Triangular color codes on trivalent graphs with flag qubits
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available superconducting hardware despite constrained qubit connectivity. To guide...
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| Veröffentlicht in: | New journal of physics 2020-02, Vol.22 (2), p.23019, Article 023019 |
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| creator | Chamberland, Christopher Kubica, Aleksander Yoder, Theodore J Zhu, Guanyu |
| description | The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available superconducting hardware despite constrained qubit connectivity. To guide this experimental effort, we study the storage threshold of the triangular color code against circuit-level depolarizing noise. First, we adapt the Restriction Decoder to the setting of the triangular color code and to phenomenological noise. Then, we propose a fault-tolerant implementation of the stabilizer measurement circuits, which incorporates flag qubits. We show how information from flag qubits can be used in an efficient and scalable way with the Restriction Decoder to maintain the effective distance of the code. We numerically estimate the threshold of the triangular color code to be 0.2%, which is competitive with the thresholds of other topological quantum codes. We also prove that 1-flag stabilizer measurement circuits are sufficient to preserve the full code distance, which may be used to find simpler syndrome extraction circuits of the color code. |
| doi_str_mv | 10.1088/1367-2630/ab68fd |
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Its two-dimensional version, the triangular color code, may soon be realized with currently available superconducting hardware despite constrained qubit connectivity. To guide this experimental effort, we study the storage threshold of the triangular color code against circuit-level depolarizing noise. First, we adapt the Restriction Decoder to the setting of the triangular color code and to phenomenological noise. Then, we propose a fault-tolerant implementation of the stabilizer measurement circuits, which incorporates flag qubits. We show how information from flag qubits can be used in an efficient and scalable way with the Restriction Decoder to maintain the effective distance of the code. We numerically estimate the threshold of the triangular color code to be 0.2%, which is competitive with the thresholds of other topological quantum codes. We also prove that 1-flag stabilizer measurement circuits are sufficient to preserve the full code distance, which may be used to find simpler syndrome extraction circuits of the color code.</description><identifier>ISSN: 1367-2630</identifier><identifier>EISSN: 1367-2630</identifier><identifier>DOI: 10.1088/1367-2630/ab68fd</identifier><identifier>CODEN: NJOPFM</identifier><language>eng</language><publisher>BRISTOL: IOP Publishing</publisher><subject>Circuits ; Color ; Depolarization ; Dimensional tolerances ; Error correcting codes ; Error correction ; Fault tolerance ; fault-tolerant quantum error correction ; Flags ; Gates (circuits) ; Logic circuits ; Physical Sciences ; Physics ; Physics, Multidisciplinary ; quantum error correction ; Qubits (quantum computing) ; Science & Technology ; topological codes ; Topology</subject><ispartof>New journal of physics, 2020-02, Vol.22 (2), p.23019, Article 023019</ispartof><rights>2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft</rights><rights>2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). 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Phys</addtitle><description>The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available superconducting hardware despite constrained qubit connectivity. To guide this experimental effort, we study the storage threshold of the triangular color code against circuit-level depolarizing noise. First, we adapt the Restriction Decoder to the setting of the triangular color code and to phenomenological noise. Then, we propose a fault-tolerant implementation of the stabilizer measurement circuits, which incorporates flag qubits. We show how information from flag qubits can be used in an efficient and scalable way with the Restriction Decoder to maintain the effective distance of the code. We numerically estimate the threshold of the triangular color code to be 0.2%, which is competitive with the thresholds of other topological quantum codes. We also prove that 1-flag stabilizer measurement circuits are sufficient to preserve the full code distance, which may be used to find simpler syndrome extraction circuits of the color code.</description><subject>Circuits</subject><subject>Color</subject><subject>Depolarization</subject><subject>Dimensional tolerances</subject><subject>Error correcting codes</subject><subject>Error correction</subject><subject>Fault tolerance</subject><subject>fault-tolerant quantum error correction</subject><subject>Flags</subject><subject>Gates (circuits)</subject><subject>Logic circuits</subject><subject>Physical Sciences</subject><subject>Physics</subject><subject>Physics, Multidisciplinary</subject><subject>quantum error correction</subject><subject>Qubits (quantum computing)</subject><subject>Science & Technology</subject><subject>topological codes</subject><subject>Topology</subject><issn>1367-2630</issn><issn>1367-2630</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>O3W</sourceid><sourceid>AOWDO</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>DOA</sourceid><recordid>eNqNkM1v1DAQxS0EEmXpvcdIHDjA0vFHHFuc0IqPSpW4tGdrbMdbr0Kc2g4V_z3ZBi0cEOJij0bvvXn6EXJB4R0FpS4pl92WSQ6XaKUK_gk5O62e_jE_Jy9KOQBQqhg7I-9vcsRxPw-YG5eGdHx9X5o0NjXH7zj0Y232Gae70jzEeteEAffN_WxjLS_Js4BD6c9__Rty--njze7L9vrr56vdh-utE0LVrXfWSu2daClFGbz30DqpAypOmdCy7TpLFdDWC-4gaBQarQCrnWDet8g35GrN9QkPZsrxG-YfJmE0j4uU9wZzjW7oDZXAucMlwzEhhdVcqKCkdlQoHihfsl6tWVNO93NfqjmkOY9LfcN4y0EDWyhtCKwql1MpuQ-nqxTMEbc58jRHnmbFvVjerJaH3qZQXOxH159sANDyru0oXSboFrX6f_UuVqwxjbs0j3Wxvl2tMU2_y_-j1-u_yMfDZBgzzADjQLWZfOA_ATDkrWQ</recordid><startdate>20200201</startdate><enddate>20200201</enddate><creator>Chamberland, Christopher</creator><creator>Kubica, Aleksander</creator><creator>Yoder, Theodore J</creator><creator>Zhu, Guanyu</creator><general>IOP Publishing</general><general>Iop Publishing Ltd</general><scope>O3W</scope><scope>TSCCA</scope><scope>AOWDO</scope><scope>BLEPL</scope><scope>DTL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>H8D</scope><scope>L7M</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0003-3239-5783</orcidid></search><sort><creationdate>20200201</creationdate><title>Triangular color codes on trivalent graphs with flag qubits</title><author>Chamberland, Christopher ; Kubica, Aleksander ; Yoder, Theodore J ; Zhu, Guanyu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c448t-dcbb69dc4511a6fddd05c69fa8312496577b18015d43c0f9a49ab40b9c42dd5a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Circuits</topic><topic>Color</topic><topic>Depolarization</topic><topic>Dimensional tolerances</topic><topic>Error correcting codes</topic><topic>Error correction</topic><topic>Fault tolerance</topic><topic>fault-tolerant quantum error correction</topic><topic>Flags</topic><topic>Gates (circuits)</topic><topic>Logic circuits</topic><topic>Physical Sciences</topic><topic>Physics</topic><topic>Physics, Multidisciplinary</topic><topic>quantum error correction</topic><topic>Qubits (quantum computing)</topic><topic>Science & Technology</topic><topic>topological codes</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chamberland, Christopher</creatorcontrib><creatorcontrib>Kubica, Aleksander</creatorcontrib><creatorcontrib>Yoder, Theodore J</creatorcontrib><creatorcontrib>Zhu, Guanyu</creatorcontrib><collection>Institute of Physics Open Access Journal Titles</collection><collection>IOPscience (Open Access)</collection><collection>Web of Science - Science Citation Index Expanded - 2020</collection><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>New journal of physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chamberland, Christopher</au><au>Kubica, Aleksander</au><au>Yoder, Theodore J</au><au>Zhu, Guanyu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Triangular color codes on trivalent graphs with flag qubits</atitle><jtitle>New journal of physics</jtitle><stitle>NJP</stitle><stitle>NEW J PHYS</stitle><addtitle>New J. 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We show how information from flag qubits can be used in an efficient and scalable way with the Restriction Decoder to maintain the effective distance of the code. We numerically estimate the threshold of the triangular color code to be 0.2%, which is competitive with the thresholds of other topological quantum codes. We also prove that 1-flag stabilizer measurement circuits are sufficient to preserve the full code distance, which may be used to find simpler syndrome extraction circuits of the color code.</abstract><cop>BRISTOL</cop><pub>IOP Publishing</pub><doi>10.1088/1367-2630/ab68fd</doi><tpages>23</tpages><orcidid>https://orcid.org/0000-0003-3239-5783</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Circuits Color Depolarization Dimensional tolerances Error correcting codes Error correction Fault tolerance fault-tolerant quantum error correction Flags Gates (circuits) Logic circuits Physical Sciences Physics Physics, Multidisciplinary quantum error correction Qubits (quantum computing) Science & Technology topological codes Topology |
| title | Triangular color codes on trivalent graphs with flag qubits |
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