[{"data":1,"prerenderedAt":1425},["ShallowReactive",2],{"blog-post-docs\u002Fx-gate":3,"sibling-dives-docs\u002Fx-gate":1261,"learn-track-docs\u002Fx-gate":1262,"learn-docs-groups":1263},{"id":4,"title":5,"authors":6,"body":7,"breadcrumb":6,"builders":6,"byline":6,"category":1243,"categoryName":1244,"challenge":6,"courseAuthor":6,"courseLead":6,"dek":6,"description":1245,"draft":1246,"extension":1247,"eyebrow":6,"featured":1246,"finish":6,"fork":6,"group":1248,"groupName":1249,"hero":6,"heroAlt":6,"heroCta":6,"heroImage":6,"homepageFeatured":1246,"kind":1250,"lessonCount":6,"meta":1251,"navigation":1025,"newsItems":6,"next":6,"ogImage":6,"order":1022,"outcomes":6,"path":1252,"publishDate":1253,"readingTime":6,"related":1254,"relatedProjects":6,"seo":1255,"stem":1258,"tags":1259,"track":6,"trackName":6,"__hash__":1260},"blog\u002Fblog\u002Flearn\u002Fdocs\u002Fx-gate.md","X gate",null,{"type":8,"value":9,"toc":1234},"minimark",[10,191,236,241,304,308,550,557,561,901,982,986,989,993,1086,1179,1184,1188,1199,1203,1230],[11,12,13,14,75,76,114,115,75,150,185,186,190],"p",{},"The X gate, the quantum NOT, flips a qubit: ",[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 ",[15,77,79,98],{"className":78},[18],[15,80,82],{"className":81},[22],[24,83,84],{"xmlns":26},[28,85,86,95],{},[31,87,88,90,93],{},[34,89,37],{"mathvariant":36},[39,91,92],{},"1",[43,94,46],{"stretchy":45},[48,96,97],{"encoding":50},"\\vert 1 \\rangle",[15,99,101],{"className":100,"ariaHidden":56},[55],[15,102,104,107,111],{"className":103},[60],[15,105],{"className":106,"style":65},[64],[15,108,110],{"className":109},[69],"∣1",[15,112,46],{"className":113},[74]," and ",[15,116,118,135],{"className":117},[18],[15,119,121],{"className":120},[22],[24,122,123],{"xmlns":26},[28,124,125,133],{},[31,126,127,129,131],{},[34,128,37],{"mathvariant":36},[39,130,92],{},[43,132,46],{"stretchy":45},[48,134,97],{"encoding":50},[15,136,138],{"className":137,"ariaHidden":56},[55],[15,139,141,144,147],{"className":140},[60],[15,142],{"className":143,"style":65},[64],[15,145,110],{"className":146},[69],[15,148,46],{"className":149},[74],[15,151,153,170],{"className":152},[18],[15,154,156],{"className":155},[22],[24,157,158],{"xmlns":26},[28,159,160,168],{},[31,161,162,164,166],{},[34,163,37],{"mathvariant":36},[39,165,41],{},[43,167,46],{"stretchy":45},[48,169,51],{"encoding":50},[15,171,173],{"className":172,"ariaHidden":56},[55],[15,174,176,179,182],{"className":175},[60],[15,177],{"className":178,"style":65},[64],[15,180,70],{"className":181},[69],[15,183,46],{"className":184},[74],". It acts on one qubit and takes no parameters. The Circuit panel draws it as ",[187,188,189],"strong",{},"X",". Measured straight after it, a qubit that started as 0 reads 1.",[11,192,193,194,229,230,235],{},"Kets such as ",[15,195,197,214],{"className":196},[18],[15,198,200],{"className":199},[22],[24,201,202],{"xmlns":26},[28,203,204,212],{},[31,205,206,208,210],{},[34,207,37],{"mathvariant":36},[39,209,41],{},[43,211,46],{"stretchy":45},[48,213,51],{"encoding":50},[15,215,217],{"className":216,"ariaHidden":56},[55],[15,218,220,223,226],{"className":219},[60],[15,221],{"className":222,"style":65},[64],[15,224,70],{"className":225},[69],[15,227,46],{"className":228},[74]," name the basis states and rotations are described on the Bloch sphere; the ",[231,232,234],"a",{"href":233},"\u002Flearn\u002Fquantum-foundations\u002Fqubits","qubits lesson"," introduces both.",[237,238,240],"h2",{"id":239},"call","Call",[242,243,244,256],"table",{},[245,246,247],"thead",{},[248,249,250,254],"tr",{},[251,252,253],"th",{},"Where",[251,255,240],{},[257,258,259,271,281,291],"tbody",{},[248,260,261,265],{},[262,263,264],"td",{},"Python",[262,266,267],{},[268,269,270],"code",{},"qc.x(qubit)",[248,272,273,276],{},[262,274,275],{},"JS",[262,277,278],{},[268,279,280],{},"circuit.x(qubit)",[248,282,283,286],{},[262,284,285],{},"Qiskit class",[262,287,288],{},[268,289,290],{},"XGate",[248,292,293,296],{},[262,294,295],{},"Controlled form",[262,297,298],{},[231,299,301],{"href":300},"\u002Flearn\u002Fdocs\u002Fcx-gate",[268,302,303],{},"cx(control, target)",[237,305,307],{"id":306},"matrix","Matrix",[15,309,312],{"className":310},[311],"katex-display",[15,313,315,378],{"className":314},[18],[15,316,318],{"className":317},[22],[24,319,321],{"xmlns":26,"display":320},"block",[28,322,323,375],{},[31,324,325,327,330],{},[34,326,189],{},[43,328,329],{},"=",[31,331,332,335,372],{},[43,333,334],{"fence":56},"(",[336,337,341,358],"mtable",{"rowspacing":338,"columnalign":339,"columnspacing":340},"0.16em","center center","1em",[342,343,344,352],"mtr",{},[345,346,347],"mtd",{},[348,349,350],"mstyle",{"scriptlevel":41,"displaystyle":45},[39,351,41],{},[345,353,354],{},[348,355,356],{"scriptlevel":41,"displaystyle":45},[39,357,92],{},[342,359,360,366],{},[345,361,362],{},[348,363,364],{"scriptlevel":41,"displaystyle":45},[39,365,92],{},[345,367,368],{},[348,369,370],{"scriptlevel":41,"displaystyle":45},[39,371,41],{},[43,373,374],{"fence":56},")",[48,376,377],{"encoding":50},"X = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix}",[15,379,381,405],{"className":380,"ariaHidden":56},[55],[15,382,384,388,393,398,402],{"className":383},[60],[15,385],{"className":386,"style":387},[64],"height:0.6833em;",[15,389,189],{"className":390,"style":392},[69,391],"mathnormal","margin-right:0.0785em;",[15,394],{"className":395,"style":397},[396],"mspace","margin-right:0.2778em;",[15,399,329],{"className":400},[401],"mrel",[15,403],{"className":404,"style":397},[396],[15,406,408,412],{"className":407},[60],[15,409],{"className":410,"style":411},[64],"height:2.4em;vertical-align:-0.95em;",[15,413,416,427,544],{"className":414},[415],"minner",[15,417,422],{"className":418,"style":421},[419,420],"mopen","delimcenter","top:0em;",[15,423,334],{"className":424},[425,426],"delimsizing","size3",[15,428,430],{"className":429},[69],[15,431,433,491,496,499],{"className":432},[336],[15,434,437],{"className":435},[436],"col-align-c",[15,438,442,482],{"className":439},[440,441],"vlist-t","vlist-t2",[15,443,446,477],{"className":444},[445],"vlist-r",[15,447,451,465],{"className":448,"style":450},[449],"vlist","height:1.45em;",[15,452,454,459],{"style":453},"top:-3.61em;",[15,455],{"className":456,"style":458},[457],"pstrut","height:3em;",[15,460,462],{"className":461},[69],[15,463,41],{"className":464},[69],[15,466,468,471],{"style":467},"top:-2.41em;",[15,469],{"className":470,"style":458},[457],[15,472,474],{"className":473},[69],[15,475,92],{"className":476},[69],[15,478,481],{"className":479},[480],"vlist-s","​",[15,483,485],{"className":484},[445],[15,486,489],{"className":487,"style":488},[449],"height:0.95em;",[15,490],{},[15,492],{"className":493,"style":495},[494],"arraycolsep","width:0.5em;",[15,497],{"className":498,"style":495},[494],[15,500,502],{"className":501},[436],[15,503,505,536],{"className":504},[440,441],[15,506,508,533],{"className":507},[445],[15,509,511,522],{"className":510,"style":450},[449],[15,512,513,516],{"style":453},[15,514],{"className":515,"style":458},[457],[15,517,519],{"className":518},[69],[15,520,92],{"className":521},[69],[15,523,524,527],{"style":467},[15,525],{"className":526,"style":458},[457],[15,528,530],{"className":529},[69],[15,531,41],{"className":532},[69],[15,534,481],{"className":535},[480],[15,537,539],{"className":538},[445],[15,540,542],{"className":541,"style":488},[449],[15,543],{},[15,545,547],{"className":546,"style":421},[74,420],[15,548,374],{"className":549},[425,426],[11,551,552,553,556],{},"On the Bloch sphere this is a half-turn about the X axis. It is the same operation as ",[268,554,555],{},"rx(π)"," up to a global phase.",[237,558,560],{"id":559},"effect-on-basis-states","Effect on basis states",[242,562,563,573],{},[245,564,565],{},[248,566,567,570],{},[251,568,569],{},"Input",[251,571,572],{},"Output",[257,574,575,651,727,811],{},[248,576,577,614],{},[262,578,579],{},[15,580,582,599],{"className":581},[18],[15,583,585],{"className":584},[22],[24,586,587],{"xmlns":26},[28,588,589,597],{},[31,590,591,593,595],{},[34,592,37],{"mathvariant":36},[39,594,41],{},[43,596,46],{"stretchy":45},[48,598,51],{"encoding":50},[15,600,602],{"className":601,"ariaHidden":56},[55],[15,603,605,608,611],{"className":604},[60],[15,606],{"className":607,"style":65},[64],[15,609,70],{"className":610},[69],[15,612,46],{"className":613},[74],[262,615,616],{},[15,617,619,636],{"className":618},[18],[15,620,622],{"className":621},[22],[24,623,624],{"xmlns":26},[28,625,626,634],{},[31,627,628,630,632],{},[34,629,37],{"mathvariant":36},[39,631,92],{},[43,633,46],{"stretchy":45},[48,635,97],{"encoding":50},[15,637,639],{"className":638,"ariaHidden":56},[55],[15,640,642,645,648],{"className":641},[60],[15,643],{"className":644,"style":65},[64],[15,646,110],{"className":647},[69],[15,649,46],{"className":650},[74],[248,652,653,690],{},[262,654,655],{},[15,656,658,675],{"className":657},[18],[15,659,661],{"className":660},[22],[24,662,663],{"xmlns":26},[28,664,665,673],{},[31,666,667,669,671],{},[34,668,37],{"mathvariant":36},[39,670,92],{},[43,672,46],{"stretchy":45},[48,674,97],{"encoding":50},[15,676,678],{"className":677,"ariaHidden":56},[55],[15,679,681,684,687],{"className":680},[60],[15,682],{"className":683,"style":65},[64],[15,685,110],{"className":686},[69],[15,688,46],{"className":689},[74],[262,691,692],{},[15,693,695,712],{"className":694},[18],[15,696,698],{"className":697},[22],[24,699,700],{"xmlns":26},[28,701,702,710],{},[31,703,704,706,708],{},[34,705,37],{"mathvariant":36},[39,707,41],{},[43,709,46],{"stretchy":45},[48,711,51],{"encoding":50},[15,713,715],{"className":714,"ariaHidden":56},[55],[15,716,718,721,724],{"className":717},[60],[15,719],{"className":720,"style":65},[64],[15,722,70],{"className":723},[69],[15,725,46],{"className":726},[74],[248,728,729,771],{},[262,730,731],{},[15,732,734,753],{"className":733},[18],[15,735,737],{"className":736},[22],[24,738,739],{"xmlns":26},[28,740,741,750],{},[31,742,743,745,748],{},[34,744,37],{"mathvariant":36},[43,746,747],{},"+",[43,749,46],{"stretchy":45},[48,751,752],{"encoding":50},"\\vert + \\rangle",[15,754,756],{"className":755,"ariaHidden":56},[55],[15,757,759,762,765,768],{"className":758},[60],[15,760],{"className":761,"style":65},[64],[15,763,37],{"className":764},[69],[15,766,747],{"className":767},[69],[15,769,46],{"className":770},[74],[262,772,773],{},[15,774,776,793],{"className":775},[18],[15,777,779],{"className":778},[22],[24,780,781],{"xmlns":26},[28,782,783,791],{},[31,784,785,787,789],{},[34,786,37],{"mathvariant":36},[43,788,747],{},[43,790,46],{"stretchy":45},[48,792,752],{"encoding":50},[15,794,796],{"className":795,"ariaHidden":56},[55],[15,797,799,802,805,808],{"className":798},[60],[15,800],{"className":801,"style":65},[64],[15,803,37],{"className":804},[69],[15,806,747],{"className":807},[69],[15,809,46],{"className":810},[74],[248,812,813,855],{},[262,814,815],{},[15,816,818,837],{"className":817},[18],[15,819,821],{"className":820},[22],[24,822,823],{"xmlns":26},[28,824,825,834],{},[31,826,827,829,832],{},[34,828,37],{"mathvariant":36},[43,830,831],{},"−",[43,833,46],{"stretchy":45},[48,835,836],{"encoding":50},"\\vert - \\rangle",[15,838,840],{"className":839,"ariaHidden":56},[55],[15,841,843,846,849,852],{"className":842},[60],[15,844],{"className":845,"style":65},[64],[15,847,37],{"className":848},[69],[15,850,831],{"className":851},[69],[15,853,46],{"className":854},[74],[262,856,857],{},[15,858,860,880],{"className":859},[18],[15,861,863],{"className":862},[22],[24,864,865],{"xmlns":26},[28,866,867,877],{},[31,868,869,871,873,875],{},[43,870,831],{},[34,872,37],{"mathvariant":36},[43,874,831],{},[43,876,46],{"stretchy":45},[48,878,879],{"encoding":50},"-\\vert - \\rangle",[15,881,883],{"className":882,"ariaHidden":56},[55],[15,884,886,889,892,895,898],{"className":885},[60],[15,887],{"className":888,"style":65},[64],[15,890,831],{"className":891},[69],[15,893,37],{"className":894},[69],[15,896,831],{"className":897},[69],[15,899,46],{"className":900},[74],[11,902,903,904,942,943,981],{},"On a superposition it swaps the two amplitudes, so ",[15,905,907,924],{"className":906},[18],[15,908,910],{"className":909},[22],[24,911,912],{"xmlns":26},[28,913,914,922],{},[31,915,916,918,920],{},[34,917,37],{"mathvariant":36},[43,919,747],{},[43,921,46],{"stretchy":45},[48,923,752],{"encoding":50},[15,925,927],{"className":926,"ariaHidden":56},[55],[15,928,930,933,936,939],{"className":929},[60],[15,931],{"className":932,"style":65},[64],[15,934,37],{"className":935},[69],[15,937,747],{"className":938},[69],[15,940,46],{"className":941},[74]," is unchanged and ",[15,944,946,963],{"className":945},[18],[15,947,949],{"className":948},[22],[24,950,951],{"xmlns":26},[28,952,953,961],{},[31,954,955,957,959],{},[34,956,37],{"mathvariant":36},[43,958,831],{},[43,960,46],{"stretchy":45},[48,962,836],{"encoding":50},[15,964,966],{"className":965,"ariaHidden":56},[55],[15,967,969,972,975,978],{"className":968},[60],[15,970],{"className":971,"style":65},[64],[15,973,37],{"className":974},[69],[15,976,831],{"className":977},[69],[15,979,46],{"className":980},[74]," only picks up a sign.",[237,983,985],{"id":984},"inverse","Inverse",[11,987,988],{},"X is its own inverse. Two X gates in a row on the same qubit cancel.",[237,990,992],{"id":991},"usage","Usage",[994,995,1000],"pre",{"className":996,"code":997,"language":998,"meta":999,"style":999},"language-python shiki shiki-themes one-dark-pro","from qiskit import QuantumCircuit\n\nqc = QuantumCircuit(1, 1)\nqc.x(0)\nqc.measure(0, 0)\n","python","",[268,1001,1002,1020,1027,1053,1068],{"__ignoreMap":999},[15,1003,1006,1010,1014,1017],{"class":1004,"line":1005},"line",1,[15,1007,1009],{"class":1008},"seHd6","from",[15,1011,1013],{"class":1012},"sn6KH"," qiskit ",[15,1015,1016],{"class":1008},"import",[15,1018,1019],{"class":1012}," QuantumCircuit\n",[15,1021,1023],{"class":1004,"line":1022},2,[15,1024,1026],{"emptyLinePlaceholder":1025},true,"\n",[15,1028,1030,1033,1036,1040,1042,1045,1048,1050],{"class":1004,"line":1029},3,[15,1031,1032],{"class":1012},"qc ",[15,1034,329],{"class":1035},"sjrmR",[15,1037,1039],{"class":1038},"sVbv2"," QuantumCircuit",[15,1041,334],{"class":1012},[15,1043,92],{"class":1044},"sVC51",[15,1046,1047],{"class":1012},", ",[15,1049,92],{"class":1044},[15,1051,1052],{"class":1012},")\n",[15,1054,1056,1059,1062,1064,1066],{"class":1004,"line":1055},4,[15,1057,1058],{"class":1012},"qc.",[15,1060,1061],{"class":1038},"x",[15,1063,334],{"class":1012},[15,1065,41],{"class":1044},[15,1067,1052],{"class":1012},[15,1069,1071,1073,1076,1078,1080,1082,1084],{"class":1004,"line":1070},5,[15,1072,1058],{"class":1012},[15,1074,1075],{"class":1038},"measure",[15,1077,334],{"class":1012},[15,1079,41],{"class":1044},[15,1081,1047],{"class":1012},[15,1083,41],{"class":1044},[15,1085,1052],{"class":1012},[994,1087,1091],{"className":1088,"code":1089,"language":1090,"meta":999,"style":999},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\n\nconst circuit = QuantumCircuit(1, 1);\ncircuit.x(0);\ncircuit.measure(0, 0);\n","js",[268,1092,1093,1116,1120,1145,1161],{"__ignoreMap":999},[15,1094,1095,1097,1100,1104,1107,1109,1113],{"class":1004,"line":1005},[15,1096,1016],{"class":1008},[15,1098,1099],{"class":1012}," { ",[15,1101,1103],{"class":1102},"sVyAn","QuantumCircuit",[15,1105,1106],{"class":1012}," } ",[15,1108,1009],{"class":1008},[15,1110,1112],{"class":1111},"subq3"," 'qiskit'",[15,1114,1115],{"class":1012},";\n",[15,1117,1118],{"class":1004,"line":1022},[15,1119,1026],{"emptyLinePlaceholder":1025},[15,1121,1122,1125,1129,1132,1134,1136,1138,1140,1142],{"class":1004,"line":1029},[15,1123,1124],{"class":1008},"const",[15,1126,1128],{"class":1127},"sU0A5"," circuit",[15,1130,1131],{"class":1035}," =",[15,1133,1039],{"class":1038},[15,1135,334],{"class":1012},[15,1137,92],{"class":1044},[15,1139,1047],{"class":1012},[15,1141,92],{"class":1044},[15,1143,1144],{"class":1012},");\n",[15,1146,1147,1150,1153,1155,1157,1159],{"class":1004,"line":1055},[15,1148,1149],{"class":1127},"circuit",[15,1151,1152],{"class":1012},".",[15,1154,1061],{"class":1038},[15,1156,334],{"class":1012},[15,1158,41],{"class":1044},[15,1160,1144],{"class":1012},[15,1162,1163,1165,1167,1169,1171,1173,1175,1177],{"class":1004,"line":1070},[15,1164,1149],{"class":1127},[15,1166,1152],{"class":1012},[15,1168,1075],{"class":1038},[15,1170,334],{"class":1012},[15,1172,41],{"class":1044},[15,1174,1047],{"class":1012},[15,1176,41],{"class":1044},[15,1178,1144],{"class":1012},[11,1180,1181,1182,1152],{},"Every shot reads ",[268,1183,92],{},[237,1185,1187],{"id":1186},"on-ionq-hardware","On IonQ hardware",[11,1189,1190,1191,1194,1195,1152],{},"X is exactly ",[268,1192,1193],{},"GPi(0)",", a native gate, so it costs one physical pulse. See ",[231,1196,1198],{"href":1197},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",[237,1200,1202],{"id":1201},"related","Related",[1204,1205,1206,1212,1218,1224],"ul",{},[1207,1208,1209],"li",{},[231,1210,1211],{"href":300},"CX gate",[1207,1213,1214],{},[231,1215,1217],{"href":1216},"\u002Flearn\u002Fdocs\u002Fsx-gate","√X gate",[1207,1219,1220],{},[231,1221,1223],{"href":1222},"\u002Flearn\u002Fdocs\u002Frx-gate","RX gate",[1207,1225,1226],{},[231,1227,1229],{"href":1228},"\u002Flearn\u002Fdocs\u002Fgates","Gate reference",[1231,1232,1233],"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 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