[{"data":1,"prerenderedAt":1817},["ShallowReactive",2],{"blog-post-docs\u002Fcz-gate":3,"sibling-dives-docs\u002Fcz-gate":1657,"learn-track-docs\u002Fcz-gate":1658,"learn-docs-groups":1659},{"id":4,"title":5,"authors":6,"body":7,"breadcrumb":6,"builders":6,"byline":6,"category":1638,"categoryName":1639,"challenge":6,"courseAuthor":6,"courseLead":6,"dek":6,"description":1640,"draft":1641,"extension":1642,"eyebrow":6,"featured":1641,"finish":6,"fork":6,"group":1643,"groupName":1644,"hero":6,"heroAlt":6,"heroCta":6,"heroImage":6,"homepageFeatured":1641,"kind":1645,"lessonCount":6,"meta":1646,"navigation":1298,"newsItems":6,"next":6,"ogImage":6,"order":1647,"outcomes":6,"path":1648,"publishDate":1649,"readingTime":6,"related":1650,"relatedProjects":6,"seo":1651,"stem":1654,"tags":1655,"track":6,"trackName":6,"__hash__":1656},"blog\u002Fblog\u002Flearn\u002Fdocs\u002Fcz-gate.md","CZ gate",null,{"type":8,"value":9,"toc":1629},"minimark",[10,90,138,143,192,196,306,901,912,916,1243,1255,1259,1262,1266,1415,1562,1571,1575,1590,1594,1625],[11,12,13,14,75,76,80,81,84,85,89],"p",{},"The CZ gate flips the sign of the ",[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",{},"11",[43,44,46],"mo",{"stretchy":45},"false","⟩",[48,49,51],"annotation",{"encoding":50},"application\u002Fx-tex","\\vert 11 \\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","∣11",[15,72,46],{"className":73},[74],"mclose"," amplitude and leaves the other three basis states alone. It acts on two qubits and takes no parameters. Control and target are interchangeable: ",[77,78,79],"code",{},"cz(0, 1)"," and ",[77,82,83],{},"cz(1, 0)"," are the same gate. The Circuit panel draws a dot on the control wire joined to a ",[86,87,88],"strong",{},"Z"," box on the target wire. On its own it changes nothing a measurement can see; the sign shows once the qubits are in superposition.",[11,91,92,93,131,132,137],{},"Kets such as ",[15,94,96,115],{"className":95},[18],[15,97,99],{"className":98},[22],[24,100,101],{"xmlns":26},[28,102,103,112],{},[31,104,105,107,110],{},[34,106,37],{"mathvariant":36},[39,108,109],{},"0",[43,111,46],{"stretchy":45},[48,113,114],{"encoding":50},"\\vert 0 \\rangle",[15,116,118],{"className":117,"ariaHidden":56},[55],[15,119,121,124,128],{"className":120},[60],[15,122],{"className":123,"style":65},[64],[15,125,127],{"className":126},[69],"∣0",[15,129,46],{"className":130},[74]," name the basis states and rotations are described on the Bloch sphere; the ",[133,134,136],"a",{"href":135},"\u002Flearn\u002Fquantum-foundations\u002Fqubits","qubits lesson"," introduces both.",[139,140,142],"h2",{"id":141},"call","Call",[144,145,146,158],"table",{},[147,148,149],"thead",{},[150,151,152,156],"tr",{},[153,154,155],"th",{},"Where",[153,157,142],{},[159,160,161,172,182],"tbody",{},[150,162,163,167],{},[164,165,166],"td",{},"Python",[164,168,169],{},[77,170,171],{},"qc.cz(control, target)",[150,173,174,177],{},[164,175,176],{},"JS",[164,178,179],{},[77,180,181],{},"circuit.cz(control, target)",[150,183,184,187],{},[164,185,186],{},"Qiskit class",[164,188,189],{},[77,190,191],{},"CZGate",[139,193,195],{"id":194},"matrix","Matrix",[11,197,198,199,305],{},"The matrix uses the basis order ",[15,200,202,248],{"className":201},[18],[15,203,205],{"className":204},[22],[24,206,207],{"xmlns":26},[28,208,209,245],{},[31,210,211,213,216,218,221,223,226,228,230,232,235,237,239,241,243],{},[34,212,37],{"mathvariant":36},[39,214,215],{},"00",[43,217,46],{"stretchy":45},[43,219,220],{"separator":56},",",[34,222,37],{"mathvariant":36},[39,224,225],{},"01",[43,227,46],{"stretchy":45},[43,229,220],{"separator":56},[34,231,37],{"mathvariant":36},[39,233,234],{},"10",[43,236,46],{"stretchy":45},[43,238,220],{"separator":56},[34,240,37],{"mathvariant":36},[39,242,41],{},[43,244,46],{"stretchy":45},[48,246,247],{"encoding":50},"\\vert 00 \\rangle, \\vert 01 \\rangle, \\vert 10 \\rangle, \\vert 11 \\rangle",[15,249,251],{"className":250,"ariaHidden":56},[55],[15,252,254,257,261,264,268,273,277,280,283,286,290,293,296,299,302],{"className":253},[60],[15,255],{"className":256,"style":65},[64],[15,258,260],{"className":259},[69],"∣00",[15,262,46],{"className":263},[74],[15,265,220],{"className":266},[267],"mpunct",[15,269],{"className":270,"style":272},[271],"mspace","margin-right:0.1667em;",[15,274,276],{"className":275},[69],"∣01",[15,278,46],{"className":279},[74],[15,281,220],{"className":282},[267],[15,284],{"className":285,"style":272},[271],[15,287,289],{"className":288},[69],"∣10",[15,291,46],{"className":292},[74],[15,294,220],{"className":295},[267],[15,297],{"className":298,"style":272},[271],[15,300,70],{"className":301},[69],[15,303,46],{"className":304},[74],".",[15,307,310],{"className":308},[309],"katex-display",[15,311,313,461],{"className":312},[18],[15,314,316],{"className":315},[22],[24,317,319],{"xmlns":26,"display":318},"block",[28,320,321,458],{},[31,322,323,326,328,331],{},[34,324,325],{},"C",[34,327,88],{},[43,329,330],{},"=",[31,332,333,336,455],{},[43,334,335],{"fence":56},"(",[337,338,342,372,398,424],"mtable",{"rowspacing":339,"columnalign":340,"columnspacing":341},"0.16em","center center center center","1em",[343,344,345,354,360,366],"mtr",{},[346,347,348],"mtd",{},[349,350,351],"mstyle",{"scriptlevel":109,"displaystyle":45},[39,352,353],{},"1",[346,355,356],{},[349,357,358],{"scriptlevel":109,"displaystyle":45},[39,359,109],{},[346,361,362],{},[349,363,364],{"scriptlevel":109,"displaystyle":45},[39,365,109],{},[346,367,368],{},[349,369,370],{"scriptlevel":109,"displaystyle":45},[39,371,109],{},[343,373,374,380,386,392],{},[346,375,376],{},[349,377,378],{"scriptlevel":109,"displaystyle":45},[39,379,109],{},[346,381,382],{},[349,383,384],{"scriptlevel":109,"displaystyle":45},[39,385,353],{},[346,387,388],{},[349,389,390],{"scriptlevel":109,"displaystyle":45},[39,391,109],{},[346,393,394],{},[349,395,396],{"scriptlevel":109,"displaystyle":45},[39,397,109],{},[343,399,400,406,412,418],{},[346,401,402],{},[349,403,404],{"scriptlevel":109,"displaystyle":45},[39,405,109],{},[346,407,408],{},[349,409,410],{"scriptlevel":109,"displaystyle":45},[39,411,109],{},[346,413,414],{},[349,415,416],{"scriptlevel":109,"displaystyle":45},[39,417,353],{},[346,419,420],{},[349,421,422],{"scriptlevel":109,"displaystyle":45},[39,423,109],{},[343,425,426,432,438,444],{},[346,427,428],{},[349,429,430],{"scriptlevel":109,"displaystyle":45},[39,431,109],{},[346,433,434],{},[349,435,436],{"scriptlevel":109,"displaystyle":45},[39,437,109],{},[346,439,440],{},[349,441,442],{"scriptlevel":109,"displaystyle":45},[39,443,109],{},[346,445,446],{},[349,447,448],{"scriptlevel":109,"displaystyle":45},[31,449,450,453],{},[43,451,452],{},"−",[39,454,353],{},[43,456,457],{"fence":56},")",[48,459,460],{"encoding":50},"CZ = \\begin{pmatrix} 1 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 \\\\ 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & -1 \\end{pmatrix}",[15,462,464,490],{"className":463,"ariaHidden":56},[55],[15,465,467,471,476,479,483,487],{"className":466},[60],[15,468],{"className":469,"style":470},[64],"height:0.6833em;",[15,472,325],{"className":473,"style":475},[69,474],"mathnormal","margin-right:0.0715em;",[15,477,88],{"className":478,"style":475},[69,474],[15,480],{"className":481,"style":482},[271],"margin-right:0.2778em;",[15,484,330],{"className":485},[486],"mrel",[15,488],{"className":489,"style":482},[271],[15,491,493,497],{"className":492},[60],[15,494],{"className":495,"style":496},[64],"height:4.8em;vertical-align:-2.15em;",[15,498,501,560,863],{"className":499},[500],"minner",[15,502,505],{"className":503},[504],"mopen",[15,506,510],{"className":507},[508,509],"delimsizing","mult",[15,511,515,551],{"className":512},[513,514],"vlist-t","vlist-t2",[15,516,519,546],{"className":517},[518],"vlist-r",[15,520,524],{"className":521,"style":523},[522],"vlist","height:2.65em;",[15,525,527,532],{"style":526},"top:-4.65em;",[15,528],{"className":529,"style":531},[530],"pstrut","height:6.8em;",[15,533,535],{"style":534},"width:0.875em;height:4.8em;",[536,537,542],"svg",{"xmlns":538,"width":539,"height":540,"viewBox":541},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.875em","4.8em","0 0 875 4800",[543,544],"path",{"d":545},"M863,9c0,-2,-2,-5,-6,-9c0,0,-17,0,-17,0c-12.7,0,-19.3,0.3,-20,1\nc-5.3,5.3,-10.3,11,-15,17c-242.7,294.7,-395.3,682,-458,1162c-21.3,163.3,-33.3,349,\n-36,557 l0,1284c0.2,6,0,26,0,60c2,159.3,10,310.7,24,454c53.3,528,210,\n949.7,470,1265c4.7,6,9.7,11.7,15,17c0.7,0.7,7,1,19,1c0,0,18,0,18,0c4,-4,6,-7,6,-9\nc0,-2.7,-3.3,-8.7,-10,-18c-135.3,-192.7,-235.5,-414.3,-300.5,-665c-65,-250.7,-102.5,\n-544.7,-112.5,-882c-2,-104,-3,-167,-3,-189\nl0,-1292c0,-162.7,5.7,-314,17,-454c20.7,-272,63.7,-513,129,-723c65.3,\n-210,155.3,-396.3,270,-559c6.7,-9.3,10,-15.3,10,-18z",[15,547,550],{"className":548},[549],"vlist-s","​",[15,552,554],{"className":553},[518],[15,555,558],{"className":556,"style":557},[522],"height:2.15em;",[15,559],{},[15,561,563],{"className":562},[69],[15,564,566,639,644,647,714,717,720,787,790,793],{"className":565},[337],[15,567,570],{"className":568},[569],"col-align-c",[15,571,573,631],{"className":572},[513,514],[15,574,576,628],{"className":575},[518],[15,577,579,592,604,616],{"className":578,"style":523},[522],[15,580,582,586],{"style":581},"top:-4.81em;",[15,583],{"className":584,"style":585},[530],"height:3em;",[15,587,589],{"className":588},[69],[15,590,353],{"className":591},[69],[15,593,595,598],{"style":594},"top:-3.61em;",[15,596],{"className":597,"style":585},[530],[15,599,601],{"className":600},[69],[15,602,109],{"className":603},[69],[15,605,607,610],{"style":606},"top:-2.41em;",[15,608],{"className":609,"style":585},[530],[15,611,613],{"className":612},[69],[15,614,109],{"className":615},[69],[15,617,619,622],{"style":618},"top:-1.21em;",[15,620],{"className":621,"style":585},[530],[15,623,625],{"className":624},[69],[15,626,109],{"className":627},[69],[15,629,550],{"className":630},[549],[15,632,634],{"className":633},[518],[15,635,637],{"className":636,"style":557},[522],[15,638],{},[15,640],{"className":641,"style":643},[642],"arraycolsep","width:0.5em;",[15,645],{"className":646,"style":643},[642],[15,648,650],{"className":649},[569],[15,651,653,706],{"className":652},[513,514],[15,654,656,703],{"className":655},[518],[15,657,659,670,681,692],{"className":658,"style":523},[522],[15,660,661,664],{"style":581},[15,662],{"className":663,"style":585},[530],[15,665,667],{"className":666},[69],[15,668,109],{"className":669},[69],[15,671,672,675],{"style":594},[15,673],{"className":674,"style":585},[530],[15,676,678],{"className":677},[69],[15,679,353],{"className":680},[69],[15,682,683,686],{"style":606},[15,684],{"className":685,"style":585},[530],[15,687,689],{"className":688},[69],[15,690,109],{"className":691},[69],[15,693,694,697],{"style":618},[15,695],{"className":696,"style":585},[530],[15,698,700],{"className":699},[69],[15,701,109],{"className":702},[69],[15,704,550],{"className":705},[549],[15,707,709],{"className":708},[518],[15,710,712],{"className":711,"style":557},[522],[15,713],{},[15,715],{"className":716,"style":643},[642],[15,718],{"className":719,"style":643},[642],[15,721,723],{"className":722},[569],[15,724,726,779],{"className":725},[513,514],[15,727,729,776],{"className":728},[518],[15,730,732,743,754,765],{"className":731,"style":523},[522],[15,733,734,737],{"style":581},[15,735],{"className":736,"style":585},[530],[15,738,740],{"className":739},[69],[15,741,109],{"className":742},[69],[15,744,745,748],{"style":594},[15,746],{"className":747,"style":585},[530],[15,749,751],{"className":750},[69],[15,752,109],{"className":753},[69],[15,755,756,759],{"style":606},[15,757],{"className":758,"style":585},[530],[15,760,762],{"className":761},[69],[15,763,353],{"className":764},[69],[15,766,767,770],{"style":618},[15,768],{"className":769,"style":585},[530],[15,771,773],{"className":772},[69],[15,774,109],{"className":775},[69],[15,777,550],{"className":778},[549],[15,780,782],{"className":781},[518],[15,783,785],{"className":784,"style":557},[522],[15,786],{},[15,788],{"className":789,"style":643},[642],[15,791],{"className":792,"style":643},[642],[15,794,796],{"className":795},[569],[15,797,799,855],{"className":798},[513,514],[15,800,802,852],{"className":801},[518],[15,803,805,816,827,838],{"className":804,"style":523},[522],[15,806,807,810],{"style":581},[15,808],{"className":809,"style":585},[530],[15,811,813],{"className":812},[69],[15,814,109],{"className":815},[69],[15,817,818,821],{"style":594},[15,819],{"className":820,"style":585},[530],[15,822,824],{"className":823},[69],[15,825,109],{"className":826},[69],[15,828,829,832],{"style":606},[15,830],{"className":831,"style":585},[530],[15,833,835],{"className":834},[69],[15,836,109],{"className":837},[69],[15,839,840,843],{"style":618},[15,841],{"className":842,"style":585},[530],[15,844,846,849],{"className":845},[69],[15,847,452],{"className":848},[69],[15,850,353],{"className":851},[69],[15,853,550],{"className":854},[549],[15,856,858],{"className":857},[518],[15,859,861],{"className":860,"style":557},[522],[15,862],{},[15,864,866],{"className":865},[74],[15,867,869],{"className":868},[508,509],[15,870,872,893],{"className":871},[513,514],[15,873,875,890],{"className":874},[518],[15,876,878],{"className":877,"style":523},[522],[15,879,880,883],{"style":526},[15,881],{"className":882,"style":531},[530],[15,884,885],{"style":534},[536,886,887],{"xmlns":538,"width":539,"height":540,"viewBox":541},[543,888],{"d":889},"M76,0c-16.7,0,-25,3,-25,9c0,2,2,6.3,6,13c21.3,28.7,42.3,60.3,\n63,95c96.7,156.7,172.8,332.5,228.5,527.5c55.7,195,92.8,416.5,111.5,664.5\nc11.3,139.3,17,290.7,17,454c0,28,1.7,43,3.3,45l0,1209\nc-3,4,-3.3,16.7,-3.3,38c0,162,-5.7,313.7,-17,455c-18.7,248,-55.8,469.3,-111.5,664\nc-55.7,194.7,-131.8,370.3,-228.5,527c-20.7,34.7,-41.7,66.3,-63,95c-2,3.3,-4,7,-6,11\nc0,7.3,5.7,11,17,11c0,0,11,0,11,0c9.3,0,14.3,-0.3,15,-1c5.3,-5.3,10.3,-11,15,-17\nc242.7,-294.7,395.3,-681.7,458,-1161c21.3,-164.7,33.3,-350.7,36,-558\nl0,-1344c-2,-159.3,-10,-310.7,-24,-454c-53.3,-528,-210,-949.7,\n-470,-1265c-4.7,-6,-9.7,-11.7,-15,-17c-0.7,-0.7,-6.7,-1,-18,-1z",[15,891,550],{"className":892},[549],[15,894,896],{"className":895},[518],[15,897,899],{"className":898,"style":557},[522],[15,900],{},[11,902,903,904,907,908,305],{},"The matrix is diagonal and symmetric in the two qubits, which is why the roles of control and target do not matter. CZ is the special case ",[77,905,906],{},"cp(π)"," of the ",[133,909,911],{"href":910},"\u002Flearn\u002Fdocs\u002Fcp-gate","CP gate",[139,913,915],{"id":914},"effect-on-basis-states","Effect on basis states",[144,917,918,928],{},[147,919,920],{},[150,921,922,925],{},[153,923,924],{},"Input",[153,926,927],{},"Output",[159,929,930,1007,1084,1161],{},[150,931,932,970],{},[164,933,934],{},[15,935,937,955],{"className":936},[18],[15,938,940],{"className":939},[22],[24,941,942],{"xmlns":26},[28,943,944,952],{},[31,945,946,948,950],{},[34,947,37],{"mathvariant":36},[39,949,215],{},[43,951,46],{"stretchy":45},[48,953,954],{"encoding":50},"\\vert 00 \\rangle",[15,956,958],{"className":957,"ariaHidden":56},[55],[15,959,961,964,967],{"className":960},[60],[15,962],{"className":963,"style":65},[64],[15,965,260],{"className":966},[69],[15,968,46],{"className":969},[74],[164,971,972],{},[15,973,975,992],{"className":974},[18],[15,976,978],{"className":977},[22],[24,979,980],{"xmlns":26},[28,981,982,990],{},[31,983,984,986,988],{},[34,985,37],{"mathvariant":36},[39,987,215],{},[43,989,46],{"stretchy":45},[48,991,954],{"encoding":50},[15,993,995],{"className":994,"ariaHidden":56},[55],[15,996,998,1001,1004],{"className":997},[60],[15,999],{"className":1000,"style":65},[64],[15,1002,260],{"className":1003},[69],[15,1005,46],{"className":1006},[74],[150,1008,1009,1047],{},[164,1010,1011],{},[15,1012,1014,1032],{"className":1013},[18],[15,1015,1017],{"className":1016},[22],[24,1018,1019],{"xmlns":26},[28,1020,1021,1029],{},[31,1022,1023,1025,1027],{},[34,1024,37],{"mathvariant":36},[39,1026,225],{},[43,1028,46],{"stretchy":45},[48,1030,1031],{"encoding":50},"\\vert 01 \\rangle",[15,1033,1035],{"className":1034,"ariaHidden":56},[55],[15,1036,1038,1041,1044],{"className":1037},[60],[15,1039],{"className":1040,"style":65},[64],[15,1042,276],{"className":1043},[69],[15,1045,46],{"className":1046},[74],[164,1048,1049],{},[15,1050,1052,1069],{"className":1051},[18],[15,1053,1055],{"className":1054},[22],[24,1056,1057],{"xmlns":26},[28,1058,1059,1067],{},[31,1060,1061,1063,1065],{},[34,1062,37],{"mathvariant":36},[39,1064,225],{},[43,1066,46],{"stretchy":45},[48,1068,1031],{"encoding":50},[15,1070,1072],{"className":1071,"ariaHidden":56},[55],[15,1073,1075,1078,1081],{"className":1074},[60],[15,1076],{"className":1077,"style":65},[64],[15,1079,276],{"className":1080},[69],[15,1082,46],{"className":1083},[74],[150,1085,1086,1124],{},[164,1087,1088],{},[15,1089,1091,1109],{"className":1090},[18],[15,1092,1094],{"className":1093},[22],[24,1095,1096],{"xmlns":26},[28,1097,1098,1106],{},[31,1099,1100,1102,1104],{},[34,1101,37],{"mathvariant":36},[39,1103,234],{},[43,1105,46],{"stretchy":45},[48,1107,1108],{"encoding":50},"\\vert 10 \\rangle",[15,1110,1112],{"className":1111,"ariaHidden":56},[55],[15,1113,1115,1118,1121],{"className":1114},[60],[15,1116],{"className":1117,"style":65},[64],[15,1119,289],{"className":1120},[69],[15,1122,46],{"className":1123},[74],[164,1125,1126],{},[15,1127,1129,1146],{"className":1128},[18],[15,1130,1132],{"className":1131},[22],[24,1133,1134],{"xmlns":26},[28,1135,1136,1144],{},[31,1137,1138,1140,1142],{},[34,1139,37],{"mathvariant":36},[39,1141,234],{},[43,1143,46],{"stretchy":45},[48,1145,1108],{"encoding":50},[15,1147,1149],{"className":1148,"ariaHidden":56},[55],[15,1150,1152,1155,1158],{"className":1151},[60],[15,1153],{"className":1154,"style":65},[64],[15,1156,289],{"className":1157},[69],[15,1159,46],{"className":1160},[74],[150,1162,1163,1200],{},[164,1164,1165],{},[15,1166,1168,1185],{"className":1167},[18],[15,1169,1171],{"className":1170},[22],[24,1172,1173],{"xmlns":26},[28,1174,1175,1183],{},[31,1176,1177,1179,1181],{},[34,1178,37],{"mathvariant":36},[39,1180,41],{},[43,1182,46],{"stretchy":45},[48,1184,51],{"encoding":50},[15,1186,1188],{"className":1187,"ariaHidden":56},[55],[15,1189,1191,1194,1197],{"className":1190},[60],[15,1192],{"className":1193,"style":65},[64],[15,1195,70],{"className":1196},[69],[15,1198,46],{"className":1199},[74],[164,1201,1202],{},[15,1203,1205,1225],{"className":1204},[18],[15,1206,1208],{"className":1207},[22],[24,1209,1210],{"xmlns":26},[28,1211,1212,1222],{},[31,1213,1214,1216,1218,1220],{},[43,1215,452],{},[34,1217,37],{"mathvariant":36},[39,1219,41],{},[43,1221,46],{"stretchy":45},[48,1223,1224],{"encoding":50},"-\\vert 11 \\rangle",[15,1226,1228],{"className":1227,"ariaHidden":56},[55],[15,1229,1231,1234,1237,1240],{"className":1230},[60],[15,1232],{"className":1233,"style":65},[64],[15,1235,452],{"className":1236},[69],[15,1238,70],{"className":1239},[69],[15,1241,46],{"className":1242},[74],[11,1244,1245,1246,1250,1251,305],{},"A measurement straight after CZ shows no change on any basis state. The sign flip shows once the qubits are in superposition: an ",[133,1247,1249],{"href":1248},"\u002Flearn\u002Fdocs\u002Fh-gate","H gate"," on the target before and after a CZ turns it into a ",[133,1252,1254],{"href":1253},"\u002Flearn\u002Fdocs\u002Fcx-gate","CX",[139,1256,1258],{"id":1257},"inverse","Inverse",[11,1260,1261],{},"CZ is its own inverse. Two CZ gates in a row on the same pair cancel.",[139,1263,1265],{"id":1264},"usage","Usage",[1267,1268,1273],"pre",{"className":1269,"code":1270,"language":1271,"meta":1272,"style":1272},"language-python shiki shiki-themes one-dark-pro","from qiskit import QuantumCircuit\n\nqc = QuantumCircuit(2, 2)\nqc.h(0)\nqc.h(1)\nqc.cz(0, 1)\nqc.h(1)\nqc.measure([0, 1], [0, 1])\n","python","",[77,1274,1275,1293,1300,1327,1342,1355,1373,1386],{"__ignoreMap":1272},[15,1276,1279,1283,1287,1290],{"class":1277,"line":1278},"line",1,[15,1280,1282],{"class":1281},"seHd6","from",[15,1284,1286],{"class":1285},"sn6KH"," qiskit ",[15,1288,1289],{"class":1281},"import",[15,1291,1292],{"class":1285}," QuantumCircuit\n",[15,1294,1296],{"class":1277,"line":1295},2,[15,1297,1299],{"emptyLinePlaceholder":1298},true,"\n",[15,1301,1303,1306,1309,1313,1315,1319,1322,1324],{"class":1277,"line":1302},3,[15,1304,1305],{"class":1285},"qc ",[15,1307,330],{"class":1308},"sjrmR",[15,1310,1312],{"class":1311},"sVbv2"," QuantumCircuit",[15,1314,335],{"class":1285},[15,1316,1318],{"class":1317},"sVC51","2",[15,1320,1321],{"class":1285},", ",[15,1323,1318],{"class":1317},[15,1325,1326],{"class":1285},")\n",[15,1328,1330,1333,1336,1338,1340],{"class":1277,"line":1329},4,[15,1331,1332],{"class":1285},"qc.",[15,1334,1335],{"class":1311},"h",[15,1337,335],{"class":1285},[15,1339,109],{"class":1317},[15,1341,1326],{"class":1285},[15,1343,1345,1347,1349,1351,1353],{"class":1277,"line":1344},5,[15,1346,1332],{"class":1285},[15,1348,1335],{"class":1311},[15,1350,335],{"class":1285},[15,1352,353],{"class":1317},[15,1354,1326],{"class":1285},[15,1356,1358,1360,1363,1365,1367,1369,1371],{"class":1277,"line":1357},6,[15,1359,1332],{"class":1285},[15,1361,1362],{"class":1311},"cz",[15,1364,335],{"class":1285},[15,1366,109],{"class":1317},[15,1368,1321],{"class":1285},[15,1370,353],{"class":1317},[15,1372,1326],{"class":1285},[15,1374,1376,1378,1380,1382,1384],{"class":1277,"line":1375},7,[15,1377,1332],{"class":1285},[15,1379,1335],{"class":1311},[15,1381,335],{"class":1285},[15,1383,353],{"class":1317},[15,1385,1326],{"class":1285},[15,1387,1389,1391,1394,1397,1399,1401,1403,1406,1408,1410,1412],{"class":1277,"line":1388},8,[15,1390,1332],{"class":1285},[15,1392,1393],{"class":1311},"measure",[15,1395,1396],{"class":1285},"([",[15,1398,109],{"class":1317},[15,1400,1321],{"class":1285},[15,1402,353],{"class":1317},[15,1404,1405],{"class":1285},"], [",[15,1407,109],{"class":1317},[15,1409,1321],{"class":1285},[15,1411,353],{"class":1317},[15,1413,1414],{"class":1285},"])\n",[1267,1416,1420],{"className":1417,"code":1418,"language":1419,"meta":1272,"style":1272},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\n\nconst circuit = QuantumCircuit(2, 2);\ncircuit.h(0);\ncircuit.h(1);\ncircuit.cz(0, 1);\ncircuit.h(1);\ncircuit.measure([0, 1], [0, 1]);\n","js",[77,1421,1422,1445,1449,1474,1489,1503,1521,1535],{"__ignoreMap":1272},[15,1423,1424,1426,1429,1433,1436,1438,1442],{"class":1277,"line":1278},[15,1425,1289],{"class":1281},[15,1427,1428],{"class":1285}," { ",[15,1430,1432],{"class":1431},"sVyAn","QuantumCircuit",[15,1434,1435],{"class":1285}," } ",[15,1437,1282],{"class":1281},[15,1439,1441],{"class":1440},"subq3"," 'qiskit'",[15,1443,1444],{"class":1285},";\n",[15,1446,1447],{"class":1277,"line":1295},[15,1448,1299],{"emptyLinePlaceholder":1298},[15,1450,1451,1454,1458,1461,1463,1465,1467,1469,1471],{"class":1277,"line":1302},[15,1452,1453],{"class":1281},"const",[15,1455,1457],{"class":1456},"sU0A5"," circuit",[15,1459,1460],{"class":1308}," =",[15,1462,1312],{"class":1311},[15,1464,335],{"class":1285},[15,1466,1318],{"class":1317},[15,1468,1321],{"class":1285},[15,1470,1318],{"class":1317},[15,1472,1473],{"class":1285},");\n",[15,1475,1476,1479,1481,1483,1485,1487],{"class":1277,"line":1329},[15,1477,1478],{"class":1456},"circuit",[15,1480,305],{"class":1285},[15,1482,1335],{"class":1311},[15,1484,335],{"class":1285},[15,1486,109],{"class":1317},[15,1488,1473],{"class":1285},[15,1490,1491,1493,1495,1497,1499,1501],{"class":1277,"line":1344},[15,1492,1478],{"class":1456},[15,1494,305],{"class":1285},[15,1496,1335],{"class":1311},[15,1498,335],{"class":1285},[15,1500,353],{"class":1317},[15,1502,1473],{"class":1285},[15,1504,1505,1507,1509,1511,1513,1515,1517,1519],{"class":1277,"line":1357},[15,1506,1478],{"class":1456},[15,1508,305],{"class":1285},[15,1510,1362],{"class":1311},[15,1512,335],{"class":1285},[15,1514,109],{"class":1317},[15,1516,1321],{"class":1285},[15,1518,353],{"class":1317},[15,1520,1473],{"class":1285},[15,1522,1523,1525,1527,1529,1531,1533],{"class":1277,"line":1375},[15,1524,1478],{"class":1456},[15,1526,305],{"class":1285},[15,1528,1335],{"class":1311},[15,1530,335],{"class":1285},[15,1532,353],{"class":1317},[15,1534,1473],{"class":1285},[15,1536,1537,1539,1541,1543,1545,1547,1549,1551,1553,1555,1557,1559],{"class":1277,"line":1388},[15,1538,1478],{"class":1456},[15,1540,305],{"class":1285},[15,1542,1393],{"class":1311},[15,1544,1396],{"class":1285},[15,1546,109],{"class":1317},[15,1548,1321],{"class":1285},[15,1550,353],{"class":1317},[15,1552,1405],{"class":1285},[15,1554,109],{"class":1317},[15,1556,1321],{"class":1285},[15,1558,353],{"class":1317},[15,1560,1561],{"class":1285},"]);\n",[11,1563,1564,1565,1567,1568,1570],{},"On a noiseless simulator every shot reads ",[77,1566,215],{}," or ",[77,1569,41],{},", in close to equal numbers: the H, CZ, H on the target is a CX, so this is the Bell pair.",[139,1572,1574],{"id":1573},"on-ionq-hardware","On IonQ hardware",[11,1576,1577,1578,1581,1582,1585,1586,305],{},"CZ is not a native gate, but it is close to one. On Forte it is a single ",[77,1579,1580],{},"ZZ"," gate with virtual Z rotations on both qubits, up to a global phase, and no single-qubit pulses at all; on Aria it is one ",[77,1583,1584],{},"MS"," gate with single-qubit pulses around it. Either way it is one entangling gate before IonQ's optimiser runs. See ",[133,1587,1589],{"href":1588},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",[139,1591,1593],{"id":1592},"related","Related",[1595,1596,1597,1603,1607,1613,1619],"ul",{},[1598,1599,1600],"li",{},[133,1601,1602],{"href":1253},"CX gate",[1598,1604,1605],{},[133,1606,911],{"href":910},[1598,1608,1609],{},[133,1610,1612],{"href":1611},"\u002Flearn\u002Fdocs\u002Fz-gate","Z gate",[1598,1614,1615],{},[133,1616,1618],{"href":1617},"\u002Flearn\u002Fdocs\u002Fzz-gate","ZZ gate",[1598,1620,1621],{},[133,1622,1624],{"href":1623},"\u002Flearn\u002Fdocs\u002Fgates","Gate reference",[1626,1627,1628],"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":1272,"searchDepth":1295,"depth":1295,"links":1630},[1631,1632,1633,1634,1635,1636,1637],{"id":141,"depth":1295,"text":142},{"id":194,"depth":1295,"text":195},{"id":914,"depth":1295,"text":915},{"id":1257,"depth":1295,"text":1258},{"id":1264,"depth":1295,"text":1265},{"id":1573,"depth":1295,"text":1574},{"id":1592,"depth":1295,"text":1593},"gates","Gates","The controlled-Z gate: matrix, effect on the basis states, the cz() call in Python and JS, and what it becomes on IonQ hardware.",false,"md","two-qubit","Two-qubit gates","doc",{},17,"\u002Fblog\u002Flearn\u002Fdocs\u002Fcz-gate","2026-09-16",[],{"title":1652,"description":1653},"CZ gate · Qollab docs","Reference for the controlled-Z gate: matrix, action on the basis states, the Qiskit cz() call in Python and JS, and its IonQ native-gate form.","blog\u002Flearn\u002Fdocs\u002Fcz-gate",[],"A55vHbLyWvUtuegoJ9zCi-0Q4JWhEWKp20rZG7xH4j0",[],[],[1660,1667,1683,1712,1794,1804],{"category":1661,"categoryName":1662,"articles":1663},"account","Account",[1664],{"title":1665,"href":1666},"Account and profile","\u002Flearn\u002Fdocs\u002Faccount-and-profile",{"category":1668,"categoryName":1669,"articles":1670},"projects","Projects",[1671,1674,1677,1680],{"title":1672,"href":1673},"The project page","\u002Flearn\u002Fdocs\u002Fproject-anatomy",{"title":1675,"href":1676},"Editing your project","\u002Flearn\u002Fdocs\u002Fwrite-your-project-page",{"title":1678,"href":1679},"Publishing and versions","\u002Flearn\u002Fdocs\u002Fpublish",{"title":1681,"href":1682},"Forking a project","\u002Flearn\u002Fdocs\u002Ffork-and-remix",{"category":1684,"categoryName":1685,"articles":1686},"running-code","Running code",[1687,1690,1693,1696,1699,1702,1703,1706,1709],{"title":1688,"href":1689},"Running your code","\u002Flearn\u002Fdocs\u002Frun-your-code",{"title":1691,"href":1692},"Compute backends","\u002Flearn\u002Fdocs\u002Fcompute-backends",{"title":1694,"href":1695},"The runtime environment","\u002Flearn\u002Fdocs\u002Fruntime-environment",{"title":1697,"href":1698},"JS \u002F Qiskit projects","\u002Flearn\u002Fdocs\u002Fjs-qiskit-projects",{"title":1700,"href":1701},"Python \u002F Qiskit projects","\u002Flearn\u002Fdocs\u002Fpython-qiskit-projects",{"title":1589,"href":1588},{"title":1704,"href":1705},"Error mitigation and debiasing","\u002Flearn\u002Fdocs\u002Ferror-mitigation",{"title":1707,"href":1708},"Transpilation","\u002Flearn\u002Fdocs\u002Ftranspilation",{"title":1710,"href":1711},"Primitives","\u002Flearn\u002Fdocs\u002Fprimitives",{"category":1638,"categoryName":1639,"articles":1713},[1714,1715,1718,1721,1724,1725,1728,1731,1734,1737,1740,1743,1746,1749,1752,1755,1756,1759,1761,1762,1765,1768,1771,1774,1779,1782,1787,1790,1793],{"title":1624,"href":1623},{"title":1249,"href":1248,"group":1716,"groupName":1717},"single-qubit","Single-qubit gates",{"title":1719,"href":1720,"group":1716,"groupName":1717},"X gate","\u002Flearn\u002Fdocs\u002Fx-gate",{"title":1722,"href":1723,"group":1716,"groupName":1717},"Y gate","\u002Flearn\u002Fdocs\u002Fy-gate",{"title":1612,"href":1611,"group":1716,"groupName":1717},{"title":1726,"href":1727,"group":1716,"groupName":1717},"S gate","\u002Flearn\u002Fdocs\u002Fs-gate",{"title":1729,"href":1730,"group":1716,"groupName":1717},"Sdg gate","\u002Flearn\u002Fdocs\u002Fsdg-gate",{"title":1732,"href":1733,"group":1716,"groupName":1717},"T gate","\u002Flearn\u002Fdocs\u002Ft-gate",{"title":1735,"href":1736,"group":1716,"groupName":1717},"Tdg gate","\u002Flearn\u002Fdocs\u002Ftdg-gate",{"title":1738,"href":1739,"group":1716,"groupName":1717},"√X gate","\u002Flearn\u002Fdocs\u002Fsx-gate",{"title":1741,"href":1742,"group":1716,"groupName":1717},"√X† gate","\u002Flearn\u002Fdocs\u002Fsxdg-gate",{"title":1744,"href":1745,"group":1716,"groupName":1717},"P gate","\u002Flearn\u002Fdocs\u002Fp-gate",{"title":1747,"href":1748,"group":1716,"groupName":1717},"RX gate","\u002Flearn\u002Fdocs\u002Frx-gate",{"title":1750,"href":1751,"group":1716,"groupName":1717},"RY gate","\u002Flearn\u002Fdocs\u002Fry-gate",{"title":1753,"href":1754,"group":1716,"groupName":1717},"RZ gate","\u002Flearn\u002Fdocs\u002Frz-gate",{"title":1602,"href":1253,"group":1643,"groupName":1644},{"title":1757,"href":1758,"group":1643,"groupName":1644},"CY gate","\u002Flearn\u002Fdocs\u002Fcy-gate",{"title":5,"href":1760,"group":1643,"groupName":1644},"\u002Flearn\u002Fdocs\u002Fcz-gate",{"title":911,"href":910,"group":1643,"groupName":1644},{"title":1763,"href":1764,"group":1643,"groupName":1644},"Swap gate","\u002Flearn\u002Fdocs\u002Fswap-gate",{"title":1766,"href":1767,"group":1643,"groupName":1644},"RXX gate","\u002Flearn\u002Fdocs\u002Frxx-gate",{"title":1769,"href":1770,"group":1643,"groupName":1644},"RYY gate","\u002Flearn\u002Fdocs\u002Fryy-gate",{"title":1772,"href":1773,"group":1643,"groupName":1644},"RZZ gate","\u002Flearn\u002Fdocs\u002Frzz-gate",{"title":1775,"href":1776,"group":1777,"groupName":1778},"CCX gate","\u002Flearn\u002Fdocs\u002Fccx-gate","multi-qubit","Multi-qubit gates",{"title":1780,"href":1781,"group":1777,"groupName":1778},"Pauli evolution gate","\u002Flearn\u002Fdocs\u002Fpauli-evolution-gate",{"title":1783,"href":1784,"group":1785,"groupName":1786},"GPi gate","\u002Flearn\u002Fdocs\u002Fgpi-gate","native","IonQ native gates",{"title":1788,"href":1789,"group":1785,"groupName":1786},"GPi2 gate","\u002Flearn\u002Fdocs\u002Fgpi2-gate",{"title":1791,"href":1792,"group":1785,"groupName":1786},"MS gate","\u002Flearn\u002Fdocs\u002Fms-gate",{"title":1618,"href":1617,"group":1785,"groupName":1786},{"category":1795,"categoryName":1796,"articles":1797},"credits","Credits",[1798,1801],{"title":1799,"href":1800},"How credits work","\u002Flearn\u002Fdocs\u002Fhow-credits-work",{"title":1802,"href":1803},"Before you spend credits","\u002Flearn\u002Fdocs\u002Fbefore-you-spend-credits",{"category":1805,"categoryName":1806,"articles":1807},"troubleshooting","Troubleshooting",[1808,1811,1814],{"title":1809,"href":1810},"Troubleshooting and FAQ","\u002Flearn\u002Fdocs\u002Ffaq",{"title":1812,"href":1813},"Error reference","\u002Flearn\u002Fdocs\u002Ferror-reference",{"title":1815,"href":1816},"Why your results look wrong","\u002Flearn\u002Fdocs\u002Fwhy-your-results-look-wrong",1789652389695]