayam,
• Abstract summary: We describe the smallest quantum error correcting (QEC) code to correct for amplitude-damping (AD) noise, namely, a 3-qubit code. We generalize this construction to create a family of codes that correct AD noise up to any fixed order.
• Score: 6.58877386288094
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We describe the smallest quantum error correcting (QEC) code to correct for amplitude-damping (AD) noise, namely, a 3-qubit code that corrects up to first order in the damping strength. We generalize this construction to create a family of codes that correct AD noise up to any fixed order. We underpin the fundamental connection between the structure of our codes and the noise structure via a relaxed form of the Knill-Laflamme conditions, that are different from existing formulations of approximate QEC conditions. Although the recovery procedure for this code is non-deterministic, our codes are optimal with respect to overheads and outperform existing codes to tackle AD noise in terms of entanglement fidelity. This alternate formulation of approximate QEC in fact leads us to a new class of quantum codes tailored to AD noise and also gives rise to a noise-adapted quantum Hamming bound for AD noise.

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