Low-Overhead Magic State Distillation with Color Codes
Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but requires significant resources. Hence, it is crucial to tailor...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-07-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/ch5r-cnfq |
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| author | Seok-Hyung Lee Felix Thomsen Nicholas Fazio Benjamin J. Brown Stephen D. Bartlett |
| author_facet | Seok-Hyung Lee Felix Thomsen Nicholas Fazio Benjamin J. Brown Stephen D. Bartlett |
| author_sort | Seok-Hyung Lee |
| collection | DOAJ |
| description | Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but requires significant resources. Hence, it is crucial to tailor and optimize magic state distillation for specific codes from both logical- and physical-level perspectives. In this work, we perform such optimization for two-dimensional color codes, which are promising due to their higher encoding rates compared to surface codes, transversal implementation of Clifford gates, and efficient lattice surgery. We propose two carefully designed distillation schemes based on the 15-to-1 distillation circuit and lattice surgery, differing in their methods for handling faulty rotations. Our first scheme employs faulty T measurement, achieving infidelities of O(p^{3}) for physical noise strength p. To achieve lower infidelities, our second scheme integrates distillation with “cultivation” (a distillation-free approach to fault tolerantly prepare magic states through transversal Clifford measurements). Our second scheme achieves significantly lower infidelities (e.g., approximately 2×10^{−16} at p=10^{−3}), surpassing the capabilities of both cultivation and single-level distillation. Notably, to reach a given target infidelity, our schemes require approximately 2 orders of magnitude fewer resources than the previous best magic-state-distillation schemes for color codes. |
| format | Article |
| id | doaj-art-e1694b391b4a434a8d53c03de9df25eb |
| institution | Kabale University |
| issn | 2691-3399 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj-art-e1694b391b4a434a8d53c03de9df25eb2025-08-20T03:58:49ZengAmerican Physical SocietyPRX Quantum2691-33992025-07-016303031710.1103/ch5r-cnfqLow-Overhead Magic State Distillation with Color CodesSeok-Hyung LeeFelix ThomsenNicholas FazioBenjamin J. BrownStephen D. BartlettFault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but requires significant resources. Hence, it is crucial to tailor and optimize magic state distillation for specific codes from both logical- and physical-level perspectives. In this work, we perform such optimization for two-dimensional color codes, which are promising due to their higher encoding rates compared to surface codes, transversal implementation of Clifford gates, and efficient lattice surgery. We propose two carefully designed distillation schemes based on the 15-to-1 distillation circuit and lattice surgery, differing in their methods for handling faulty rotations. Our first scheme employs faulty T measurement, achieving infidelities of O(p^{3}) for physical noise strength p. To achieve lower infidelities, our second scheme integrates distillation with “cultivation” (a distillation-free approach to fault tolerantly prepare magic states through transversal Clifford measurements). Our second scheme achieves significantly lower infidelities (e.g., approximately 2×10^{−16} at p=10^{−3}), surpassing the capabilities of both cultivation and single-level distillation. Notably, to reach a given target infidelity, our schemes require approximately 2 orders of magnitude fewer resources than the previous best magic-state-distillation schemes for color codes.http://doi.org/10.1103/ch5r-cnfq |
| spellingShingle | Seok-Hyung Lee Felix Thomsen Nicholas Fazio Benjamin J. Brown Stephen D. Bartlett Low-Overhead Magic State Distillation with Color Codes PRX Quantum |
| title | Low-Overhead Magic State Distillation with Color Codes |
| title_full | Low-Overhead Magic State Distillation with Color Codes |
| title_fullStr | Low-Overhead Magic State Distillation with Color Codes |
| title_full_unstemmed | Low-Overhead Magic State Distillation with Color Codes |
| title_short | Low-Overhead Magic State Distillation with Color Codes |
| title_sort | low overhead magic state distillation with color codes |
| url | http://doi.org/10.1103/ch5r-cnfq |
| work_keys_str_mv | AT seokhyunglee lowoverheadmagicstatedistillationwithcolorcodes AT felixthomsen lowoverheadmagicstatedistillationwithcolorcodes AT nicholasfazio lowoverheadmagicstatedistillationwithcolorcodes AT benjaminjbrown lowoverheadmagicstatedistillationwithcolorcodes AT stephendbartlett lowoverheadmagicstatedistillationwithcolorcodes |