[{"data":1,"prerenderedAt":1412},["ShallowReactive",2],{"blog-post-docs\u002Fgpi-gate":3,"sibling-dives-docs\u002Fgpi-gate":1248,"learn-track-docs\u002Fgpi-gate":1249,"learn-docs-groups":1250},{"id":4,"title":5,"authors":6,"body":7,"breadcrumb":6,"builders":6,"byline":6,"category":1229,"categoryName":1230,"challenge":6,"courseAuthor":6,"courseLead":6,"dek":6,"description":1231,"draft":1232,"extension":1233,"eyebrow":6,"featured":1232,"finish":6,"fork":6,"group":1234,"groupName":1235,"hero":6,"heroAlt":6,"heroCta":6,"heroImage":6,"homepageFeatured":1232,"kind":1236,"lessonCount":6,"meta":1237,"navigation":990,"newsItems":6,"next":6,"ogImage":6,"order":1238,"outcomes":6,"path":1239,"publishDate":1240,"readingTime":6,"related":1241,"relatedProjects":6,"seo":1242,"stem":1245,"tags":1246,"track":6,"trackName":6,"__hash__":1247},"blog\u002Fblog\u002Flearn\u002Fdocs\u002Fgpi-gate.md","GPi gate",null,{"type":8,"value":9,"toc":1220},"minimark",[10,111,166,171,191,195,248,252,636,640,927,930,934,941,945,1061,1179,1188,1192,1216],[11,12,13,14,61,62,90,91,95,96,101,102,105,106,110],"p",{},"The GPi gate is an IonQ native gate: a half-turn (π) rotation about an axis in the XY plane of the Bloch sphere, with the axis set by a phase ",[15,16,19,42],"span",{"className":17},[18],"katex",[15,20,23],{"className":21},[22],"katex-mathml",[24,25,27],"math",{"xmlns":26},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[28,29,30,37],"semantics",{},[31,32,33],"mrow",{},[34,35,36],"mi",{},"ϕ",[38,39,41],"annotation",{"encoding":40},"application\u002Fx-tex","\\phi",[15,43,47],{"className":44,"ariaHidden":46},[45],"katex-html","true",[15,48,51,56],{"className":49},[50],"base",[15,52],{"className":53,"style":55},[54],"strut","height:0.8889em;vertical-align:-0.1944em;",[15,57,36],{"className":58},[59,60],"mord","mathnormal",". It acts on one qubit and takes one parameter, ",[15,63,65,78],{"className":64},[18],[15,66,68],{"className":67},[22],[24,69,70],{"xmlns":26},[28,71,72,76],{},[31,73,74],{},[34,75,36],{},[38,77,41],{"encoding":40},[15,79,81],{"className":80,"ariaHidden":46},[45],[15,82,84,87],{"className":83},[50],[15,85],{"className":86,"style":55},[54],[15,88,36],{"className":89},[59,60]," in turns, where 1 is a full rotation of the axis: ",[92,93,94],"code",{},"GPi(0)"," is an ",[97,98,100],"a",{"href":99},"\u002Flearn\u002Fdocs\u002Fx-gate","X gate"," and ",[92,103,104],{},"GPi(0.25)"," is a ",[97,107,109],{"href":108},"\u002Flearn\u002Fdocs\u002Fy-gate","Y gate",". It runs on Aria and Forte. Measured straight after it, a qubit that started as 0 reads 1, whatever the phase.",[11,112,113,114,160,161,165],{},"Kets such as ",[15,115,117,142],{"className":116},[18],[15,118,120],{"className":119},[22],[24,121,122],{"xmlns":26},[28,123,124,139],{},[31,125,126,130,134],{},[34,127,129],{"mathvariant":128},"normal","∣",[131,132,133],"mn",{},"0",[135,136,138],"mo",{"stretchy":137},"false","⟩",[38,140,141],{"encoding":40},"\\vert 0 \\rangle",[15,143,145],{"className":144,"ariaHidden":46},[45],[15,146,148,152,156],{"className":147},[50],[15,149],{"className":150,"style":151},[54],"height:1em;vertical-align:-0.25em;",[15,153,155],{"className":154},[59],"∣0",[15,157,138],{"className":158},[159],"mclose"," name the basis states and rotations are described on the Bloch sphere; the ",[97,162,164],{"href":163},"\u002Flearn\u002Fquantum-foundations\u002Fqubits","qubits lesson"," introduces both.",[167,168,170],"h2",{"id":169},"before-you-use-a-native-gate","Before you use a native gate",[11,172,173,174,177,178,181,182,185,186,190],{},"Native gates only run in a native-gate circuit, and a circuit cannot mix native and standard gates. In ",[92,175,176],{},"qiskit-ionq"," a backend is created for one gateset, ",[92,179,180],{},"provider.get_backend(name, gateset=\"native\")","; the pre-created ",[92,183,184],{},"backend"," on Qollab uses the standard gateset. Submitting native gates bypasses IonQ's compiler and optimiser and turns error mitigation off by default, which is why IonQ recommends them only for research work. See ",[97,187,189],{"href":188},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",".",[167,192,194],{"id":193},"call","Call",[196,197,198,210],"table",{},[199,200,201],"thead",{},[202,203,204,208],"tr",{},[205,206,207],"th",{},"Where",[205,209,194],{},[211,212,213,224,234],"tbody",{},[202,214,215,219],{},[216,217,218],"td",{},"Python",[216,220,221],{},[92,222,223],{},"qc.append(GPIGate(φ), [qubit])",[202,225,226,229],{},[216,227,228],{},"JS",[216,230,231],{},[92,232,233],{},"circuit.append(GPIGate(φ), [qubit])",[202,235,236,239],{},[216,237,238],{},"Class",[216,240,241,244,245],{},[92,242,243],{},"GPIGate",", from ",[92,246,247],{},"qiskit_ionq",[167,249,251],{"id":250},"matrix","Matrix",[15,253,256],{"className":254},[255],"katex-display",[15,257,259,366],{"className":258},[18],[15,260,262],{"className":261},[22],[24,263,265],{"xmlns":26,"display":264},"block",[28,266,267,363],{},[31,268,269,272,275,278,281,283,286,289],{},[34,270,271],{},"G",[34,273,274],{},"P",[34,276,277],{},"i",[135,279,280],{"stretchy":137},"(",[34,282,36],{},[135,284,285],{"stretchy":137},")",[135,287,288],{},"=",[31,290,291,293,361],{},[135,292,280],{"fence":46},[294,295,299,335],"mtable",{"rowspacing":296,"columnalign":297,"columnspacing":298},"0.16em","center center","1em",[300,301,302,310],"mtr",{},[303,304,305],"mtd",{},[306,307,308],"mstyle",{"scriptlevel":133,"displaystyle":137},[131,309,133],{},[303,311,312],{},[306,313,314],{"scriptlevel":133,"displaystyle":137},[315,316,317,320],"msup",{},[34,318,319],{},"e",[31,321,322,325,328,331,333],{},[135,323,324],{},"−",[131,326,327],{},"2",[34,329,330],{},"π",[34,332,277],{},[34,334,36],{},[300,336,337,355],{},[303,338,339],{},[306,340,341],{"scriptlevel":133,"displaystyle":137},[315,342,343,345],{},[34,344,319],{},[31,346,347,349,351,353],{},[131,348,327],{},[34,350,330],{},[34,352,277],{},[34,354,36],{},[303,356,357],{},[306,358,359],{"scriptlevel":133,"displaystyle":137},[131,360,133],{},[135,362,285],{"fence":46},[38,364,365],{"encoding":40},"GPi(\\phi) = \\begin{pmatrix} 0 & e^{-2\\pi i\\phi} \\\\ e^{2\\pi i\\phi} & 0 \\end{pmatrix}",[15,367,369,405],{"className":368,"ariaHidden":46},[45],[15,370,372,375,380,383,387,390,393,398,402],{"className":371},[50],[15,373],{"className":374,"style":151},[54],[15,376,379],{"className":377,"style":378},[59,60],"margin-right:0.1389em;","GP",[15,381,277],{"className":382},[59,60],[15,384,280],{"className":385},[386],"mopen",[15,388,36],{"className":389},[59,60],[15,391,285],{"className":392},[159],[15,394],{"className":395,"style":397},[396],"mspace","margin-right:0.2778em;",[15,399,288],{"className":400},[401],"mrel",[15,403],{"className":404,"style":397},[396],[15,406,408,412],{"className":407},[50],[15,409],{"className":410,"style":411},[54],"height:2.4182em;vertical-align:-0.9591em;",[15,413,416,426,630],{"className":414},[415],"minner",[15,417,421],{"className":418,"style":420},[386,419],"delimcenter","top:0em;",[15,422,280],{"className":423},[424,425],"delimsizing","size3",[15,427,429],{"className":428},[59],[15,430,432,536,541,544],{"className":431},[294],[15,433,436],{"className":434},[435],"col-align-c",[15,437,441,527],{"className":438},[439,440],"vlist-t","vlist-t2",[15,442,445,522],{"className":443},[444],"vlist-r",[15,446,450,464],{"className":447,"style":449},[448],"vlist","height:1.4591em;",[15,451,453,458],{"style":452},"top:-3.61em;",[15,454],{"className":455,"style":457},[456],"pstrut","height:3em;",[15,459,461],{"className":460},[59],[15,462,133],{"className":463},[59],[15,465,467,470],{"style":466},"top:-2.4009em;",[15,468],{"className":469,"style":457},[456],[15,471,473],{"className":472},[59],[15,474,476,479],{"className":475},[59],[15,477,319],{"className":478},[59,60],[15,480,483],{"className":481},[482],"msupsub",[15,484,486],{"className":485},[439],[15,487,489],{"className":488},[444],[15,490,493],{"className":491,"style":492},[448],"height:0.8491em;",[15,494,496,500],{"style":495},"top:-3.063em;margin-right:0.05em;",[15,497],{"className":498,"style":499},[456],"height:2.7em;",[15,501,506],{"className":502},[503,504,425,505],"sizing","reset-size6","mtight",[15,507,509,512,516,519],{"className":508},[59,505],[15,510,327],{"className":511},[59,505],[15,513,330],{"className":514,"style":515},[59,60,505],"margin-right:0.0359em;",[15,517,277],{"className":518},[59,60,505],[15,520,36],{"className":521},[59,60,505],[15,523,526],{"className":524},[525],"vlist-s","​",[15,528,530],{"className":529},[444],[15,531,534],{"className":532,"style":533},[448],"height:0.9591em;",[15,535],{},[15,537],{"className":538,"style":540},[539],"arraycolsep","width:0.5em;",[15,542],{"className":543,"style":540},[539],[15,545,547],{"className":546},[435],[15,548,550,622],{"className":549},[439,440],[15,551,553,619],{"className":552},[444],[15,554,556,608],{"className":555,"style":449},[448],[15,557,558,561],{"style":452},[15,559],{"className":560,"style":457},[456],[15,562,564],{"className":563},[59],[15,565,567,570],{"className":566},[59],[15,568,319],{"className":569},[59,60],[15,571,573],{"className":572},[482],[15,574,576],{"className":575},[439],[15,577,579],{"className":578},[444],[15,580,582],{"className":581,"style":492},[448],[15,583,584,587],{"style":495},[15,585],{"className":586,"style":499},[456],[15,588,590],{"className":589},[503,504,425,505],[15,591,593,596,599,602,605],{"className":592},[59,505],[15,594,324],{"className":595},[59,505],[15,597,327],{"className":598},[59,505],[15,600,330],{"className":601,"style":515},[59,60,505],[15,603,277],{"className":604},[59,60,505],[15,606,36],{"className":607},[59,60,505],[15,609,610,613],{"style":466},[15,611],{"className":612,"style":457},[456],[15,614,616],{"className":615},[59],[15,617,133],{"className":618},[59],[15,620,526],{"className":621},[525],[15,623,625],{"className":624},[444],[15,626,628],{"className":627,"style":533},[448],[15,629],{},[15,631,633],{"className":632,"style":420},[159,419],[15,634,285],{"className":635},[424,425],[167,637,639],{"id":638},"effect-on-basis-states","Effect on basis states",[196,641,642,652],{},[199,643,644],{},[202,645,646,649],{},[205,647,648],{},"Input",[205,650,651],{},"Output",[211,653,654,789],{},[202,655,656,693],{},[216,657,658],{},[15,659,661,678],{"className":660},[18],[15,662,664],{"className":663},[22],[24,665,666],{"xmlns":26},[28,667,668,676],{},[31,669,670,672,674],{},[34,671,129],{"mathvariant":128},[131,673,133],{},[135,675,138],{"stretchy":137},[38,677,141],{"encoding":40},[15,679,681],{"className":680,"ariaHidden":46},[45],[15,682,684,687,690],{"className":683},[50],[15,685],{"className":686,"style":151},[54],[15,688,155],{"className":689},[59],[15,691,138],{"className":692},[159],[216,694,695],{},[15,696,698,731],{"className":697},[18],[15,699,701],{"className":700},[22],[24,702,703],{"xmlns":26},[28,704,705,728],{},[31,706,707,721,723,726],{},[315,708,709,711],{},[34,710,319],{},[31,712,713,715,717,719],{},[131,714,327],{},[34,716,330],{},[34,718,277],{},[34,720,36],{},[34,722,129],{"mathvariant":128},[131,724,725],{},"1",[135,727,138],{"stretchy":137},[38,729,730],{"encoding":40},"e^{2\\pi i\\phi}\\vert 1 \\rangle",[15,732,734],{"className":733,"ariaHidden":46},[45],[15,735,737,741,782,786],{"className":736},[50],[15,738],{"className":739,"style":740},[54],"height:1.0991em;vertical-align:-0.25em;",[15,742,744,747],{"className":743},[59],[15,745,319],{"className":746},[59,60],[15,748,750],{"className":749},[482],[15,751,753],{"className":752},[439],[15,754,756],{"className":755},[444],[15,757,759],{"className":758,"style":492},[448],[15,760,761,764],{"style":495},[15,762],{"className":763,"style":499},[456],[15,765,767],{"className":766},[503,504,425,505],[15,768,770,773,776,779],{"className":769},[59,505],[15,771,327],{"className":772},[59,505],[15,774,330],{"className":775,"style":515},[59,60,505],[15,777,277],{"className":778},[59,60,505],[15,780,36],{"className":781},[59,60,505],[15,783,785],{"className":784},[59],"∣1",[15,787,138],{"className":788},[159],[202,790,791,829],{},[216,792,793],{},[15,794,796,814],{"className":795},[18],[15,797,799],{"className":798},[22],[24,800,801],{"xmlns":26},[28,802,803,811],{},[31,804,805,807,809],{},[34,806,129],{"mathvariant":128},[131,808,725],{},[135,810,138],{"stretchy":137},[38,812,813],{"encoding":40},"\\vert 1 \\rangle",[15,815,817],{"className":816,"ariaHidden":46},[45],[15,818,820,823,826],{"className":819},[50],[15,821],{"className":822,"style":151},[54],[15,824,785],{"className":825},[59],[15,827,138],{"className":828},[159],[216,830,831],{},[15,832,834,868],{"className":833},[18],[15,835,837],{"className":836},[22],[24,838,839],{"xmlns":26},[28,840,841,865],{},[31,842,843,859,861,863],{},[315,844,845,847],{},[34,846,319],{},[31,848,849,851,853,855,857],{},[135,850,324],{},[131,852,327],{},[34,854,330],{},[34,856,277],{},[34,858,36],{},[34,860,129],{"mathvariant":128},[131,862,133],{},[135,864,138],{"stretchy":137},[38,866,867],{"encoding":40},"e^{-2\\pi i\\phi}\\vert 0 \\rangle",[15,869,871],{"className":870,"ariaHidden":46},[45],[15,872,874,877,921,924],{"className":873},[50],[15,875],{"className":876,"style":740},[54],[15,878,880,883],{"className":879},[59],[15,881,319],{"className":882},[59,60],[15,884,886],{"className":885},[482],[15,887,889],{"className":888},[439],[15,890,892],{"className":891},[444],[15,893,895],{"className":894,"style":492},[448],[15,896,897,900],{"style":495},[15,898],{"className":899,"style":499},[456],[15,901,903],{"className":902},[503,504,425,505],[15,904,906,909,912,915,918],{"className":905},[59,505],[15,907,324],{"className":908},[59,505],[15,910,327],{"className":911},[59,505],[15,913,330],{"className":914,"style":515},[59,60,505],[15,916,277],{"className":917},[59,60,505],[15,919,36],{"className":920},[59,60,505],[15,922,155],{"className":923},[59],[15,925,138],{"className":926},[159],[11,928,929],{},"A basis state always flips, whatever the phase. The phase only shows once the qubit is in superposition or meets other gates.",[167,931,933],{"id":932},"inverse","Inverse",[11,935,936,937,940],{},"GPi is its own inverse for any phase. Two ",[92,938,939],{},"GPi(φ)"," in a row on the same qubit cancel.",[167,942,944],{"id":943},"usage","Usage",[946,947,952],"pre",{"className":948,"code":949,"language":950,"meta":951,"style":951},"language-python shiki shiki-themes one-dark-pro","from qiskit import QuantumCircuit\nfrom qiskit_ionq import GPIGate\n\nqc = QuantumCircuit(1, 1)\nqc.append(GPIGate(0), [0])\nqc.measure(0, 0)\n","python","",[92,953,954,972,985,992,1018,1043],{"__ignoreMap":951},[15,955,958,962,966,969],{"class":956,"line":957},"line",1,[15,959,961],{"class":960},"seHd6","from",[15,963,965],{"class":964},"sn6KH"," qiskit ",[15,967,968],{"class":960},"import",[15,970,971],{"class":964}," QuantumCircuit\n",[15,973,975,977,980,982],{"class":956,"line":974},2,[15,976,961],{"class":960},[15,978,979],{"class":964}," qiskit_ionq ",[15,981,968],{"class":960},[15,983,984],{"class":964}," GPIGate\n",[15,986,988],{"class":956,"line":987},3,[15,989,991],{"emptyLinePlaceholder":990},true,"\n",[15,993,995,998,1001,1005,1007,1010,1013,1015],{"class":956,"line":994},4,[15,996,997],{"class":964},"qc ",[15,999,288],{"class":1000},"sjrmR",[15,1002,1004],{"class":1003},"sVbv2"," QuantumCircuit",[15,1006,280],{"class":964},[15,1008,725],{"class":1009},"sVC51",[15,1011,1012],{"class":964},", ",[15,1014,725],{"class":1009},[15,1016,1017],{"class":964},")\n",[15,1019,1021,1024,1027,1029,1031,1033,1035,1038,1040],{"class":956,"line":1020},5,[15,1022,1023],{"class":964},"qc.",[15,1025,1026],{"class":1003},"append",[15,1028,280],{"class":964},[15,1030,243],{"class":1003},[15,1032,280],{"class":964},[15,1034,133],{"class":1009},[15,1036,1037],{"class":964},"), [",[15,1039,133],{"class":1009},[15,1041,1042],{"class":964},"])\n",[15,1044,1046,1048,1051,1053,1055,1057,1059],{"class":956,"line":1045},6,[15,1047,1023],{"class":964},[15,1049,1050],{"class":1003},"measure",[15,1052,280],{"class":964},[15,1054,133],{"class":1009},[15,1056,1012],{"class":964},[15,1058,133],{"class":1009},[15,1060,1017],{"class":964},[946,1062,1066],{"className":1063,"code":1064,"language":1065,"meta":951,"style":951},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\nimport { GPIGate } from 'qiskit_ionq';\n\nconst circuit = QuantumCircuit(1, 1);\ncircuit.append(GPIGate(0), [0]);\ncircuit.measure(0, 0);\n","js",[92,1067,1068,1091,1108,1112,1137,1161],{"__ignoreMap":951},[15,1069,1070,1072,1075,1079,1082,1084,1088],{"class":956,"line":957},[15,1071,968],{"class":960},[15,1073,1074],{"class":964}," { ",[15,1076,1078],{"class":1077},"sVyAn","QuantumCircuit",[15,1080,1081],{"class":964}," } 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