Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective
We conceive and investigate the family of classical topological error correction codes (TECCs), which have the bits of a codeword arranged in a lattice structure. We then present the classical-to-quantum isomorphism to pave the way for constructing their quantum dual pairs, namely, the quantum TECCs...
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IEEE
2018-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8218756/ |
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| author | Daryus Chandra Zunaira Babar Hung Viet Nguyen Dimitrios Alanis Panagiotis Botsinis Soon Xin Ng Lajos Hanzo |
| author_facet | Daryus Chandra Zunaira Babar Hung Viet Nguyen Dimitrios Alanis Panagiotis Botsinis Soon Xin Ng Lajos Hanzo |
| author_sort | Daryus Chandra |
| collection | DOAJ |
| description | We conceive and investigate the family of classical topological error correction codes (TECCs), which have the bits of a codeword arranged in a lattice structure. We then present the classical-to-quantum isomorphism to pave the way for constructing their quantum dual pairs, namely, the quantum TECCs (QTECCs). Finally, we characterize the performance of QTECCs in the face of the quantum depolarizing channel in terms of both the quantum-bit error rate (QBER) and fidelity. Specifically, from our simulation results, the threshold probability of the QBER curves for the color codes, rotated-surface codes, surface codes, and toric codes are given by <inline-formula> <tex-math notation="LaTeX">$1.8 \times 10^{-2}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$1.3 \times 10^{-2}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$6.3 \times 10^{-2}$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$6.8 \times 10^{-2}$ </tex-math></inline-formula>, respectively. Furthermore, we also demonstrate that we can achieve the benefit of fidelity improvement at the minimum fidelity of 0.94, 0.97, and 0.99 by employing the 1/7-rate color code, the 1/9-rate rotated-surface code, and 1/13-rate surface code, respectively. |
| first_indexed | 2024-04-12T05:29:03Z |
| format | Article |
| id | doaj.art-8c2bc20db6d54f9caf975439c94e4d99 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-12T05:29:03Z |
| publishDate | 2018-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-8c2bc20db6d54f9caf975439c94e4d992022-12-22T03:46:10ZengIEEEIEEE Access2169-35362018-01-016137291375710.1109/ACCESS.2017.27844178218756Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism PerspectiveDaryus Chandra0https://orcid.org/0000-0003-2406-7229Zunaira Babar1Hung Viet Nguyen2https://orcid.org/0000-0001-6349-1044Dimitrios Alanis3https://orcid.org/0000-0002-6654-1702Panagiotis Botsinis4Soon Xin Ng5Lajos Hanzo6https://orcid.org/0000-0002-2636-5214School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.School of Electronics and Computer Science, University of Southampton, Southampton, U.K.We conceive and investigate the family of classical topological error correction codes (TECCs), which have the bits of a codeword arranged in a lattice structure. We then present the classical-to-quantum isomorphism to pave the way for constructing their quantum dual pairs, namely, the quantum TECCs (QTECCs). Finally, we characterize the performance of QTECCs in the face of the quantum depolarizing channel in terms of both the quantum-bit error rate (QBER) and fidelity. Specifically, from our simulation results, the threshold probability of the QBER curves for the color codes, rotated-surface codes, surface codes, and toric codes are given by <inline-formula> <tex-math notation="LaTeX">$1.8 \times 10^{-2}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$1.3 \times 10^{-2}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$6.3 \times 10^{-2}$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$6.8 \times 10^{-2}$ </tex-math></inline-formula>, respectively. Furthermore, we also demonstrate that we can achieve the benefit of fidelity improvement at the minimum fidelity of 0.94, 0.97, and 0.99 by employing the 1/7-rate color code, the 1/9-rate rotated-surface code, and 1/13-rate surface code, respectively.https://ieeexplore.ieee.org/document/8218756/Quantum error correction codesquantum stabilizer codesquantum topological codeslattice codeLDPC |
| spellingShingle | Daryus Chandra Zunaira Babar Hung Viet Nguyen Dimitrios Alanis Panagiotis Botsinis Soon Xin Ng Lajos Hanzo Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective IEEE Access Quantum error correction codes quantum stabilizer codes quantum topological codes lattice code LDPC |
| title | Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective |
| title_full | Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective |
| title_fullStr | Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective |
| title_full_unstemmed | Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective |
| title_short | Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective |
| title_sort | quantum topological error correction codes the classical to quantum isomorphism perspective |
| topic | Quantum error correction codes quantum stabilizer codes quantum topological codes lattice code LDPC |
| url | https://ieeexplore.ieee.org/document/8218756/ |
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