Noise-adapted qudit codes for amplitude-damping noise

• URL: http://arxiv.org/abs/2406.02444v1
• Date: Tue, 4 Jun 2024 16:07:26 GMT
• Title: Noise-adapted qudit codes for amplitude-damping noise
• Authors: Sourav Dutta, Debjyoti Biswas, Prabha Mandayam,
• Abstract summary: We propose a class of qudit error correcting codes tailored to protect against amplitude-damping noise. Specifically, we construct a class of four-qudit codes that satisfies the error correction conditions for all single-qudit and a few two-qudit damping errors. For the $d=2$ case, our QEC scheme is identical to the known example of the $4$-qubit code and the associated syndrome-based recovery.
• Score: 6.320926638892934
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum error correction (QEC) plays a critical role in preventing information loss in quantum systems and provides a framework for reliable quantum computation. Identifying quantum codes with nice code parameters for physically motivated noise models remains an interesting challenge. Going beyond qubit codes, here we propose a class of qudit error correcting codes tailored to protect against amplitude-damping noise. Specifically, we construct a class of four-qudit codes that satisfies the error correction conditions for all single-qudit and a few two-qudit damping errors up to the leading order in the damping parameter $\gamma$. We devise a protocol to extract syndromes that identify this set of errors unambiguously, leading to a noise-adapted recovery scheme that achieves a fidelity loss of $\cO(\gamma^{2})$. For the $d=2$ case, our QEC scheme is identical to the known example of the $4$-qubit code and the associated syndrome-based recovery. We also assess the performance of our class of codes using the Petz recovery map and note some interesting deviations from the qubit case.

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