Quantum Codes for Generalized Amplitude-damping Noise
Abstract
Quantum error correcting (QEC) plays a crucial role in protecting quantum information against decoherence and enabling scalable, reliable quantum computing. One of the most realistic and ubiquitous sources of noise affecting quantum hardware today is generalized amplitude-damping (GAD) noise. Conventional, deterministic QEC codes struggle to correct for GAD noise because of their inherent structure, leading to fidelity losses that scale linearly with the damping strength. In this work, we introduce the framework of probabilistic approximate quantum error correction (PAQEC), that combines the flexibility of approximate QEC with the potential of post-selected recovery, enabling high-fidelity, resource-efficient error correction. We construct a five-qubit permutation-invariant code that, under probabilistic recovery, achieves a fidelity loss quadratic in the damping strength, thus outperforming existing QEC codes. Formulating PAQEC as an optimization problem, we present a numerical technique based on Charnes-Cooper and semidefinite programming to identify the optimal recovery map for any PAQEC code. Our results establish PAQEC as a powerful tool for developing resource-efficient, high-fidelity quantum codes tailored to realistic noise, with promising implications for near-term quantum devices and future fault-tolerant architectures.
Related
- The classical capacity of generalized amplitude-damping channels and its strong-converse exponent
- Convergence Analysis of the Quantum Blahut-Arimoto Algorithm and the Contraction Coefficient of Qubit Amplitude-Damping Channels
- Maximum-Likelihood Amplitude Estimation for Quantum Monte Carlo Integration on Trapped-Ion Hardware: Convergence, Noise-Floor Saturation, Depth-Dependent Bias
- Exact series formulas for the capacities of the amplitude damping channel
- Two-qubit binegativity can increase under local amplitude damping
BibTeX
@misc{dutta2026quantum,
title = {{Quantum Codes for Generalized Amplitude-damping Noise}},
author = {Sourav Dutta and Anubhab Rudra and Manav Seksaria and Anil Prabhakar and Prabha Mandayam},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15924},
eprint = {2609.15924},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15924},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Codes for Generalized Amplitude-damping Noise
AU - Sourav Dutta
AU - Anubhab Rudra
AU - Manav Seksaria
AU - Anil Prabhakar
AU - Prabha Mandayam
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15924
UR - https://arxiv.org/abs/2609.15924
AB - Quantum error correcting (QEC) plays a crucial role in protecting quantum information against decoherence and enabling scalable, reliable quantum computing. One of the most realistic and ubiquitous sources of noise affecting quantum hardware today is generalized amplitude-damping (GAD) noise. Conventional, deterministic QEC codes struggle to correct for GAD noise because of their inherent structure, leading to fidelity losses that scale linearly with the damping strength. In this work, we introduce the framework of probabilistic approximate quantum error correction (PAQEC), that combines the flexibility of approximate QEC with the potential of post-selected recovery, enabling high-fidelity, resource-efficient error correction. We construct a five-qubit permutation-invariant code that, under probabilistic recovery, achieves a fidelity loss quadratic in the damping strength, thus outperforming existing QEC codes. Formulating PAQEC as an optimization problem, we present a numerical technique based on Charnes-Cooper and semidefinite programming to identify the optimal recovery map for any PAQEC code. Our results establish PAQEC as a powerful tool for developing resource-efficient, high-fidelity quantum codes tailored to realistic noise, with promising implications for near-term quantum devices and future fault-tolerant architectures.
ER -