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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.19833 |
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| _version_ | 1866918002200412160 |
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| author | Nyirahafashimana, Valentine Shah, Nurisya Mohd Halim, Umair Abdul Othman, Mohamed Husain, Sharifah Kartini Said |
| author_facet | Nyirahafashimana, Valentine Shah, Nurisya Mohd Halim, Umair Abdul Othman, Mohamed Husain, Sharifah Kartini Said |
| contents | We propose quaternion-based strategies for quantum error correction by extending quantum mechanics into quaternionic Hilbert spaces. Building on the properties of quaternionic quantum states, we define quaternionic analogues of Pauli operators and quantum gates, ensuring inner product preservation and Hilbert space conditions. A simple encoding scheme maps logical qubits into quaternionic systems, introducing natural redundancy and enhanced resilience against noise. We construct a quaternionic extension of the five-qubit code, introducing a framework of 15 syndrome measurements to detect quaternionic errors, including quaternionically rotated error components. Numerical estimates show that the quaternionic five-qubit code achieves a logical error threshold of approximately $p_{th} \approx 0.015$, demonstrating improved performance compared to the standard complex-valued code. These results suggest a new pathway for quantum error correction in high-noise environments, leveraging the richer structure of quaternionic quantum mechanics to improve fault tolerance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19833 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Error Correction in Quaternionic Hilbert Spaces Nyirahafashimana, Valentine Shah, Nurisya Mohd Halim, Umair Abdul Othman, Mohamed Husain, Sharifah Kartini Said Quantum Physics Mathematical Physics We propose quaternion-based strategies for quantum error correction by extending quantum mechanics into quaternionic Hilbert spaces. Building on the properties of quaternionic quantum states, we define quaternionic analogues of Pauli operators and quantum gates, ensuring inner product preservation and Hilbert space conditions. A simple encoding scheme maps logical qubits into quaternionic systems, introducing natural redundancy and enhanced resilience against noise. We construct a quaternionic extension of the five-qubit code, introducing a framework of 15 syndrome measurements to detect quaternionic errors, including quaternionically rotated error components. Numerical estimates show that the quaternionic five-qubit code achieves a logical error threshold of approximately $p_{th} \approx 0.015$, demonstrating improved performance compared to the standard complex-valued code. These results suggest a new pathway for quantum error correction in high-noise environments, leveraging the richer structure of quaternionic quantum mechanics to improve fault tolerance. |
| title | Quantum Error Correction in Quaternionic Hilbert Spaces |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2504.19833 |