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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Main Authors: Seok-Hyung Lee, Felix Thomsen, Nicholas Fazio, Benjamin J. Brown, Stephen D. Bartlett
Format: Article
Language:English
Published: American Physical Society 2025-07-01
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.
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institution Kabale University
issn 2691-3399
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publishDate 2025-07-01
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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
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AT felixthomsen lowoverheadmagicstatedistillationwithcolorcodes
AT nicholasfazio lowoverheadmagicstatedistillationwithcolorcodes
AT benjaminjbrown lowoverheadmagicstatedistillationwithcolorcodes
AT stephendbartlett lowoverheadmagicstatedistillationwithcolorcodes