[{"data":1,"prerenderedAt":1402},["ShallowReactive",2],{"blog-post-docs\u002Fy-gate":3,"sibling-dives-docs\u002Fy-gate":1238,"learn-track-docs\u002Fy-gate":1239,"learn-docs-groups":1240},{"id":4,"title":5,"authors":6,"body":7,"breadcrumb":6,"builders":6,"byline":6,"category":1220,"categoryName":1221,"challenge":6,"courseAuthor":6,"courseLead":6,"dek":6,"description":1222,"draft":1223,"extension":1224,"eyebrow":6,"featured":1223,"finish":6,"fork":6,"group":1225,"groupName":1226,"hero":6,"heroAlt":6,"heroCta":6,"heroImage":6,"homepageFeatured":1223,"kind":1227,"lessonCount":6,"meta":1228,"navigation":1003,"newsItems":6,"next":6,"ogImage":6,"order":1007,"outcomes":6,"path":1229,"publishDate":1230,"readingTime":6,"related":1231,"relatedProjects":6,"seo":1232,"stem":1235,"tags":1236,"track":6,"trackName":6,"__hash__":1237},"blog\u002Fblog\u002Flearn\u002Fdocs\u002Fy-gate.md","Y gate",null,{"type":8,"value":9,"toc":1211},"minimark",[10,211,256,261,324,328,576,583,587,952,960,964,967,971,1064,1157,1162,1166,1177,1181,1207],[11,12,13,14,75,76,121,122,75,158,205,206,210],"p",{},"The Y gate flips a qubit and adds a phase: ",[15,16,19,52],"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",[28,29,30,47],"semantics",{},[31,32,33,38,42],"mrow",{},[34,35,37],"mi",{"mathvariant":36},"normal","∣",[39,40,41],"mn",{},"0",[43,44,46],"mo",{"stretchy":45},"false","⟩",[48,49,51],"annotation",{"encoding":50},"application\u002Fx-tex","\\vert 0 \\rangle",[15,53,57],{"className":54,"ariaHidden":56},[55],"katex-html","true",[15,58,61,66,71],{"className":59},[60],"base",[15,62],{"className":63,"style":65},[64],"strut","height:1em;vertical-align:-0.25em;",[15,67,70],{"className":68},[69],"mord","∣0",[15,72,46],{"className":73},[74],"mclose"," becomes ",[15,77,79,101],{"className":78},[18],[15,80,82],{"className":81},[22],[24,83,84],{"xmlns":26},[28,85,86,98],{},[31,87,88,91,93,96],{},[34,89,90],{},"i",[34,92,37],{"mathvariant":36},[39,94,95],{},"1",[43,97,46],{"stretchy":45},[48,99,100],{"encoding":50},"i\\vert 1 \\rangle",[15,102,104],{"className":103,"ariaHidden":56},[55],[15,105,107,110,114,118],{"className":106},[60],[15,108],{"className":109,"style":65},[64],[15,111,90],{"className":112},[69,113],"mathnormal",[15,115,117],{"className":116},[69],"∣1",[15,119,46],{"className":120},[74]," and ",[15,123,125,143],{"className":124},[18],[15,126,128],{"className":127},[22],[24,129,130],{"xmlns":26},[28,131,132,140],{},[31,133,134,136,138],{},[34,135,37],{"mathvariant":36},[39,137,95],{},[43,139,46],{"stretchy":45},[48,141,142],{"encoding":50},"\\vert 1 \\rangle",[15,144,146],{"className":145,"ariaHidden":56},[55],[15,147,149,152,155],{"className":148},[60],[15,150],{"className":151,"style":65},[64],[15,153,117],{"className":154},[69],[15,156,46],{"className":157},[74],[15,159,161,184],{"className":160},[18],[15,162,164],{"className":163},[22],[24,165,166],{"xmlns":26},[28,167,168,181],{},[31,169,170,173,175,177,179],{},[43,171,172],{},"−",[34,174,90],{},[34,176,37],{"mathvariant":36},[39,178,41],{},[43,180,46],{"stretchy":45},[48,182,183],{"encoding":50},"-i\\vert 0 \\rangle",[15,185,187],{"className":186,"ariaHidden":56},[55],[15,188,190,193,196,199,202],{"className":189},[60],[15,191],{"className":192,"style":65},[64],[15,194,172],{"className":195},[69],[15,197,90],{"className":198},[69,113],[15,200,70],{"className":201},[69],[15,203,46],{"className":204},[74],". It acts on one qubit and takes no parameters. The Circuit panel draws it as ",[207,208,209],"strong",{},"Y",". Measured straight after it, a qubit that started as 0 reads 1, the same as after an X; the phase shows only once the qubit meets other gates.",[11,212,213,214,249,250,255],{},"Kets such as ",[15,215,217,234],{"className":216},[18],[15,218,220],{"className":219},[22],[24,221,222],{"xmlns":26},[28,223,224,232],{},[31,225,226,228,230],{},[34,227,37],{"mathvariant":36},[39,229,41],{},[43,231,46],{"stretchy":45},[48,233,51],{"encoding":50},[15,235,237],{"className":236,"ariaHidden":56},[55],[15,238,240,243,246],{"className":239},[60],[15,241],{"className":242,"style":65},[64],[15,244,70],{"className":245},[69],[15,247,46],{"className":248},[74]," name the basis states and rotations are described on the Bloch sphere; the ",[251,252,254],"a",{"href":253},"\u002Flearn\u002Fquantum-foundations\u002Fqubits","qubits lesson"," introduces both.",[257,258,260],"h2",{"id":259},"call","Call",[262,263,264,276],"table",{},[265,266,267],"thead",{},[268,269,270,274],"tr",{},[271,272,273],"th",{},"Where",[271,275,260],{},[277,278,279,291,301,311],"tbody",{},[268,280,281,285],{},[282,283,284],"td",{},"Python",[282,286,287],{},[288,289,290],"code",{},"qc.y(qubit)",[268,292,293,296],{},[282,294,295],{},"JS",[282,297,298],{},[288,299,300],{},"circuit.y(qubit)",[268,302,303,306],{},[282,304,305],{},"Qiskit class",[282,307,308],{},[288,309,310],{},"YGate",[268,312,313,316],{},[282,314,315],{},"Controlled form",[282,317,318],{},[251,319,321],{"href":320},"\u002Flearn\u002Fdocs\u002Fcy-gate",[288,322,323],{},"cy(control, target)",[257,325,327],{"id":326},"matrix","Matrix",[15,329,332],{"className":330},[331],"katex-display",[15,333,335,402],{"className":334},[18],[15,336,338],{"className":337},[22],[24,339,341],{"xmlns":26,"display":340},"block",[28,342,343,399],{},[31,344,345,347,350],{},[34,346,209],{},[43,348,349],{},"=",[31,351,352,355,396],{},[43,353,354],{"fence":56},"(",[356,357,361,382],"mtable",{"rowspacing":358,"columnalign":359,"columnspacing":360},"0.16em","center center","1em",[362,363,364,372],"mtr",{},[365,366,367],"mtd",{},[368,369,370],"mstyle",{"scriptlevel":41,"displaystyle":45},[39,371,41],{},[365,373,374],{},[368,375,376],{"scriptlevel":41,"displaystyle":45},[31,377,378,380],{},[43,379,172],{},[34,381,90],{},[362,383,384,390],{},[365,385,386],{},[368,387,388],{"scriptlevel":41,"displaystyle":45},[34,389,90],{},[365,391,392],{},[368,393,394],{"scriptlevel":41,"displaystyle":45},[39,395,41],{},[43,397,398],{"fence":56},")",[48,400,401],{"encoding":50},"Y = \\begin{pmatrix} 0 & -i \\\\ i & 0 \\end{pmatrix}",[15,403,405,428],{"className":404,"ariaHidden":56},[55],[15,406,408,412,416,421,425],{"className":407},[60],[15,409],{"className":410,"style":411},[64],"height:0.6833em;",[15,413,209],{"className":414,"style":415},[69,113],"margin-right:0.2222em;",[15,417],{"className":418,"style":420},[419],"mspace","margin-right:0.2778em;",[15,422,349],{"className":423},[424],"mrel",[15,426],{"className":427,"style":420},[419],[15,429,431,435],{"className":430},[60],[15,432],{"className":433,"style":434},[64],"height:2.4em;vertical-align:-0.95em;",[15,436,439,450,570],{"className":437},[438],"minner",[15,440,445],{"className":441,"style":444},[442,443],"mopen","delimcenter","top:0em;",[15,446,354],{"className":447},[448,449],"delimsizing","size3",[15,451,453],{"className":452},[69],[15,454,456,514,519,522],{"className":455},[356],[15,457,460],{"className":458},[459],"col-align-c",[15,461,465,505],{"className":462},[463,464],"vlist-t","vlist-t2",[15,466,469,500],{"className":467},[468],"vlist-r",[15,470,474,488],{"className":471,"style":473},[472],"vlist","height:1.45em;",[15,475,477,482],{"style":476},"top:-3.61em;",[15,478],{"className":479,"style":481},[480],"pstrut","height:3em;",[15,483,485],{"className":484},[69],[15,486,41],{"className":487},[69],[15,489,491,494],{"style":490},"top:-2.41em;",[15,492],{"className":493,"style":481},[480],[15,495,497],{"className":496},[69],[15,498,90],{"className":499},[69,113],[15,501,504],{"className":502},[503],"vlist-s","​",[15,506,508],{"className":507},[468],[15,509,512],{"className":510,"style":511},[472],"height:0.95em;",[15,513],{},[15,515],{"className":516,"style":518},[517],"arraycolsep","width:0.5em;",[15,520],{"className":521,"style":518},[517],[15,523,525],{"className":524},[459],[15,526,528,562],{"className":527},[463,464],[15,529,531,559],{"className":530},[468],[15,532,534,548],{"className":533,"style":473},[472],[15,535,536,539],{"style":476},[15,537],{"className":538,"style":481},[480],[15,540,542,545],{"className":541},[69],[15,543,172],{"className":544},[69],[15,546,90],{"className":547},[69,113],[15,549,550,553],{"style":490},[15,551],{"className":552,"style":481},[480],[15,554,556],{"className":555},[69],[15,557,41],{"className":558},[69],[15,560,504],{"className":561},[503],[15,563,565],{"className":564},[468],[15,566,568],{"className":567,"style":511},[472],[15,569],{},[15,571,573],{"className":572,"style":444},[74,443],[15,574,398],{"className":575},[448,449],[11,577,578,579,582],{},"On the Bloch sphere this is a half-turn about the Y axis. It is the same operation as ",[288,580,581],{},"ry(π)"," up to a global phase.",[257,584,586],{"id":585},"effect-on-basis-states","Effect on basis states",[262,588,589,599],{},[265,590,591],{},[268,592,593,596],{},[271,594,595],{},"Input",[271,597,598],{},"Output",[277,600,601,682,768,863],{},[268,602,603,640],{},[282,604,605],{},[15,606,608,625],{"className":607},[18],[15,609,611],{"className":610},[22],[24,612,613],{"xmlns":26},[28,614,615,623],{},[31,616,617,619,621],{},[34,618,37],{"mathvariant":36},[39,620,41],{},[43,622,46],{"stretchy":45},[48,624,51],{"encoding":50},[15,626,628],{"className":627,"ariaHidden":56},[55],[15,629,631,634,637],{"className":630},[60],[15,632],{"className":633,"style":65},[64],[15,635,70],{"className":636},[69],[15,638,46],{"className":639},[74],[282,641,642],{},[15,643,645,664],{"className":644},[18],[15,646,648],{"className":647},[22],[24,649,650],{"xmlns":26},[28,651,652,662],{},[31,653,654,656,658,660],{},[34,655,90],{},[34,657,37],{"mathvariant":36},[39,659,95],{},[43,661,46],{"stretchy":45},[48,663,100],{"encoding":50},[15,665,667],{"className":666,"ariaHidden":56},[55],[15,668,670,673,676,679],{"className":669},[60],[15,671],{"className":672,"style":65},[64],[15,674,90],{"className":675},[69,113],[15,677,117],{"className":678},[69],[15,680,46],{"className":681},[74],[268,683,684,721],{},[282,685,686],{},[15,687,689,706],{"className":688},[18],[15,690,692],{"className":691},[22],[24,693,694],{"xmlns":26},[28,695,696,704],{},[31,697,698,700,702],{},[34,699,37],{"mathvariant":36},[39,701,95],{},[43,703,46],{"stretchy":45},[48,705,142],{"encoding":50},[15,707,709],{"className":708,"ariaHidden":56},[55],[15,710,712,715,718],{"className":711},[60],[15,713],{"className":714,"style":65},[64],[15,716,117],{"className":717},[69],[15,719,46],{"className":720},[74],[282,722,723],{},[15,724,726,747],{"className":725},[18],[15,727,729],{"className":728},[22],[24,730,731],{"xmlns":26},[28,732,733,745],{},[31,734,735,737,739,741,743],{},[43,736,172],{},[34,738,90],{},[34,740,37],{"mathvariant":36},[39,742,41],{},[43,744,46],{"stretchy":45},[48,746,183],{"encoding":50},[15,748,750],{"className":749,"ariaHidden":56},[55],[15,751,753,756,759,762,765],{"className":752},[60],[15,754],{"className":755,"style":65},[64],[15,757,172],{"className":758},[69],[15,760,90],{"className":761},[69,113],[15,763,70],{"className":764},[69],[15,766,46],{"className":767},[74],[268,769,770,812],{},[282,771,772],{},[15,773,775,794],{"className":774},[18],[15,776,778],{"className":777},[22],[24,779,780],{"xmlns":26},[28,781,782,791],{},[31,783,784,786,789],{},[34,785,37],{"mathvariant":36},[43,787,788],{},"+",[43,790,46],{"stretchy":45},[48,792,793],{"encoding":50},"\\vert + \\rangle",[15,795,797],{"className":796,"ariaHidden":56},[55],[15,798,800,803,806,809],{"className":799},[60],[15,801],{"className":802,"style":65},[64],[15,804,37],{"className":805},[69],[15,807,788],{"className":808},[69],[15,810,46],{"className":811},[74],[282,813,814],{},[15,815,817,839],{"className":816},[18],[15,818,820],{"className":819},[22],[24,821,822],{"xmlns":26},[28,823,824,836],{},[31,825,826,828,830,832,834],{},[43,827,172],{},[34,829,90],{},[34,831,37],{"mathvariant":36},[43,833,172],{},[43,835,46],{"stretchy":45},[48,837,838],{"encoding":50},"-i\\vert - \\rangle",[15,840,842],{"className":841,"ariaHidden":56},[55],[15,843,845,848,851,854,857,860],{"className":844},[60],[15,846],{"className":847,"style":65},[64],[15,849,172],{"className":850},[69],[15,852,90],{"className":853},[69,113],[15,855,37],{"className":856},[69],[15,858,172],{"className":859},[69],[15,861,46],{"className":862},[74],[268,864,865,906],{},[282,866,867],{},[15,868,870,888],{"className":869},[18],[15,871,873],{"className":872},[22],[24,874,875],{"xmlns":26},[28,876,877,885],{},[31,878,879,881,883],{},[34,880,37],{"mathvariant":36},[43,882,172],{},[43,884,46],{"stretchy":45},[48,886,887],{"encoding":50},"\\vert - \\rangle",[15,889,891],{"className":890,"ariaHidden":56},[55],[15,892,894,897,900,903],{"className":893},[60],[15,895],{"className":896,"style":65},[64],[15,898,37],{"className":899},[69],[15,901,172],{"className":902},[69],[15,904,46],{"className":905},[74],[282,907,908],{},[15,909,911,931],{"className":910},[18],[15,912,914],{"className":913},[22],[24,915,916],{"xmlns":26},[28,917,918,928],{},[31,919,920,922,924,926],{},[34,921,90],{},[34,923,37],{"mathvariant":36},[43,925,788],{},[43,927,46],{"stretchy":45},[48,929,930],{"encoding":50},"i\\vert + \\rangle",[15,932,934],{"className":933,"ariaHidden":56},[55],[15,935,937,940,943,946,949],{"className":936},[60],[15,938],{"className":939,"style":65},[64],[15,941,90],{"className":942},[69,113],[15,944,37],{"className":945},[69],[15,947,788],{"className":948},[69],[15,950,46],{"className":951},[74],[11,953,954,955,959],{},"Measured straight away, a basis state flips exactly as it does under ",[251,956,958],{"href":957},"\u002Flearn\u002Fdocs\u002Fx-gate","X","; the phases only matter once the qubit meets other gates.",[257,961,963],{"id":962},"inverse","Inverse",[11,965,966],{},"Y is its own inverse. Two Y gates in a row on the same qubit cancel.",[257,968,970],{"id":969},"usage","Usage",[972,973,978],"pre",{"className":974,"code":975,"language":976,"meta":977,"style":977},"language-python shiki shiki-themes one-dark-pro","from qiskit import QuantumCircuit\n\nqc = QuantumCircuit(1, 1)\nqc.y(0)\nqc.measure(0, 0)\n","python","",[288,979,980,998,1005,1031,1046],{"__ignoreMap":977},[15,981,984,988,992,995],{"class":982,"line":983},"line",1,[15,985,987],{"class":986},"seHd6","from",[15,989,991],{"class":990},"sn6KH"," qiskit ",[15,993,994],{"class":986},"import",[15,996,997],{"class":990}," QuantumCircuit\n",[15,999,1001],{"class":982,"line":1000},2,[15,1002,1004],{"emptyLinePlaceholder":1003},true,"\n",[15,1006,1008,1011,1014,1018,1020,1023,1026,1028],{"class":982,"line":1007},3,[15,1009,1010],{"class":990},"qc ",[15,1012,349],{"class":1013},"sjrmR",[15,1015,1017],{"class":1016},"sVbv2"," QuantumCircuit",[15,1019,354],{"class":990},[15,1021,95],{"class":1022},"sVC51",[15,1024,1025],{"class":990},", ",[15,1027,95],{"class":1022},[15,1029,1030],{"class":990},")\n",[15,1032,1034,1037,1040,1042,1044],{"class":982,"line":1033},4,[15,1035,1036],{"class":990},"qc.",[15,1038,1039],{"class":1016},"y",[15,1041,354],{"class":990},[15,1043,41],{"class":1022},[15,1045,1030],{"class":990},[15,1047,1049,1051,1054,1056,1058,1060,1062],{"class":982,"line":1048},5,[15,1050,1036],{"class":990},[15,1052,1053],{"class":1016},"measure",[15,1055,354],{"class":990},[15,1057,41],{"class":1022},[15,1059,1025],{"class":990},[15,1061,41],{"class":1022},[15,1063,1030],{"class":990},[972,1065,1069],{"className":1066,"code":1067,"language":1068,"meta":977,"style":977},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\n\nconst circuit = QuantumCircuit(1, 1);\ncircuit.y(0);\ncircuit.measure(0, 0);\n","js",[288,1070,1071,1094,1098,1123,1139],{"__ignoreMap":977},[15,1072,1073,1075,1078,1082,1085,1087,1091],{"class":982,"line":983},[15,1074,994],{"class":986},[15,1076,1077],{"class":990}," { ",[15,1079,1081],{"class":1080},"sVyAn","QuantumCircuit",[15,1083,1084],{"class":990}," } ",[15,1086,987],{"class":986},[15,1088,1090],{"class":1089},"subq3"," 'qiskit'",[15,1092,1093],{"class":990},";\n",[15,1095,1096],{"class":982,"line":1000},[15,1097,1004],{"emptyLinePlaceholder":1003},[15,1099,1100,1103,1107,1110,1112,1114,1116,1118,1120],{"class":982,"line":1007},[15,1101,1102],{"class":986},"const",[15,1104,1106],{"class":1105},"sU0A5"," circuit",[15,1108,1109],{"class":1013}," =",[15,1111,1017],{"class":1016},[15,1113,354],{"class":990},[15,1115,95],{"class":1022},[15,1117,1025],{"class":990},[15,1119,95],{"class":1022},[15,1121,1122],{"class":990},");\n",[15,1124,1125,1128,1131,1133,1135,1137],{"class":982,"line":1033},[15,1126,1127],{"class":1105},"circuit",[15,1129,1130],{"class":990},".",[15,1132,1039],{"class":1016},[15,1134,354],{"class":990},[15,1136,41],{"class":1022},[15,1138,1122],{"class":990},[15,1140,1141,1143,1145,1147,1149,1151,1153,1155],{"class":982,"line":1048},[15,1142,1127],{"class":1105},[15,1144,1130],{"class":990},[15,1146,1053],{"class":1016},[15,1148,354],{"class":990},[15,1150,41],{"class":1022},[15,1152,1025],{"class":990},[15,1154,41],{"class":1022},[15,1156,1122],{"class":990},[11,1158,1159,1160,1130],{},"Every shot reads ",[288,1161,95],{},[257,1163,1165],{"id":1164},"on-ionq-hardware","On IonQ hardware",[11,1167,1168,1169,1172,1173,1130],{},"Y is exactly ",[288,1170,1171],{},"GPi(0.25)",", a native gate with its phase a quarter turn from X, so it costs one physical pulse. See ",[251,1174,1176],{"href":1175},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",[257,1178,1180],{"id":1179},"related","Related",[1182,1183,1184,1190,1196,1201],"ul",{},[1185,1186,1187],"li",{},[251,1188,1189],{"href":957},"X gate",[1185,1191,1192],{},[251,1193,1195],{"href":1194},"\u002Flearn\u002Fdocs\u002Fz-gate","Z gate",[1185,1197,1198],{},[251,1199,1200],{"href":320},"CY gate",[1185,1202,1203],{},[251,1204,1206],{"href":1205},"\u002Flearn\u002Fdocs\u002Fgates","Gate reference",[1208,1209,1210],"style",{},"html pre.shiki code .seHd6, html code.shiki .seHd6{--shiki-default:#C678DD}html pre.shiki code .sn6KH, html code.shiki .sn6KH{--shiki-default:#ABB2BF}html pre.shiki code .sjrmR, html code.shiki .sjrmR{--shiki-default:#56B6C2}html pre.shiki code .sVbv2, html code.shiki .sVbv2{--shiki-default:#61AFEF}html pre.shiki code .sVC51, html code.shiki .sVC51{--shiki-default:#D19A66}html .default .shiki span {color: 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