[{"data":1,"prerenderedAt":2710},["ShallowReactive",2],{"blog-post-docs\u002Fry-gate":3,"sibling-dives-docs\u002Fry-gate":2548,"learn-track-docs\u002Fry-gate":2549,"learn-docs-groups":2550},{"id":4,"title":5,"authors":6,"body":7,"breadcrumb":6,"builders":6,"byline":6,"category":2529,"categoryName":2530,"challenge":6,"courseAuthor":6,"courseLead":6,"dek":6,"description":2531,"draft":2532,"extension":2533,"eyebrow":6,"featured":2532,"finish":6,"fork":6,"group":2534,"groupName":2535,"hero":6,"heroAlt":6,"heroCta":6,"heroImage":6,"homepageFeatured":2532,"kind":2536,"lessonCount":6,"meta":2537,"navigation":2158,"newsItems":6,"next":6,"ogImage":6,"order":2538,"outcomes":6,"path":2539,"publishDate":2540,"readingTime":6,"related":2541,"relatedProjects":6,"seo":2542,"stem":2545,"tags":2546,"track":6,"trackName":6,"__hash__":2547},"blog\u002Fblog\u002Flearn\u002Fdocs\u002Fry-gate.md","RY gate",null,{"type":8,"value":9,"toc":2520},"minimark",[10,384,433,438,498,502,1097,1230,1234,1809,2096,2100,2109,2113,2227,2334,2450,2454,2482,2486,2516],[11,12,13,14,62,63,91,92,96,97,210,211,268,269,330,331,383],"p",{},"The RY gate rotates a qubit about the Y axis of the Bloch sphere by an angle ",[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",{},"θ",[38,39,41],"annotation",{"encoding":40},"application\u002Fx-tex","\\theta",[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:0.6944em;",[15,57,36],{"className":58,"style":61},[59,60],"mord","mathnormal","margin-right:0.0278em;",". It acts on one qubit and takes one parameter, ",[15,64,66,79],{"className":65},[18],[15,67,69],{"className":68},[22],[24,70,71],{"xmlns":26},[28,72,73,77],{},[31,74,75],{},[34,76,36],{},[38,78,41],{"encoding":40},[15,80,82],{"className":81,"ariaHidden":46},[45],[15,83,85,88],{"className":84},[50],[15,86],{"className":87,"style":55},[54],[15,89,36],{"className":90,"style":61},[59,60]," in radians. The Circuit panel draws it as ",[93,94,95],"strong",{},"Ry(θ)"," with the angle shown as a multiple of π. Measured straight after it, a qubit that started as 0 reads 1 with probability ",[15,98,100,143],{"className":99},[18],[15,101,103],{"className":102},[22],[24,104,105],{"xmlns":26},[28,106,107,140],{},[31,108,109,125,129,131,135,137],{},[110,111,112,121],"msup",{},[31,113,114,117],{},[34,115,116],{},"sin",[118,119,120],"mo",{},"⁡",[122,123,124],"mn",{},"2",[118,126,128],{"stretchy":127},"false","(",[34,130,36],{},[34,132,134],{"mathvariant":133},"normal","\u002F",[122,136,124],{},[118,138,139],{"stretchy":127},")",[38,141,142],{"encoding":40},"\\sin^2(\\theta\u002F2)",[15,144,146],{"className":145,"ariaHidden":46},[45],[15,147,149,153,195,199,202,206],{"className":148},[50],[15,150],{"className":151,"style":152},[54],"height:1.1219em;vertical-align:-0.25em;",[15,154,157,160],{"className":155},[156],"mop",[15,158,116],{"className":159},[156],[15,161,164],{"className":162},[163],"msupsub",[15,165,168],{"className":166},[167],"vlist-t",[15,169,172],{"className":170},[171],"vlist-r",[15,173,177],{"className":174,"style":176},[175],"vlist","height:0.8719em;",[15,178,180,185],{"style":179},"top:-3.1208em;margin-right:0.05em;",[15,181],{"className":182,"style":184},[183],"pstrut","height:2.7em;",[15,186,192],{"className":187},[188,189,190,191],"sizing","reset-size6","size3","mtight",[15,193,124],{"className":194},[59,191],[15,196,128],{"className":197},[198],"mopen",[15,200,36],{"className":201,"style":61},[59,60],[15,203,205],{"className":204},[59],"\u002F2",[15,207,139],{"className":208},[209],"mclose",": never at ",[15,212,214,234],{"className":213},[18],[15,215,217],{"className":216},[22],[24,218,219],{"xmlns":26},[28,220,221,231],{},[31,222,223,225,228],{},[34,224,36],{},[118,226,227],{},"=",[122,229,230],{},"0",[38,232,233],{"encoding":40},"\\theta = 0",[15,235,237,258],{"className":236,"ariaHidden":46},[45],[15,238,240,243,246,251,255],{"className":239},[50],[15,241],{"className":242,"style":55},[54],[15,244,36],{"className":245,"style":61},[59,60],[15,247],{"className":248,"style":250},[249],"mspace","margin-right:0.2778em;",[15,252,227],{"className":253},[254],"mrel",[15,256],{"className":257,"style":250},[249],[15,259,261,265],{"className":260},[50],[15,262],{"className":263,"style":264},[54],"height:0.6444em;",[15,266,230],{"className":267},[59],", half the time at ",[15,270,272,295],{"className":271},[18],[15,273,275],{"className":274},[22],[24,276,277],{"xmlns":26},[28,278,279,292],{},[31,280,281,283,285,288,290],{},[34,282,36],{},[118,284,227],{},[34,286,287],{},"π",[34,289,134],{"mathvariant":133},[122,291,124],{},[38,293,294],{"encoding":40},"\\theta = \\pi\u002F2",[15,296,298,316],{"className":297,"ariaHidden":46},[45],[15,299,301,304,307,310,313],{"className":300},[50],[15,302],{"className":303,"style":55},[54],[15,305,36],{"className":306,"style":61},[59,60],[15,308],{"className":309,"style":250},[249],[15,311,227],{"className":312},[254],[15,314],{"className":315,"style":250},[249],[15,317,319,323,327],{"className":318},[50],[15,320],{"className":321,"style":322},[54],"height:1em;vertical-align:-0.25em;",[15,324,287],{"className":325,"style":326},[59,60],"margin-right:0.0359em;",[15,328,205],{"className":329},[59],", always at ",[15,332,334,352],{"className":333},[18],[15,335,337],{"className":336},[22],[24,338,339],{"xmlns":26},[28,340,341,349],{},[31,342,343,345,347],{},[34,344,36],{},[118,346,227],{},[34,348,287],{},[38,350,351],{"encoding":40},"\\theta = \\pi",[15,353,355,373],{"className":354,"ariaHidden":46},[45],[15,356,358,361,364,367,370],{"className":357},[50],[15,359],{"className":360,"style":55},[54],[15,362,36],{"className":363,"style":61},[59,60],[15,365],{"className":366,"style":250},[249],[15,368,227],{"className":369},[254],[15,371],{"className":372,"style":250},[249],[15,374,376,380],{"className":375},[50],[15,377],{"className":378,"style":379},[54],"height:0.4306em;",[15,381,287],{"className":382,"style":326},[59,60],".",[11,385,386,387,426,427,432],{},"Kets such as ",[15,388,390,410],{"className":389},[18],[15,391,393],{"className":392},[22],[24,394,395],{"xmlns":26},[28,396,397,407],{},[31,398,399,402,404],{},[34,400,401],{"mathvariant":133},"∣",[122,403,230],{},[118,405,406],{"stretchy":127},"⟩",[38,408,409],{"encoding":40},"\\vert 0 \\rangle",[15,411,413],{"className":412,"ariaHidden":46},[45],[15,414,416,419,423],{"className":415},[50],[15,417],{"className":418,"style":322},[54],[15,420,422],{"className":421},[59],"∣0",[15,424,406],{"className":425},[209]," name the basis states and rotations are described on the Bloch sphere; the ",[428,429,431],"a",{"href":430},"\u002Flearn\u002Fquantum-foundations\u002Fqubits","qubits lesson"," introduces both.",[434,435,437],"h2",{"id":436},"call","Call",[439,440,441,453],"table",{},[442,443,444],"thead",{},[445,446,447,451],"tr",{},[448,449,450],"th",{},"Where",[448,452,437],{},[454,455,456,468,478,488],"tbody",{},[445,457,458,462],{},[459,460,461],"td",{},"Python",[459,463,464],{},[465,466,467],"code",{},"qc.ry(θ, qubit)",[445,469,470,473],{},[459,471,472],{},"JS",[459,474,475],{},[465,476,477],{},"circuit.ry(θ, qubit)",[445,479,480,483],{},[459,481,482],{},"Qiskit class",[459,484,485],{},[465,486,487],{},"RYGate",[445,489,490,493],{},[459,491,492],{},"Controlled form",[459,494,495],{},[465,496,497],{},"cry(θ, control, target)",[434,499,501],{"id":500},"matrix","Matrix",[15,503,506],{"className":504},[505],"katex-display",[15,507,509,624],{"className":508},[18],[15,510,512],{"className":511},[22],[24,513,515],{"xmlns":26,"display":514},"block",[28,516,517,621],{},[31,518,519,522,525,527,529,531,533],{},[34,520,521],{},"R",[34,523,524],{},"Y",[118,526,128],{"stretchy":127},[34,528,36],{},[118,530,139],{"stretchy":127},[118,532,227],{},[31,534,535,537,619],{},[118,536,128],{"fence":46},[538,539,543,585],"mtable",{"rowspacing":540,"columnalign":541,"columnspacing":542},"0.16em","center center","1em",[544,545,546,566],"mtr",{},[547,548,549],"mtd",{},[550,551,552],"mstyle",{"scriptlevel":230,"displaystyle":127},[31,553,554,557,559],{},[34,555,556],{},"cos",[118,558,120],{},[560,561,562,564],"mfrac",{},[34,563,36],{},[122,565,124],{},[547,567,568],{},[550,569,570],{"scriptlevel":230,"displaystyle":127},[31,571,572,575,577,579],{},[118,573,574],{},"−",[34,576,116],{},[118,578,120],{},[560,580,581,583],{},[34,582,36],{},[122,584,124],{},[544,586,587,603],{},[547,588,589],{},[550,590,591],{"scriptlevel":230,"displaystyle":127},[31,592,593,595,597],{},[34,594,116],{},[118,596,120],{},[560,598,599,601],{},[34,600,36],{},[122,602,124],{},[547,604,605],{},[550,606,607],{"scriptlevel":230,"displaystyle":127},[31,608,609,611,613],{},[34,610,556],{},[118,612,120],{},[560,614,615,617],{},[34,616,36],{},[122,618,124],{},[118,620,139],{"fence":46},[38,622,623],{"encoding":40},"RY(\\theta) = \\begin{pmatrix} \\cos\\frac{\\theta}{2} & -\\sin\\frac{\\theta}{2} \\\\ \\sin\\frac{\\theta}{2} & \\cos\\frac{\\theta}{2} \\end{pmatrix}",[15,625,627,659],{"className":626,"ariaHidden":46},[45],[15,628,630,633,637,641,644,647,650,653,656],{"className":629},[50],[15,631],{"className":632,"style":322},[54],[15,634,521],{"className":635,"style":636},[59,60],"margin-right:0.0077em;",[15,638,524],{"className":639,"style":640},[59,60],"margin-right:0.2222em;",[15,642,128],{"className":643},[198],[15,645,36],{"className":646,"style":61},[59,60],[15,648,139],{"className":649},[209],[15,651],{"className":652,"style":250},[249],[15,654,227],{"className":655},[254],[15,657],{"className":658,"style":250},[249],[15,660,662,666],{"className":661},[50],[15,663],{"className":664,"style":665},[54],"height:2.4802em;vertical-align:-0.9901em;",[15,667,670,679,1091],{"className":668},[669],"minner",[15,671,675],{"className":672,"style":674},[198,673],"delimcenter","top:0em;",[15,676,128],{"className":677},[678,190],"delimsizing",[15,680,682],{"className":681},[59],[15,683,685,890,895,898],{"className":684},[538],[15,686,689],{"className":687},[688],"col-align-c",[15,690,693,881],{"className":691},[167,692],"vlist-t2",[15,694,696,878],{"className":695},[171],[15,697,700,795],{"className":698,"style":699},[175],"height:1.4901em;",[15,701,703,707],{"style":702},"top:-3.61em;",[15,704],{"className":705,"style":706},[183],"height:3em;",[15,708,710,713,717],{"className":709},[59],[15,711,556],{"className":712},[156],[15,714],{"className":715,"style":716},[249],"margin-right:0.1667em;",[15,718,720,724,792],{"className":719},[59],[15,721],{"className":722},[198,723],"nulldelimiter",[15,725,727],{"className":726},[560],[15,728,730,783],{"className":729},[167,692],[15,731,733,778],{"className":732},[171],[15,734,737,752,763],{"className":735,"style":736},[175],"height:0.8801em;",[15,738,740,743],{"style":739},"top:-2.655em;",[15,741],{"className":742,"style":706},[183],[15,744,746],{"className":745},[188,189,190,191],[15,747,749],{"className":748},[59,191],[15,750,124],{"className":751},[59,191],[15,753,755,758],{"style":754},"top:-3.23em;",[15,756],{"className":757,"style":706},[183],[15,759],{"className":760,"style":762},[761],"frac-line","border-bottom-width:0.04em;",[15,764,766,769],{"style":765},"top:-3.394em;",[15,767],{"className":768,"style":706},[183],[15,770,772],{"className":771},[188,189,190,191],[15,773,775],{"className":774},[59,191],[15,776,36],{"className":777,"style":61},[59,60,191],[15,779,782],{"className":780},[781],"vlist-s","​",[15,784,786],{"className":785},[171],[15,787,790],{"className":788,"style":789},[175],"height:0.345em;",[15,791],{},[15,793],{"className":794},[209,723],[15,796,798,801],{"style":797},"top:-2.3699em;",[15,799],{"className":800,"style":706},[183],[15,802,804,807,810],{"className":803},[59],[15,805,116],{"className":806},[156],[15,808],{"className":809,"style":716},[249],[15,811,813,816,875],{"className":812},[59],[15,814],{"className":815},[198,723],[15,817,819],{"className":818},[560],[15,820,822,867],{"className":821},[167,692],[15,823,825,864],{"className":824},[171],[15,826,828,842,850],{"className":827,"style":736},[175],[15,829,830,833],{"style":739},[15,831],{"className":832,"style":706},[183],[15,834,836],{"className":835},[188,189,190,191],[15,837,839],{"className":838},[59,191],[15,840,124],{"className":841},[59,191],[15,843,844,847],{"style":754},[15,845],{"className":846,"style":706},[183],[15,848],{"className":849,"style":762},[761],[15,851,852,855],{"style":765},[15,853],{"className":854,"style":706},[183],[15,856,858],{"className":857},[188,189,190,191],[15,859,861],{"className":860},[59,191],[15,862,36],{"className":863,"style":61},[59,60,191],[15,865,782],{"className":866},[781],[15,868,870],{"className":869},[171],[15,871,873],{"className":872,"style":789},[175],[15,874],{},[15,876],{"className":877},[209,723],[15,879,782],{"className":880},[781],[15,882,884],{"className":883},[171],[15,885,888],{"className":886,"style":887},[175],"height:0.9901em;",[15,889],{},[15,891],{"className":892,"style":894},[893],"arraycolsep","width:0.5em;",[15,896],{"className":897,"style":894},[893],[15,899,901],{"className":900},[688],[15,902,904,1083],{"className":903},[167,692],[15,905,907,1080],{"className":906},[171],[15,908,910,998],{"className":909,"style":699},[175],[15,911,912,915],{"style":702},[15,913],{"className":914,"style":706},[183],[15,916,918,921,924,927,930],{"className":917},[59],[15,919,574],{"className":920},[59],[15,922],{"className":923,"style":716},[249],[15,925,116],{"className":926},[156],[15,928],{"className":929,"style":716},[249],[15,931,933,936,995],{"className":932},[59],[15,934],{"className":935},[198,723],[15,937,939],{"className":938},[560],[15,940,942,987],{"className":941},[167,692],[15,943,945,984],{"className":944},[171],[15,946,948,962,970],{"className":947,"style":736},[175],[15,949,950,953],{"style":739},[15,951],{"className":952,"style":706},[183],[15,954,956],{"className":955},[188,189,190,191],[15,957,959],{"className":958},[59,191],[15,960,124],{"className":961},[59,191],[15,963,964,967],{"style":754},[15,965],{"className":966,"style":706},[183],[15,968],{"className":969,"style":762},[761],[15,971,972,975],{"style":765},[15,973],{"className":974,"style":706},[183],[15,976,978],{"className":977},[188,189,190,191],[15,979,981],{"className":980},[59,191],[15,982,36],{"className":983,"style":61},[59,60,191],[15,985,782],{"className":986},[781],[15,988,990],{"className":989},[171],[15,991,993],{"className":992,"style":789},[175],[15,994],{},[15,996],{"className":997},[209,723],[15,999,1000,1003],{"style":797},[15,1001],{"className":1002,"style":706},[183],[15,1004,1006,1009,1012],{"className":1005},[59],[15,1007,556],{"className":1008},[156],[15,1010],{"className":1011,"style":716},[249],[15,1013,1015,1018,1077],{"className":1014},[59],[15,1016],{"className":1017},[198,723],[15,1019,1021],{"className":1020},[560],[15,1022,1024,1069],{"className":1023},[167,692],[15,1025,1027,1066],{"className":1026},[171],[15,1028,1030,1044,1052],{"className":1029,"style":736},[175],[15,1031,1032,1035],{"style":739},[15,1033],{"className":1034,"style":706},[183],[15,1036,1038],{"className":1037},[188,189,190,191],[15,1039,1041],{"className":1040},[59,191],[15,1042,124],{"className":1043},[59,191],[15,1045,1046,1049],{"style":754},[15,1047],{"className":1048,"style":706},[183],[15,1050],{"className":1051,"style":762},[761],[15,1053,1054,1057],{"style":765},[15,1055],{"className":1056,"style":706},[183],[15,1058,1060],{"className":1059},[188,189,190,191],[15,1061,1063],{"className":1062},[59,191],[15,1064,36],{"className":1065,"style":61},[59,60,191],[15,1067,782],{"className":1068},[781],[15,1070,1072],{"className":1071},[171],[15,1073,1075],{"className":1074,"style":789},[175],[15,1076],{},[15,1078],{"className":1079},[209,723],[15,1081,782],{"className":1082},[781],[15,1084,1086],{"className":1085},[171],[15,1087,1089],{"className":1088,"style":887},[175],[15,1090],{},[15,1092,1094],{"className":1093,"style":674},[209,673],[15,1095,139],{"className":1096},[678,190],[11,1098,1099,1100,1103,1104,1108,1109,1112,1113,1148,1149,1189,1190,1194,1195,383],{},"The matrix is real, so RY never introduces complex phases. ",[465,1101,1102],{},"ry(π)"," is a ",[428,1105,1107],{"href":1106},"\u002Flearn\u002Fdocs\u002Fy-gate","Y gate"," up to a global phase, and ",[465,1110,1111],{},"ry(π\u002F2)"," takes ",[15,1114,1116,1133],{"className":1115},[18],[15,1117,1119],{"className":1118},[22],[24,1120,1121],{"xmlns":26},[28,1122,1123,1131],{},[31,1124,1125,1127,1129],{},[34,1126,401],{"mathvariant":133},[122,1128,230],{},[118,1130,406],{"stretchy":127},[38,1132,409],{"encoding":40},[15,1134,1136],{"className":1135,"ariaHidden":46},[45],[15,1137,1139,1142,1145],{"className":1138},[50],[15,1140],{"className":1141,"style":322},[54],[15,1143,422],{"className":1144},[59],[15,1146,406],{"className":1147},[209]," to ",[15,1150,1152,1171],{"className":1151},[18],[15,1153,1155],{"className":1154},[22],[24,1156,1157],{"xmlns":26},[28,1158,1159,1168],{},[31,1160,1161,1163,1166],{},[34,1162,401],{"mathvariant":133},[118,1164,1165],{},"+",[118,1167,406],{"stretchy":127},[38,1169,1170],{"encoding":40},"\\vert + \\rangle",[15,1172,1174],{"className":1173,"ariaHidden":46},[45],[15,1175,1177,1180,1183,1186],{"className":1176},[50],[15,1178],{"className":1179,"style":322},[54],[15,1181,401],{"className":1182},[59],[15,1184,1165],{"className":1185},[59],[15,1187,406],{"className":1188},[209],", the same state an ",[428,1191,1193],{"href":1192},"\u002Flearn\u002Fdocs\u002Fh-gate","H gate"," produces from ",[15,1196,1198,1215],{"className":1197},[18],[15,1199,1201],{"className":1200},[22],[24,1202,1203],{"xmlns":26},[28,1204,1205,1213],{},[31,1206,1207,1209,1211],{},[34,1208,401],{"mathvariant":133},[122,1210,230],{},[118,1212,406],{"stretchy":127},[38,1214,409],{"encoding":40},[15,1216,1218],{"className":1217,"ariaHidden":46},[45],[15,1219,1221,1224,1227],{"className":1220},[50],[15,1222],{"className":1223,"style":322},[54],[15,1225,422],{"className":1226},[59],[15,1228,406],{"className":1229},[209],[434,1231,1233],{"id":1232},"effect-on-basis-states","Effect on basis states",[439,1235,1236,1246],{},[442,1237,1238],{},[445,1239,1240,1243],{},[448,1241,1242],{},"Input",[448,1244,1245],{},"Output",[454,1247,1248,1526],{},[445,1249,1250,1287],{},[459,1251,1252],{},[15,1253,1255,1272],{"className":1254},[18],[15,1256,1258],{"className":1257},[22],[24,1259,1260],{"xmlns":26},[28,1261,1262,1270],{},[31,1263,1264,1266,1268],{},[34,1265,401],{"mathvariant":133},[122,1267,230],{},[118,1269,406],{"stretchy":127},[38,1271,409],{"encoding":40},[15,1273,1275],{"className":1274,"ariaHidden":46},[45],[15,1276,1278,1281,1284],{"className":1277},[50],[15,1279],{"className":1280,"style":322},[54],[15,1282,422],{"className":1283},[59],[15,1285,406],{"className":1286},[209],[459,1288,1289],{},[15,1290,1292,1339],{"className":1291},[18],[15,1293,1295],{"className":1294},[22],[24,1296,1297],{"xmlns":26},[28,1298,1299,1336],{},[31,1300,1301,1303,1305,1311,1313,1315,1317,1319,1321,1323,1329,1331,1334],{},[34,1302,556],{},[118,1304,120],{},[560,1306,1307,1309],{},[34,1308,36],{},[122,1310,124],{},[34,1312,401],{"mathvariant":133},[122,1314,230],{},[118,1316,406],{"stretchy":127},[118,1318,1165],{},[34,1320,116],{},[118,1322,120],{},[560,1324,1325,1327],{},[34,1326,36],{},[122,1328,124],{},[34,1330,401],{"mathvariant":133},[122,1332,1333],{},"1",[118,1335,406],{"stretchy":127},[38,1337,1338],{"encoding":40},"\\cos\\frac{\\theta}{2}\\vert 0 \\rangle + \\sin\\frac{\\theta}{2}\\vert 1 \\rangle",[15,1340,1342,1439],{"className":1341,"ariaHidden":46},[45],[15,1343,1345,1349,1352,1355,1423,1426,1429,1432,1436],{"className":1344},[50],[15,1346],{"className":1347,"style":1348},[54],"height:1.2251em;vertical-align:-0.345em;",[15,1350,556],{"className":1351},[156],[15,1353],{"className":1354,"style":716},[249],[15,1356,1358,1361,1420],{"className":1357},[59],[15,1359],{"className":1360},[198,723],[15,1362,1364],{"className":1363},[560],[15,1365,1367,1412],{"className":1366},[167,692],[15,1368,1370,1409],{"className":1369},[171],[15,1371,1373,1387,1395],{"className":1372,"style":736},[175],[15,1374,1375,1378],{"style":739},[15,1376],{"className":1377,"style":706},[183],[15,1379,1381],{"className":1380},[188,189,190,191],[15,1382,1384],{"className":1383},[59,191],[15,1385,124],{"className":1386},[59,191],[15,1388,1389,1392],{"style":754},[15,1390],{"className":1391,"style":706},[183],[15,1393],{"className":1394,"style":762},[761],[15,1396,1397,1400],{"style":765},[15,1398],{"className":1399,"style":706},[183],[15,1401,1403],{"className":1402},[188,189,190,191],[15,1404,1406],{"className":1405},[59,191],[15,1407,36],{"className":1408,"style":61},[59,60,191],[15,1410,782],{"className":1411},[781],[15,1413,1415],{"className":1414},[171],[15,1416,1418],{"className":1417,"style":789},[175],[15,1419],{},[15,1421],{"className":1422},[209,723],[15,1424,422],{"className":1425},[59],[15,1427,406],{"className":1428},[209],[15,1430],{"className":1431,"style":640},[249],[15,1433,1165],{"className":1434},[1435],"mbin",[15,1437],{"className":1438,"style":640},[249],[15,1440,1442,1445,1448,1451,1519,1523],{"className":1441},[50],[15,1443],{"className":1444,"style":1348},[54],[15,1446,116],{"className":1447},[156],[15,1449],{"className":1450,"style":716},[249],[15,1452,1454,1457,1516],{"className":1453},[59],[15,1455],{"className":1456},[198,723],[15,1458,1460],{"className":1459},[560],[15,1461,1463,1508],{"className":1462},[167,692],[15,1464,1466,1505],{"className":1465},[171],[15,1467,1469,1483,1491],{"className":1468,"style":736},[175],[15,1470,1471,1474],{"style":739},[15,1472],{"className":1473,"style":706},[183],[15,1475,1477],{"className":1476},[188,189,190,191],[15,1478,1480],{"className":1479},[59,191],[15,1481,124],{"className":1482},[59,191],[15,1484,1485,1488],{"style":754},[15,1486],{"className":1487,"style":706},[183],[15,1489],{"className":1490,"style":762},[761],[15,1492,1493,1496],{"style":765},[15,1494],{"className":1495,"style":706},[183],[15,1497,1499],{"className":1498},[188,189,190,191],[15,1500,1502],{"className":1501},[59,191],[15,1503,36],{"className":1504,"style":61},[59,60,191],[15,1506,782],{"className":1507},[781],[15,1509,1511],{"className":1510},[171],[15,1512,1514],{"className":1513,"style":789},[175],[15,1515],{},[15,1517],{"className":1518},[209,723],[15,1520,1522],{"className":1521},[59],"∣1",[15,1524,406],{"className":1525},[209],[445,1527,1528,1566],{},[459,1529,1530],{},[15,1531,1533,1551],{"className":1532},[18],[15,1534,1536],{"className":1535},[22],[24,1537,1538],{"xmlns":26},[28,1539,1540,1548],{},[31,1541,1542,1544,1546],{},[34,1543,401],{"mathvariant":133},[122,1545,1333],{},[118,1547,406],{"stretchy":127},[38,1549,1550],{"encoding":40},"\\vert 1 \\rangle",[15,1552,1554],{"className":1553,"ariaHidden":46},[45],[15,1555,1557,1560,1563],{"className":1556},[50],[15,1558],{"className":1559,"style":322},[54],[15,1561,1522],{"className":1562},[59],[15,1564,406],{"className":1565},[209],[459,1567,1568],{},[15,1569,1571,1619],{"className":1570},[18],[15,1572,1574],{"className":1573},[22],[24,1575,1576],{"xmlns":26},[28,1577,1578,1616],{},[31,1579,1580,1582,1584,1586,1592,1594,1596,1598,1600,1602,1604,1610,1612,1614],{},[118,1581,574],{},[34,1583,116],{},[118,1585,120],{},[560,1587,1588,1590],{},[34,1589,36],{},[122,1591,124],{},[34,1593,401],{"mathvariant":133},[122,1595,230],{},[118,1597,406],{"stretchy":127},[118,1599,1165],{},[34,1601,556],{},[118,1603,120],{},[560,1605,1606,1608],{},[34,1607,36],{},[122,1609,124],{},[34,1611,401],{"mathvariant":133},[122,1613,1333],{},[118,1615,406],{"stretchy":127},[38,1617,1618],{"encoding":40},"-\\sin\\frac{\\theta}{2}\\vert 0 \\rangle + \\cos\\frac{\\theta}{2}\\vert 1 \\rangle",[15,1620,1622,1723],{"className":1621,"ariaHidden":46},[45],[15,1623,1625,1628,1631,1634,1637,1640,1708,1711,1714,1717,1720],{"className":1624},[50],[15,1626],{"className":1627,"style":1348},[54],[15,1629,574],{"className":1630},[59],[15,1632],{"className":1633,"style":716},[249],[15,1635,116],{"className":1636},[156],[15,1638],{"className":1639,"style":716},[249],[15,1641,1643,1646,1705],{"className":1642},[59],[15,1644],{"className":1645},[198,723],[15,1647,1649],{"className":1648},[560],[15,1650,1652,1697],{"className":1651},[167,692],[15,1653,1655,1694],{"className":1654},[171],[15,1656,1658,1672,1680],{"className":1657,"style":736},[175],[15,1659,1660,1663],{"style":739},[15,1661],{"className":1662,"style":706},[183],[15,1664,1666],{"className":1665},[188,189,190,191],[15,1667,1669],{"className":1668},[59,191],[15,1670,124],{"className":1671},[59,191],[15,1673,1674,1677],{"style":754},[15,1675],{"className":1676,"style":706},[183],[15,1678],{"className":1679,"style":762},[761],[15,1681,1682,1685],{"style":765},[15,1683],{"className":1684,"style":706},[183],[15,1686,1688],{"className":1687},[188,189,190,191],[15,1689,1691],{"className":1690},[59,191],[15,1692,36],{"className":1693,"style":61},[59,60,191],[15,1695,782],{"className":1696},[781],[15,1698,1700],{"className":1699},[171],[15,1701,1703],{"className":1702,"style":789},[175],[15,1704],{},[15,1706],{"className":1707},[209,723],[15,1709,422],{"className":1710},[59],[15,1712,406],{"className":1713},[209],[15,1715],{"className":1716,"style":640},[249],[15,1718,1165],{"className":1719},[1435],[15,1721],{"className":1722,"style":640},[249],[15,1724,1726,1729,1732,1735,1803,1806],{"className":1725},[50],[15,1727],{"className":1728,"style":1348},[54],[15,1730,556],{"className":1731},[156],[15,1733],{"className":1734,"style":716},[249],[15,1736,1738,1741,1800],{"className":1737},[59],[15,1739],{"className":1740},[198,723],[15,1742,1744],{"className":1743},[560],[15,1745,1747,1792],{"className":1746},[167,692],[15,1748,1750,1789],{"className":1749},[171],[15,1751,1753,1767,1775],{"className":1752,"style":736},[175],[15,1754,1755,1758],{"style":739},[15,1756],{"className":1757,"style":706},[183],[15,1759,1761],{"className":1760},[188,189,190,191],[15,1762,1764],{"className":1763},[59,191],[15,1765,124],{"className":1766},[59,191],[15,1768,1769,1772],{"style":754},[15,1770],{"className":1771,"style":706},[183],[15,1773],{"className":1774,"style":762},[761],[15,1776,1777,1780],{"style":765},[15,1778],{"className":1779,"style":706},[183],[15,1781,1783],{"className":1782},[188,189,190,191],[15,1784,1786],{"className":1785},[59,191],[15,1787,36],{"className":1788,"style":61},[59,60,191],[15,1790,782],{"className":1791},[781],[15,1793,1795],{"className":1794},[171],[15,1796,1798],{"className":1797,"style":789},[175],[15,1799],{},[15,1801],{"className":1802},[209,723],[15,1804,1522],{"className":1805},[59],[15,1807,406],{"className":1808},[209],[11,1810,1811,1812,1815,1816,1851,1852,1936,1937,1987,1988,2045,2046,383],{},"Measured straight after ",[465,1813,1814],{},"ry(θ)",", a qubit that started in ",[15,1817,1819,1836],{"className":1818},[18],[15,1820,1822],{"className":1821},[22],[24,1823,1824],{"xmlns":26},[28,1825,1826,1834],{},[31,1827,1828,1830,1832],{},[34,1829,401],{"mathvariant":133},[122,1831,230],{},[118,1833,406],{"stretchy":127},[38,1835,409],{"encoding":40},[15,1837,1839],{"className":1838,"ariaHidden":46},[45],[15,1840,1842,1845,1848],{"className":1841},[50],[15,1843],{"className":1844,"style":322},[54],[15,1846,422],{"className":1847},[59],[15,1849,406],{"className":1850},[209]," reads 1 with probability ",[15,1853,1855,1886],{"className":1854},[18],[15,1856,1858],{"className":1857},[22],[24,1859,1860],{"xmlns":26},[28,1861,1862,1884],{},[31,1863,1864,1874,1876,1878,1880,1882],{},[110,1865,1866,1872],{},[31,1867,1868,1870],{},[34,1869,116],{},[118,1871,120],{},[122,1873,124],{},[118,1875,128],{"stretchy":127},[34,1877,36],{},[34,1879,134],{"mathvariant":133},[122,1881,124],{},[118,1883,139],{"stretchy":127},[38,1885,142],{"encoding":40},[15,1887,1889],{"className":1888,"ariaHidden":46},[45],[15,1890,1892,1895,1924,1927,1930,1933],{"className":1891},[50],[15,1893],{"className":1894,"style":152},[54],[15,1896,1898,1901],{"className":1897},[156],[15,1899,116],{"className":1900},[156],[15,1902,1904],{"className":1903},[163],[15,1905,1907],{"className":1906},[167],[15,1908,1910],{"className":1909},[171],[15,1911,1913],{"className":1912,"style":176},[175],[15,1914,1915,1918],{"style":179},[15,1916],{"className":1917,"style":184},[183],[15,1919,1921],{"className":1920},[188,189,190,191],[15,1922,124],{"className":1923},[59,191],[15,1925,128],{"className":1926},[198],[15,1928,36],{"className":1929,"style":61},[59,60],[15,1931,205],{"className":1932},[59],[15,1934,139],{"className":1935},[209],": 0 at ",[15,1938,1940,1957],{"className":1939},[18],[15,1941,1943],{"className":1942},[22],[24,1944,1945],{"xmlns":26},[28,1946,1947,1955],{},[31,1948,1949,1951,1953],{},[34,1950,36],{},[118,1952,227],{},[122,1954,230],{},[38,1956,233],{"encoding":40},[15,1958,1960,1978],{"className":1959,"ariaHidden":46},[45],[15,1961,1963,1966,1969,1972,1975],{"className":1962},[50],[15,1964],{"className":1965,"style":55},[54],[15,1967,36],{"className":1968,"style":61},[59,60],[15,1970],{"className":1971,"style":250},[249],[15,1973,227],{"className":1974},[254],[15,1976],{"className":1977,"style":250},[249],[15,1979,1981,1984],{"className":1980},[50],[15,1982],{"className":1983,"style":264},[54],[15,1985,230],{"className":1986},[59],", one half at ",[15,1989,1991,2012],{"className":1990},[18],[15,1992,1994],{"className":1993},[22],[24,1995,1996],{"xmlns":26},[28,1997,1998,2010],{},[31,1999,2000,2002,2004,2006,2008],{},[34,2001,36],{},[118,2003,227],{},[34,2005,287],{},[34,2007,134],{"mathvariant":133},[122,2009,124],{},[38,2011,294],{"encoding":40},[15,2013,2015,2033],{"className":2014,"ariaHidden":46},[45],[15,2016,2018,2021,2024,2027,2030],{"className":2017},[50],[15,2019],{"className":2020,"style":55},[54],[15,2022,36],{"className":2023,"style":61},[59,60],[15,2025],{"className":2026,"style":250},[249],[15,2028,227],{"className":2029},[254],[15,2031],{"className":2032,"style":250},[249],[15,2034,2036,2039,2042],{"className":2035},[50],[15,2037],{"className":2038,"style":322},[54],[15,2040,287],{"className":2041,"style":326},[59,60],[15,2043,205],{"className":2044},[59],", certainty at ",[15,2047,2049,2066],{"className":2048},[18],[15,2050,2052],{"className":2051},[22],[24,2053,2054],{"xmlns":26},[28,2055,2056,2064],{},[31,2057,2058,2060,2062],{},[34,2059,36],{},[118,2061,227],{},[34,2063,287],{},[38,2065,351],{"encoding":40},[15,2067,2069,2087],{"className":2068,"ariaHidden":46},[45],[15,2070,2072,2075,2078,2081,2084],{"className":2071},[50],[15,2073],{"className":2074,"style":55},[54],[15,2076,36],{"className":2077,"style":61},[59,60],[15,2079],{"className":2080,"style":250},[249],[15,2082,227],{"className":2083},[254],[15,2085],{"className":2086,"style":250},[249],[15,2088,2090,2093],{"className":2089},[50],[15,2091],{"className":2092,"style":379},[54],[15,2094,287],{"className":2095,"style":326},[59,60],[434,2097,2099],{"id":2098},"inverse","Inverse",[11,2101,2102,2103,2105,2106,383],{},"The inverse of ",[465,2104,1814],{}," is ",[465,2107,2108],{},"ry(-θ)",[434,2110,2112],{"id":2111},"usage","Usage",[2114,2115,2120],"pre",{"className":2116,"code":2117,"language":2118,"meta":2119,"style":2119},"language-python shiki shiki-themes one-dark-pro","from math import pi\nfrom qiskit import QuantumCircuit\n\nqc = QuantumCircuit(1, 1)\nqc.ry(pi \u002F 3, 0)\nqc.measure(0, 0)\n","python","",[465,2121,2122,2140,2153,2160,2186,2209],{"__ignoreMap":2119},[15,2123,2126,2130,2134,2137],{"class":2124,"line":2125},"line",1,[15,2127,2129],{"class":2128},"seHd6","from",[15,2131,2133],{"class":2132},"sn6KH"," math ",[15,2135,2136],{"class":2128},"import",[15,2138,2139],{"class":2132}," pi\n",[15,2141,2143,2145,2148,2150],{"class":2124,"line":2142},2,[15,2144,2129],{"class":2128},[15,2146,2147],{"class":2132}," qiskit ",[15,2149,2136],{"class":2128},[15,2151,2152],{"class":2132}," QuantumCircuit\n",[15,2154,2156],{"class":2124,"line":2155},3,[15,2157,2159],{"emptyLinePlaceholder":2158},true,"\n",[15,2161,2163,2166,2169,2173,2175,2178,2181,2183],{"class":2124,"line":2162},4,[15,2164,2165],{"class":2132},"qc ",[15,2167,227],{"class":2168},"sjrmR",[15,2170,2172],{"class":2171},"sVbv2"," QuantumCircuit",[15,2174,128],{"class":2132},[15,2176,1333],{"class":2177},"sVC51",[15,2179,2180],{"class":2132},", ",[15,2182,1333],{"class":2177},[15,2184,2185],{"class":2132},")\n",[15,2187,2189,2192,2195,2198,2200,2203,2205,2207],{"class":2124,"line":2188},5,[15,2190,2191],{"class":2132},"qc.",[15,2193,2194],{"class":2171},"ry",[15,2196,2197],{"class":2132},"(pi ",[15,2199,134],{"class":2168},[15,2201,2202],{"class":2177}," 3",[15,2204,2180],{"class":2132},[15,2206,230],{"class":2177},[15,2208,2185],{"class":2132},[15,2210,2212,2214,2217,2219,2221,2223,2225],{"class":2124,"line":2211},6,[15,2213,2191],{"class":2132},[15,2215,2216],{"class":2171},"measure",[15,2218,128],{"class":2132},[15,2220,230],{"class":2177},[15,2222,2180],{"class":2132},[15,2224,230],{"class":2177},[15,2226,2185],{"class":2132},[2114,2228,2232],{"className":2229,"code":2230,"language":2231,"meta":2119,"style":2119},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\n\nconst circuit = QuantumCircuit(1, 1);\ncircuit.ry(Math.PI \u002F 3, 0);\ncircuit.measure(0, 0);\n","js",[465,2233,2234,2257,2261,2286,2316],{"__ignoreMap":2119},[15,2235,2236,2238,2241,2245,2248,2250,2254],{"class":2124,"line":2125},[15,2237,2136],{"class":2128},[15,2239,2240],{"class":2132}," { ",[15,2242,2244],{"class":2243},"sVyAn","QuantumCircuit",[15,2246,2247],{"class":2132}," } ",[15,2249,2129],{"class":2128},[15,2251,2253],{"class":2252},"subq3"," 'qiskit'",[15,2255,2256],{"class":2132},";\n",[15,2258,2259],{"class":2124,"line":2142},[15,2260,2159],{"emptyLinePlaceholder":2158},[15,2262,2263,2266,2270,2273,2275,2277,2279,2281,2283],{"class":2124,"line":2155},[15,2264,2265],{"class":2128},"const",[15,2267,2269],{"class":2268},"sU0A5"," circuit",[15,2271,2272],{"class":2168}," =",[15,2274,2172],{"class":2171},[15,2276,128],{"class":2132},[15,2278,1333],{"class":2177},[15,2280,2180],{"class":2132},[15,2282,1333],{"class":2177},[15,2284,2285],{"class":2132},");\n",[15,2287,2288,2291,2293,2295,2297,2300,2302,2305,2308,2310,2312,2314],{"class":2124,"line":2162},[15,2289,2290],{"class":2268},"circuit",[15,2292,383],{"class":2132},[15,2294,2194],{"class":2171},[15,2296,128],{"class":2132},[15,2298,2299],{"class":2268},"Math",[15,2301,383],{"class":2132},[15,2303,2304],{"class":2243},"PI",[15,2306,2307],{"class":2168}," \u002F",[15,2309,2202],{"class":2177},[15,2311,2180],{"class":2132},[15,2313,230],{"class":2177},[15,2315,2285],{"class":2132},[15,2317,2318,2320,2322,2324,2326,2328,2330,2332],{"class":2124,"line":2188},[15,2319,2290],{"class":2268},[15,2321,383],{"class":2132},[15,2323,2216],{"class":2171},[15,2325,128],{"class":2132},[15,2327,230],{"class":2177},[15,2329,2180],{"class":2132},[15,2331,230],{"class":2177},[15,2333,2285],{"class":2132},[11,2335,2336,2337,2339,2340,383],{},"Over many shots about a quarter of them read ",[465,2338,1333],{},": ",[15,2341,2343,2381],{"className":2342},[18],[15,2344,2346],{"className":2345},[22],[24,2347,2348],{"xmlns":26},[28,2349,2350,2378],{},[31,2351,2352,2362,2364,2366,2368,2371,2373,2375],{},[110,2353,2354,2360],{},[31,2355,2356,2358],{},[34,2357,116],{},[118,2359,120],{},[122,2361,124],{},[118,2363,128],{"stretchy":127},[34,2365,287],{},[34,2367,134],{"mathvariant":133},[122,2369,2370],{},"6",[118,2372,139],{"stretchy":127},[118,2374,227],{},[122,2376,2377],{},"0.25",[38,2379,2380],{"encoding":40},"\\sin^2(\\pi\u002F6) = 0.25",[15,2382,2384,2441],{"className":2383,"ariaHidden":46},[45],[15,2385,2387,2390,2419,2422,2425,2429,2432,2435,2438],{"className":2386},[50],[15,2388],{"className":2389,"style":152},[54],[15,2391,2393,2396],{"className":2392},[156],[15,2394,116],{"className":2395},[156],[15,2397,2399],{"className":2398},[163],[15,2400,2402],{"className":2401},[167],[15,2403,2405],{"className":2404},[171],[15,2406,2408],{"className":2407,"style":176},[175],[15,2409,2410,2413],{"style":179},[15,2411],{"className":2412,"style":184},[183],[15,2414,2416],{"className":2415},[188,189,190,191],[15,2417,124],{"className":2418},[59,191],[15,2420,128],{"className":2421},[198],[15,2423,287],{"className":2424,"style":326},[59,60],[15,2426,2428],{"className":2427},[59],"\u002F6",[15,2430,139],{"className":2431},[209],[15,2433],{"className":2434,"style":250},[249],[15,2436,227],{"className":2437},[254],[15,2439],{"className":2440,"style":250},[249],[15,2442,2444,2447],{"className":2443},[50],[15,2445],{"className":2446,"style":264},[54],[15,2448,2377],{"className":2449},[59],[434,2451,2453],{"id":2452},"on-ionq-hardware","On IonQ hardware",[11,2455,2456,2457,2459,2460,2463,2464,2466,2467,2470,2471,2473,2474,2477,2478,383],{},"RY is not a native gate for a general angle. An arbitrary ",[465,2458,1814],{}," compiles to two ",[465,2461,2462],{},"GPi2"," pulses with a virtual Z of angle θ between them. The special angles are cheaper: ",[465,2465,1111],{}," is exactly ",[465,2468,2469],{},"GPi2(0.25)",", a single pulse, and ",[465,2472,1102],{}," is a single ",[465,2475,2476],{},"GPi",". See ",[428,2479,2481],{"href":2480},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",[434,2483,2485],{"id":2484},"related","Related",[2487,2488,2489,2496,2502,2506,2510],"ul",{},[2490,2491,2492],"li",{},[428,2493,2495],{"href":2494},"\u002Flearn\u002Fdocs\u002Frx-gate","RX gate",[2490,2497,2498],{},[428,2499,2501],{"href":2500},"\u002Flearn\u002Fdocs\u002Frz-gate","RZ gate",[2490,2503,2504],{},[428,2505,1107],{"href":1106},[2490,2507,2508],{},[428,2509,1193],{"href":1192},[2490,2511,2512],{},[428,2513,2515],{"href":2514},"\u002Flearn\u002Fdocs\u002Fgates","Gate reference",[2517,2518,2519],"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: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html pre.shiki code .sVyAn, html code.shiki .sVyAn{--shiki-default:#E06C75}html pre.shiki code .subq3, html code.shiki .subq3{--shiki-default:#98C379}html pre.shiki code .sU0A5, html code.shiki .sU0A5{--shiki-default:#E5C07B}",{"title":2119,"searchDepth":2142,"depth":2142,"links":2521},[2522,2523,2524,2525,2526,2527,2528],{"id":436,"depth":2142,"text":437},{"id":500,"depth":2142,"text":501},{"id":1232,"depth":2142,"text":1233},{"id":2098,"depth":2142,"text":2099},{"id":2111,"depth":2142,"text":2112},{"id":2452,"depth":2142,"text":2453},{"id":2484,"depth":2142,"text":2485},"gates","Gates","The RY gate, a rotation about Y by any angle: matrix, effect on the basis states, the ry() call in Python and JS, and its IonQ native-gate form.",false,"md","single-qubit","Single-qubit gates","doc",{},13,"\u002Fblog\u002Flearn\u002Fdocs\u002Fry-gate","2026-09-16",[],{"title":2543,"description":2544},"RY gate · Qollab docs","Reference for the RY(θ) rotation gate: matrix, action on the basis states, the Qiskit ry() call in Python and JS, and what it becomes on IonQ hardware.","blog\u002Flearn\u002Fdocs\u002Fry-gate",[],"Rv-qMErXSDGV6FqPtfAMd6lp6pWJNrki-8ylaF6KMic",[],[],[2551,2558,2574,2603,2687,2697],{"category":2552,"categoryName":2553,"articles":2554},"account","Account",[2555],{"title":2556,"href":2557},"Account and profile","\u002Flearn\u002Fdocs\u002Faccount-and-profile",{"category":2559,"categoryName":2560,"articles":2561},"projects","Projects",[2562,2565,2568,2571],{"title":2563,"href":2564},"The project page","\u002Flearn\u002Fdocs\u002Fproject-anatomy",{"title":2566,"href":2567},"Editing your project","\u002Flearn\u002Fdocs\u002Fwrite-your-project-page",{"title":2569,"href":2570},"Publishing and versions","\u002Flearn\u002Fdocs\u002Fpublish",{"title":2572,"href":2573},"Forking a project","\u002Flearn\u002Fdocs\u002Ffork-and-remix",{"category":2575,"categoryName":2576,"articles":2577},"running-code","Running code",[2578,2581,2584,2587,2590,2593,2594,2597,2600],{"title":2579,"href":2580},"Running your code","\u002Flearn\u002Fdocs\u002Frun-your-code",{"title":2582,"href":2583},"Compute backends","\u002Flearn\u002Fdocs\u002Fcompute-backends",{"title":2585,"href":2586},"The runtime environment","\u002Flearn\u002Fdocs\u002Fruntime-environment",{"title":2588,"href":2589},"JS \u002F Qiskit projects","\u002Flearn\u002Fdocs\u002Fjs-qiskit-projects",{"title":2591,"href":2592},"Python \u002F Qiskit projects","\u002Flearn\u002Fdocs\u002Fpython-qiskit-projects",{"title":2481,"href":2480},{"title":2595,"href":2596},"Error mitigation and debiasing","\u002Flearn\u002Fdocs\u002Ferror-mitigation",{"title":2598,"href":2599},"Transpilation","\u002Flearn\u002Fdocs\u002Ftranspilation",{"title":2601,"href":2602},"Primitives","\u002Flearn\u002Fdocs\u002Fprimitives",{"category":2529,"categoryName":2530,"articles":2604},[2605,2606,2607,2610,2611,2614,2617,2620,2623,2626,2629,2632,2635,2636,2638,2639,2644,2647,2650,2653,2656,2659,2662,2665,2670,2673,2678,2681,2684],{"title":2515,"href":2514},{"title":1193,"href":1192,"group":2534,"groupName":2535},{"title":2608,"href":2609,"group":2534,"groupName":2535},"X gate","\u002Flearn\u002Fdocs\u002Fx-gate",{"title":1107,"href":1106,"group":2534,"groupName":2535},{"title":2612,"href":2613,"group":2534,"groupName":2535},"Z gate","\u002Flearn\u002Fdocs\u002Fz-gate",{"title":2615,"href":2616,"group":2534,"groupName":2535},"S gate","\u002Flearn\u002Fdocs\u002Fs-gate",{"title":2618,"href":2619,"group":2534,"groupName":2535},"Sdg gate","\u002Flearn\u002Fdocs\u002Fsdg-gate",{"title":2621,"href":2622,"group":2534,"groupName":2535},"T gate","\u002Flearn\u002Fdocs\u002Ft-gate",{"title":2624,"href":2625,"group":2534,"groupName":2535},"Tdg gate","\u002Flearn\u002Fdocs\u002Ftdg-gate",{"title":2627,"href":2628,"group":2534,"groupName":2535},"√X gate","\u002Flearn\u002Fdocs\u002Fsx-gate",{"title":2630,"href":2631,"group":2534,"groupName":2535},"√X† gate","\u002Flearn\u002Fdocs\u002Fsxdg-gate",{"title":2633,"href":2634,"group":2534,"groupName":2535},"P gate","\u002Flearn\u002Fdocs\u002Fp-gate",{"title":2495,"href":2494,"group":2534,"groupName":2535},{"title":5,"href":2637,"group":2534,"groupName":2535},"\u002Flearn\u002Fdocs\u002Fry-gate",{"title":2501,"href":2500,"group":2534,"groupName":2535},{"title":2640,"href":2641,"group":2642,"groupName":2643},"CX gate","\u002Flearn\u002Fdocs\u002Fcx-gate","two-qubit","Two-qubit gates",{"title":2645,"href":2646,"group":2642,"groupName":2643},"CY gate","\u002Flearn\u002Fdocs\u002Fcy-gate",{"title":2648,"href":2649,"group":2642,"groupName":2643},"CZ gate","\u002Flearn\u002Fdocs\u002Fcz-gate",{"title":2651,"href":2652,"group":2642,"groupName":2643},"CP gate","\u002Flearn\u002Fdocs\u002Fcp-gate",{"title":2654,"href":2655,"group":2642,"groupName":2643},"Swap gate","\u002Flearn\u002Fdocs\u002Fswap-gate",{"title":2657,"href":2658,"group":2642,"groupName":2643},"RXX gate","\u002Flearn\u002Fdocs\u002Frxx-gate",{"title":2660,"href":2661,"group":2642,"groupName":2643},"RYY gate","\u002Flearn\u002Fdocs\u002Fryy-gate",{"title":2663,"href":2664,"group":2642,"groupName":2643},"RZZ gate","\u002Flearn\u002Fdocs\u002Frzz-gate",{"title":2666,"href":2667,"group":2668,"groupName":2669},"CCX gate","\u002Flearn\u002Fdocs\u002Fccx-gate","multi-qubit","Multi-qubit gates",{"title":2671,"href":2672,"group":2668,"groupName":2669},"Pauli evolution gate","\u002Flearn\u002Fdocs\u002Fpauli-evolution-gate",{"title":2674,"href":2675,"group":2676,"groupName":2677},"GPi gate","\u002Flearn\u002Fdocs\u002Fgpi-gate","native","IonQ native gates",{"title":2679,"href":2680,"group":2676,"groupName":2677},"GPi2 gate","\u002Flearn\u002Fdocs\u002Fgpi2-gate",{"title":2682,"href":2683,"group":2676,"groupName":2677},"MS gate","\u002Flearn\u002Fdocs\u002Fms-gate",{"title":2685,"href":2686,"group":2676,"groupName":2677},"ZZ gate","\u002Flearn\u002Fdocs\u002Fzz-gate",{"category":2688,"categoryName":2689,"articles":2690},"credits","Credits",[2691,2694],{"title":2692,"href":2693},"How credits work","\u002Flearn\u002Fdocs\u002Fhow-credits-work",{"title":2695,"href":2696},"Before you spend credits","\u002Flearn\u002Fdocs\u002Fbefore-you-spend-credits",{"category":2698,"categoryName":2699,"articles":2700},"troubleshooting","Troubleshooting",[2701,2704,2707],{"title":2702,"href":2703},"Troubleshooting and FAQ","\u002Flearn\u002Fdocs\u002Ffaq",{"title":2705,"href":2706},"Error reference","\u002Flearn\u002Fdocs\u002Ferror-reference",{"title":2708,"href":2709},"Why your results look wrong","\u002Flearn\u002Fdocs\u002Fwhy-your-results-look-wrong",1789652389564]