[{"data":1,"prerenderedAt":1780},["ShallowReactive",2],{"blog-post-docs\u002Fpauli-evolution-gate":3,"sibling-dives-docs\u002Fpauli-evolution-gate":1618,"learn-track-docs\u002Fpauli-evolution-gate":1619,"learn-docs-groups":1620},{"id":4,"title":5,"authors":6,"body":7,"breadcrumb":6,"builders":6,"byline":6,"category":1599,"categoryName":1600,"challenge":6,"courseAuthor":6,"courseLead":6,"dek":6,"description":1601,"draft":1602,"extension":1603,"eyebrow":6,"featured":1602,"finish":6,"fork":6,"group":1604,"groupName":1605,"hero":6,"heroAlt":6,"heroCta":6,"heroImage":6,"homepageFeatured":1602,"kind":1606,"lessonCount":6,"meta":1607,"navigation":1123,"newsItems":6,"next":6,"ogImage":6,"order":1608,"outcomes":6,"path":1609,"publishDate":1610,"readingTime":6,"related":1611,"relatedProjects":6,"seo":1612,"stem":1615,"tags":1616,"track":6,"trackName":6,"__hash__":1617},"blog\u002Fblog\u002Flearn\u002Fdocs\u002Fpauli-evolution-gate.md","Pauli evolution gate",null,{"type":8,"value":9,"toc":1589},"minimark",[10,224,279,284,338,365,369,393,397,740,987,990,994,1061,1065,1265,1471,1477,1480,1505,1508,1518,1552,1559,1563,1585],[11,12,13,14,129,130,159,160,189,190,218,219,223],"p",{},"The Pauli evolution gate applies ",[15,16,19,60],"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",[28,29,30,55],"semantics",{},[31,32,33],"mrow",{},[34,35,36,40],"msup",{},[37,38,39],"mi",{},"e",[31,41,42,46,49,52],{},[43,44,45],"mo",{},"−",[37,47,48],{},"i",[37,50,51],{},"t",[37,53,54],{},"H",[56,57,59],"annotation",{"encoding":58},"application\u002Fx-tex","e^{-itH}",[15,61,65],{"className":62,"ariaHidden":64},[63],"katex-html","true",[15,66,69,74],{"className":67},[68],"base",[15,70],{"className":71,"style":73},[72],"strut","height:0.8413em;",[15,75,78,82],{"className":76},[77],"mord",[15,79,39],{"className":80},[77,81],"mathnormal",[15,83,86],{"className":84},[85],"msupsub",[15,87,90],{"className":88},[89],"vlist-t",[15,91,94],{"className":92},[93],"vlist-r",[15,95,98],{"className":96,"style":73},[97],"vlist",[15,99,101,106],{"style":100},"top:-3.063em;margin-right:0.05em;",[15,102],{"className":103,"style":105},[104],"pstrut","height:2.7em;",[15,107,113],{"className":108},[109,110,111,112],"sizing","reset-size6","size3","mtight",[15,114,116,119,122,125],{"className":115},[77,112],[15,117,45],{"className":118},[77,112],[15,120,48],{"className":121},[77,81,112],[15,123,51],{"className":124},[77,81,112],[15,126,54],{"className":127,"style":128},[77,81,112],"margin-right:0.0813em;"," to a set of qubits, where ",[15,131,133,146],{"className":132},[18],[15,134,136],{"className":135},[22],[24,137,138],{"xmlns":26},[28,139,140,144],{},[31,141,142],{},[37,143,54],{},[56,145,54],{"encoding":58},[15,147,149],{"className":148,"ariaHidden":64},[63],[15,150,152,156],{"className":151},[68],[15,153],{"className":154,"style":155},[72],"height:0.6833em;",[15,157,54],{"className":158,"style":128},[77,81]," is a Hamiltonian written as a weighted sum of Pauli strings and ",[15,161,163,176],{"className":162},[18],[15,164,166],{"className":165},[22],[24,167,168],{"xmlns":26},[28,169,170,174],{},[31,171,172],{},[37,173,51],{},[56,175,51],{"encoding":58},[15,177,179],{"className":178,"ariaHidden":64},[63],[15,180,182,186],{"className":181},[68],[15,183],{"className":184,"style":185},[72],"height:0.6151em;",[15,187,51],{"className":188},[77,81]," is a time. It is how a circuit simulates a physical system evolving under ",[15,191,193,206],{"className":192},[18],[15,194,196],{"className":195},[22],[24,197,198],{"xmlns":26},[28,199,200,204],{},[31,201,202],{},[37,203,54],{},[56,205,54],{"encoding":58},[15,207,209],{"className":208,"ariaHidden":64},[63],[15,210,212,215],{"className":211},[68],[15,213],{"className":214,"style":155},[72],[15,216,54],{"className":217,"style":128},[77,81],", and the building block of Trotterised time evolution and QAOA layers. It acts on as many qubits as the Pauli strings are long and takes two parameters: the operator and the time. The Circuit panel draws it as ",[220,221,222],"strong",{},"exp(…)(t)",", with the weighted terms inside the brackets and the time after them. Run on fresh qubits, the example below leaves every shot reading 00: with these terms the gate only adds phases, which show once other gates put the qubits in superposition.",[11,225,226,227,272,273,278],{},"Kets such as ",[15,228,230,254],{"className":229},[18],[15,231,233],{"className":232},[22],[24,234,235],{"xmlns":26},[28,236,237,251],{},[31,238,239,243,247],{},[37,240,242],{"mathvariant":241},"normal","∣",[244,245,246],"mn",{},"0",[43,248,250],{"stretchy":249},"false","⟩",[56,252,253],{"encoding":58},"\\vert 0 \\rangle",[15,255,257],{"className":256,"ariaHidden":64},[63],[15,258,260,264,268],{"className":259},[68],[15,261],{"className":262,"style":263},[72],"height:1em;vertical-align:-0.25em;",[15,265,267],{"className":266},[77],"∣0",[15,269,250],{"className":270},[271],"mclose"," name the basis states and rotations are described on the Bloch sphere; the ",[274,275,277],"a",{"href":276},"\u002Flearn\u002Fquantum-foundations\u002Fqubits","qubits lesson"," introduces both.",[280,281,283],"h2",{"id":282},"call","Call",[285,286,287,299],"table",{},[288,289,290],"thead",{},[291,292,293,297],"tr",{},[294,295,296],"th",{},"Where",[294,298,283],{},[300,301,302,314,324],"tbody",{},[291,303,304,308],{},[305,306,307],"td",{},"Python",[305,309,310],{},[311,312,313],"code",{},"qc.append(PauliEvolutionGate(operator, time=t), qubits)",[291,315,316,319],{},[305,317,318],{},"JS",[305,320,321],{},[311,322,323],{},"circuit.append(PauliEvolutionGate.callKwargs(operator, { time: t }), qubits)",[291,325,326,329],{},[305,327,328],{},"Qiskit class",[305,330,331,334,335],{},[311,332,333],{},"PauliEvolutionGate",", from ",[311,336,337],{},"qiskit.circuit.library",[11,339,340,343,344,347,348,351,352,355,356,359,360,364],{},[311,341,342],{},"operator"," is a ",[311,345,346],{},"SparsePauliOp"," from ",[311,349,350],{},"qiskit.quantum_info",": a list of Pauli strings and a list of coefficients. In JS, keyword arguments go through ",[311,353,354],{},".callKwargs",", so the constructor call is ",[311,357,358],{},"PauliEvolutionGate.callKwargs(operator, { time: t })","; see ",[274,361,363],{"href":362},"\u002Flearn\u002Fdocs\u002Fjs-qiskit-projects","JS \u002F Qiskit projects",".",[280,366,368],{"id":367},"backend-requirements","Backend requirements",[11,370,371,372,375,376,379,380,383,384,388,389,364],{},"The built-in simulator and the IBM noise models do not take the gate as written: run ",[311,373,374],{},"transpile(qc, backend)"," first and Qiskit unrolls it into the backend's own gates. IonQ backends take it as submitted when its terms all commute with each other; terms that do not commute need IonQ's compiler synthesis, ",[311,377,378],{},"backend.set_options(extra_metadata={\"ionq_compiler_synthesis\": True})",", or the run stops before submission with ",[311,381,382],{},"IonQPauliExponentialError",". Details under ",[274,385,387],{"href":386},"#on-the-simulators","On the simulators"," and ",[274,390,392],{"href":391},"#on-ionq-hardware","On IonQ hardware",[280,394,396],{"id":395},"what-it-computes","What it computes",[15,398,401],{"className":399},[400],"katex-display",[15,402,404,480],{"className":403},[18],[15,405,407],{"className":406},[22],[24,408,410],{"xmlns":26,"display":409},"block",[28,411,412,477],{},[31,413,414,417,420,422,425,428,442,445,449,451,453,462,470],{},[37,415,416],{},"U",[43,418,419],{"stretchy":249},"(",[37,421,51],{},[43,423,424],{"stretchy":249},")",[43,426,427],{},"=",[34,429,430,432],{},[37,431,39],{},[31,433,434,436,438,440],{},[43,435,45],{},[37,437,48],{},[37,439,51],{},[37,441,54],{},[43,443,444],{"separator":64},",",[446,447],"mspace",{"width":448},"2em",[37,450,54],{},[43,452,427],{},[454,455,456,459],"munder",{},[43,457,458],{},"∑",[37,460,461],{},"k",[463,464,465,468],"msub",{},[37,466,467],{},"c",[37,469,461],{},[463,471,472,475],{},[37,473,474],{},"P",[37,476,461],{},[56,478,479],{"encoding":58},"U(t) = e^{-itH}, \\qquad H = \\sum_k c_k P_k",[15,481,483,514,588],{"className":482,"ariaHidden":64},[63],[15,484,486,489,493,497,500,503,507,511],{"className":485},[68],[15,487],{"className":488,"style":263},[72],[15,490,416],{"className":491,"style":492},[77,81],"margin-right:0.109em;",[15,494,419],{"className":495},[496],"mopen",[15,498,51],{"className":499},[77,81],[15,501,424],{"className":502},[271],[15,504],{"className":505,"style":506},[446],"margin-right:0.2778em;",[15,508,427],{"className":509},[510],"mrel",[15,512],{"className":513,"style":506},[446],[15,515,517,521,564,568,572,576,579,582,585],{"className":516},[68],[15,518],{"className":519,"style":520},[72],"height:1.0858em;vertical-align:-0.1944em;",[15,522,524,527],{"className":523},[77],[15,525,39],{"className":526},[77,81],[15,528,530],{"className":529},[85],[15,531,533],{"className":532},[89],[15,534,536],{"className":535},[93],[15,537,540],{"className":538,"style":539},[97],"height:0.8913em;",[15,541,543,546],{"style":542},"top:-3.113em;margin-right:0.05em;",[15,544],{"className":545,"style":105},[104],[15,547,549],{"className":548},[109,110,111,112],[15,550,552,555,558,561],{"className":551},[77,112],[15,553,45],{"className":554},[77,112],[15,556,48],{"className":557},[77,81,112],[15,559,51],{"className":560},[77,81,112],[15,562,54],{"className":563,"style":128},[77,81,112],[15,565,444],{"className":566},[567],"mpunct",[15,569],{"className":570,"style":571},[446],"margin-right:2em;",[15,573],{"className":574,"style":575},[446],"margin-right:0.1667em;",[15,577,54],{"className":578,"style":128},[77,81],[15,580],{"className":581,"style":506},[446],[15,583,427],{"className":584},[510],[15,586],{"className":587,"style":506},[446],[15,589,591,595,652,655,698],{"className":590},[68],[15,592],{"className":593,"style":594},[72],"height:2.3521em;vertical-align:-1.3021em;",[15,596,600],{"className":597},[598,599],"mop","op-limits",[15,601,604,643],{"className":602},[89,603],"vlist-t2",[15,605,607,638],{"className":606},[93],[15,608,611,625],{"className":609,"style":610},[97],"height:1.05em;",[15,612,614,618],{"style":613},"top:-1.8479em;margin-left:0em;",[15,615],{"className":616,"style":617},[104],"height:3.05em;",[15,619,621],{"className":620},[109,110,111,112],[15,622,461],{"className":623,"style":624},[77,81,112],"margin-right:0.0315em;",[15,626,628,631],{"style":627},"top:-3.05em;",[15,629],{"className":630,"style":617},[104],[15,632,633],{},[15,634,458],{"className":635},[598,636,637],"op-symbol","large-op",[15,639,642],{"className":640},[641],"vlist-s","​",[15,644,646],{"className":645},[93],[15,647,650],{"className":648,"style":649},[97],"height:1.3021em;",[15,651],{},[15,653],{"className":654,"style":575},[446],[15,656,658,661],{"className":657},[77],[15,659,467],{"className":660},[77,81],[15,662,664],{"className":663},[85],[15,665,667,689],{"className":666},[89,603],[15,668,670,686],{"className":669},[93],[15,671,674],{"className":672,"style":673},[97],"height:0.3361em;",[15,675,677,680],{"style":676},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[15,678],{"className":679,"style":105},[104],[15,681,683],{"className":682},[109,110,111,112],[15,684,461],{"className":685,"style":624},[77,81,112],[15,687,642],{"className":688},[641],[15,690,692],{"className":691},[93],[15,693,696],{"className":694,"style":695},[97],"height:0.15em;",[15,697],{},[15,699,701,705],{"className":700},[77],[15,702,474],{"className":703,"style":704},[77,81],"margin-right:0.1389em;",[15,706,708],{"className":707},[85],[15,709,711,732],{"className":710},[89,603],[15,712,714,729],{"className":713},[93],[15,715,717],{"className":716,"style":673},[97],[15,718,720,723],{"style":719},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[15,721],{"className":722,"style":105},[104],[15,724,726],{"className":725},[109,110,111,112],[15,727,461],{"className":728,"style":624},[77,81,112],[15,730,642],{"className":731},[641],[15,733,735],{"className":734},[93],[15,736,738],{"className":737,"style":695},[97],[15,739],{},[11,741,742,743,814,815,818,819,822,823,894,895,898,899,903,904,940,941,944,945,903,949,982,983,986],{},"Each ",[15,744,746,764],{"className":745},[18],[15,747,749],{"className":748},[22],[24,750,751],{"xmlns":26},[28,752,753,761],{},[31,754,755],{},[463,756,757,759],{},[37,758,474],{},[37,760,461],{},[56,762,763],{"encoding":58},"P_k",[15,765,767],{"className":766,"ariaHidden":64},[63],[15,768,770,774],{"className":769},[68],[15,771],{"className":772,"style":773},[72],"height:0.8333em;vertical-align:-0.15em;",[15,775,777,780],{"className":776},[77],[15,778,474],{"className":779,"style":704},[77,81],[15,781,783],{"className":782},[85],[15,784,786,806],{"className":785},[89,603],[15,787,789,803],{"className":788},[93],[15,790,792],{"className":791,"style":673},[97],[15,793,794,797],{"style":719},[15,795],{"className":796,"style":105},[104],[15,798,800],{"className":799},[109,110,111,112],[15,801,461],{"className":802,"style":624},[77,81,112],[15,804,642],{"className":805},[641],[15,807,809],{"className":808},[93],[15,810,812],{"className":811,"style":695},[97],[15,813],{}," is a Pauli string such as ",[311,816,817],{},"ZZ"," or ",[311,820,821],{},"XI"," and each ",[15,824,826,844],{"className":825},[18],[15,827,829],{"className":828},[22],[24,830,831],{"xmlns":26},[28,832,833,841],{},[31,834,835],{},[463,836,837,839],{},[37,838,467],{},[37,840,461],{},[56,842,843],{"encoding":58},"c_k",[15,845,847],{"className":846,"ariaHidden":64},[63],[15,848,850,854],{"className":849},[68],[15,851],{"className":852,"style":853},[72],"height:0.5806em;vertical-align:-0.15em;",[15,855,857,860],{"className":856},[77],[15,858,467],{"className":859},[77,81],[15,861,863],{"className":862},[85],[15,864,866,886],{"className":865},[89,603],[15,867,869,883],{"className":868},[93],[15,870,872],{"className":871,"style":673},[97],[15,873,874,877],{"style":676},[15,875],{"className":876,"style":105},[104],[15,878,880],{"className":879},[109,110,111,112],[15,881,461],{"className":882,"style":624},[77,81,112],[15,884,642],{"className":885},[641],[15,887,889],{"className":888},[93],[15,890,892],{"className":891,"style":695},[97],[15,893],{}," its real coefficient. Two single-term cases fix the scale: ",[311,896,897],{},"exp(−itZ)"," on one qubit is an ",[274,900,902],{"href":901},"\u002Flearn\u002Fdocs\u002Frz-gate","RZ gate"," of angle ",[15,905,907,924],{"className":906},[18],[15,908,910],{"className":909},[22],[24,911,912],{"xmlns":26},[28,913,914,921],{},[31,915,916,919],{},[244,917,918],{},"2",[37,920,51],{},[56,922,923],{"encoding":58},"2t",[15,925,927],{"className":926,"ariaHidden":64},[63],[15,928,930,934,937],{"className":929},[68],[15,931],{"className":932,"style":933},[72],"height:0.6444em;",[15,935,918],{"className":936},[77],[15,938,51],{"className":939},[77,81],", and ",[311,942,943],{},"exp(−itZZ)"," on two qubits is an ",[274,946,948],{"href":947},"\u002Flearn\u002Fdocs\u002Frzz-gate","RZZ gate",[15,950,952,967],{"className":951},[18],[15,953,955],{"className":954},[22],[24,956,957],{"xmlns":26},[28,958,959,965],{},[31,960,961,963],{},[244,962,918],{},[37,964,51],{},[56,966,923],{"encoding":58},[15,968,970],{"className":969,"ariaHidden":64},[63],[15,971,973,976,979],{"className":972},[68],[15,974],{"className":975,"style":933},[72],[15,977,918],{"className":978},[77],[15,980,51],{"className":981},[77,81],". The letter ",[311,984,985],{},"I"," in a string means the gate leaves that qubit alone.",[11,988,989],{},"Qiskit synthesises the gate with a product formula, Lie-Trotter by default, which is exact when every term commutes with every other and an approximation otherwise. The approximation improves with more Trotter steps, at the cost of more gates.",[280,991,993],{"id":992},"inverse","Inverse",[11,995,996,997,1025,1026,364],{},"The inverse of evolution for time ",[15,998,1000,1013],{"className":999},[18],[15,1001,1003],{"className":1002},[22],[24,1004,1005],{"xmlns":26},[28,1006,1007,1011],{},[31,1008,1009],{},[37,1010,51],{},[56,1012,51],{"encoding":58},[15,1014,1016],{"className":1015,"ariaHidden":64},[63],[15,1017,1019,1022],{"className":1018},[68],[15,1020],{"className":1021,"style":185},[72],[15,1023,51],{"className":1024},[77,81]," is evolution for time ",[15,1027,1029,1045],{"className":1028},[18],[15,1030,1032],{"className":1031},[22],[24,1033,1034],{"xmlns":26},[28,1035,1036,1042],{},[31,1037,1038,1040],{},[43,1039,45],{},[37,1041,51],{},[56,1043,1044],{"encoding":58},"-t",[15,1046,1048],{"className":1047,"ariaHidden":64},[63],[15,1049,1051,1055,1058],{"className":1050},[68],[15,1052],{"className":1053,"style":1054},[72],"height:0.6984em;vertical-align:-0.0833em;",[15,1056,45],{"className":1057},[77],[15,1059,51],{"className":1060},[77,81],[280,1062,1064],{"id":1063},"usage","Usage",[1066,1067,1072],"pre",{"className":1068,"code":1069,"language":1070,"meta":1071,"style":1071},"language-python shiki shiki-themes one-dark-pro","from qiskit import QuantumCircuit\nfrom qiskit.circuit.library import PauliEvolutionGate\nfrom qiskit.quantum_info import SparsePauliOp\n\nH = SparsePauliOp([\"ZZ\", \"ZI\", \"IZ\"], [1.0, 0.5, 0.5])\n\nqc = QuantumCircuit(2, 2)\nqc.append(PauliEvolutionGate(H, time=0.3), [0, 1])\nqc.measure([0, 1], [0, 1])\n","python","",[311,1073,1074,1092,1105,1118,1125,1175,1180,1202,1239],{"__ignoreMap":1071},[15,1075,1078,1082,1086,1089],{"class":1076,"line":1077},"line",1,[15,1079,1081],{"class":1080},"seHd6","from",[15,1083,1085],{"class":1084},"sn6KH"," qiskit ",[15,1087,1088],{"class":1080},"import",[15,1090,1091],{"class":1084}," QuantumCircuit\n",[15,1093,1095,1097,1100,1102],{"class":1076,"line":1094},2,[15,1096,1081],{"class":1080},[15,1098,1099],{"class":1084}," qiskit.circuit.library ",[15,1101,1088],{"class":1080},[15,1103,1104],{"class":1084}," PauliEvolutionGate\n",[15,1106,1108,1110,1113,1115],{"class":1076,"line":1107},3,[15,1109,1081],{"class":1080},[15,1111,1112],{"class":1084}," qiskit.quantum_info ",[15,1114,1088],{"class":1080},[15,1116,1117],{"class":1084}," SparsePauliOp\n",[15,1119,1121],{"class":1076,"line":1120},4,[15,1122,1124],{"emptyLinePlaceholder":1123},true,"\n",[15,1126,1128,1131,1134,1138,1141,1145,1148,1151,1153,1156,1159,1163,1165,1168,1170,1172],{"class":1076,"line":1127},5,[15,1129,1130],{"class":1084},"H ",[15,1132,427],{"class":1133},"sjrmR",[15,1135,1137],{"class":1136},"sVbv2"," SparsePauliOp",[15,1139,1140],{"class":1084},"([",[15,1142,1144],{"class":1143},"subq3","\"ZZ\"",[15,1146,1147],{"class":1084},", ",[15,1149,1150],{"class":1143},"\"ZI\"",[15,1152,1147],{"class":1084},[15,1154,1155],{"class":1143},"\"IZ\"",[15,1157,1158],{"class":1084},"], [",[15,1160,1162],{"class":1161},"sVC51","1.0",[15,1164,1147],{"class":1084},[15,1166,1167],{"class":1161},"0.5",[15,1169,1147],{"class":1084},[15,1171,1167],{"class":1161},[15,1173,1174],{"class":1084},"])\n",[15,1176,1178],{"class":1076,"line":1177},6,[15,1179,1124],{"emptyLinePlaceholder":1123},[15,1181,1183,1186,1188,1191,1193,1195,1197,1199],{"class":1076,"line":1182},7,[15,1184,1185],{"class":1084},"qc ",[15,1187,427],{"class":1133},[15,1189,1190],{"class":1136}," QuantumCircuit",[15,1192,419],{"class":1084},[15,1194,918],{"class":1161},[15,1196,1147],{"class":1084},[15,1198,918],{"class":1161},[15,1200,1201],{"class":1084},")\n",[15,1203,1205,1208,1211,1213,1215,1218,1222,1224,1227,1230,1232,1234,1237],{"class":1076,"line":1204},8,[15,1206,1207],{"class":1084},"qc.",[15,1209,1210],{"class":1136},"append",[15,1212,419],{"class":1084},[15,1214,333],{"class":1136},[15,1216,1217],{"class":1084},"(H, ",[15,1219,1221],{"class":1220},"s_ZVi","time",[15,1223,427],{"class":1133},[15,1225,1226],{"class":1161},"0.3",[15,1228,1229],{"class":1084},"), [",[15,1231,246],{"class":1161},[15,1233,1147],{"class":1084},[15,1235,1236],{"class":1161},"1",[15,1238,1174],{"class":1084},[15,1240,1242,1244,1247,1249,1251,1253,1255,1257,1259,1261,1263],{"class":1076,"line":1241},9,[15,1243,1207],{"class":1084},[15,1245,1246],{"class":1136},"measure",[15,1248,1140],{"class":1084},[15,1250,246],{"class":1161},[15,1252,1147],{"class":1084},[15,1254,1236],{"class":1161},[15,1256,1158],{"class":1084},[15,1258,246],{"class":1161},[15,1260,1147],{"class":1084},[15,1262,1236],{"class":1161},[15,1264,1174],{"class":1084},[1066,1266,1270],{"className":1267,"code":1268,"language":1269,"meta":1071,"style":1071},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\nimport { PauliEvolutionGate } from 'qiskit.circuit.library';\nimport { SparsePauliOp } from 'qiskit.quantum_info';\n\nconst H = SparsePauliOp(['ZZ', 'ZI', 'IZ'], [1.0, 0.5, 0.5]);\n\nconst circuit = QuantumCircuit(2, 2);\ncircuit.append(PauliEvolutionGate.callKwargs(H, { time: 0.3 }), [0, 1]);\ncircuit.measure([0, 1], [0, 1]);\n","js",[311,1271,1272,1294,1311,1328,1332,1376,1380,1402,1445],{"__ignoreMap":1071},[15,1273,1274,1276,1279,1283,1286,1288,1291],{"class":1076,"line":1077},[15,1275,1088],{"class":1080},[15,1277,1278],{"class":1084}," { ",[15,1280,1282],{"class":1281},"sVyAn","QuantumCircuit",[15,1284,1285],{"class":1084}," } ",[15,1287,1081],{"class":1080},[15,1289,1290],{"class":1143}," 'qiskit'",[15,1292,1293],{"class":1084},";\n",[15,1295,1296,1298,1300,1302,1304,1306,1309],{"class":1076,"line":1094},[15,1297,1088],{"class":1080},[15,1299,1278],{"class":1084},[15,1301,333],{"class":1281},[15,1303,1285],{"class":1084},[15,1305,1081],{"class":1080},[15,1307,1308],{"class":1143}," 'qiskit.circuit.library'",[15,1310,1293],{"class":1084},[15,1312,1313,1315,1317,1319,1321,1323,1326],{"class":1076,"line":1107},[15,1314,1088],{"class":1080},[15,1316,1278],{"class":1084},[15,1318,346],{"class":1281},[15,1320,1285],{"class":1084},[15,1322,1081],{"class":1080},[15,1324,1325],{"class":1143}," 'qiskit.quantum_info'",[15,1327,1293],{"class":1084},[15,1329,1330],{"class":1076,"line":1120},[15,1331,1124],{"emptyLinePlaceholder":1123},[15,1333,1334,1337,1341,1344,1346,1348,1351,1353,1356,1358,1361,1363,1365,1367,1369,1371,1373],{"class":1076,"line":1127},[15,1335,1336],{"class":1080},"const",[15,1338,1340],{"class":1339},"sU0A5"," H",[15,1342,1343],{"class":1133}," =",[15,1345,1137],{"class":1136},[15,1347,1140],{"class":1084},[15,1349,1350],{"class":1143},"'ZZ'",[15,1352,1147],{"class":1084},[15,1354,1355],{"class":1143},"'ZI'",[15,1357,1147],{"class":1084},[15,1359,1360],{"class":1143},"'IZ'",[15,1362,1158],{"class":1084},[15,1364,1162],{"class":1161},[15,1366,1147],{"class":1084},[15,1368,1167],{"class":1161},[15,1370,1147],{"class":1084},[15,1372,1167],{"class":1161},[15,1374,1375],{"class":1084},"]);\n",[15,1377,1378],{"class":1076,"line":1177},[15,1379,1124],{"emptyLinePlaceholder":1123},[15,1381,1382,1384,1387,1389,1391,1393,1395,1397,1399],{"class":1076,"line":1182},[15,1383,1336],{"class":1080},[15,1385,1386],{"class":1339}," circuit",[15,1388,1343],{"class":1133},[15,1390,1190],{"class":1136},[15,1392,419],{"class":1084},[15,1394,918],{"class":1161},[15,1396,1147],{"class":1084},[15,1398,918],{"class":1161},[15,1400,1401],{"class":1084},");\n",[15,1403,1404,1407,1409,1411,1413,1415,1417,1420,1422,1424,1427,1429,1432,1434,1437,1439,1441,1443],{"class":1076,"line":1204},[15,1405,1406],{"class":1339},"circuit",[15,1408,364],{"class":1084},[15,1410,1210],{"class":1136},[15,1412,419],{"class":1084},[15,1414,333],{"class":1339},[15,1416,364],{"class":1084},[15,1418,1419],{"class":1136},"callKwargs",[15,1421,419],{"class":1084},[15,1423,54],{"class":1339},[15,1425,1426],{"class":1084},", { ",[15,1428,1221],{"class":1281},[15,1430,1431],{"class":1084},": ",[15,1433,1226],{"class":1161},[15,1435,1436],{"class":1084}," }), [",[15,1438,246],{"class":1161},[15,1440,1147],{"class":1084},[15,1442,1236],{"class":1161},[15,1444,1375],{"class":1084},[15,1446,1447,1449,1451,1453,1455,1457,1459,1461,1463,1465,1467,1469],{"class":1076,"line":1241},[15,1448,1406],{"class":1339},[15,1450,364],{"class":1084},[15,1452,1246],{"class":1136},[15,1454,1140],{"class":1084},[15,1456,246],{"class":1161},[15,1458,1147],{"class":1084},[15,1460,1236],{"class":1161},[15,1462,1158],{"class":1084},[15,1464,246],{"class":1161},[15,1466,1147],{"class":1084},[15,1468,1236],{"class":1161},[15,1470,1375],{"class":1084},[11,1472,1473,1474,364],{},"The Circuit panel shows this as ",[311,1475,1476],{},"exp(ZZ + 0.5ZI + 0.5IZ)(0.3)",[280,1478,387],{"id":1479},"on-the-simulators",[11,1481,371,1482,1484,1485,388,1488,1491,1492,1147,1495,388,1498,1500,1501,364],{},[311,1483,374],{}," first and Qiskit unrolls it into the backend's own gates, ",[311,1486,1487],{},"rzz",[311,1489,1490],{},"rz"," on the built-in simulator and ",[311,1493,1494],{},"cz",[311,1496,1497],{},"sx",[311,1499,1490],{}," on an IBM noise model for the example above. See ",[274,1502,1504],{"href":1503},"\u002Flearn\u002Fdocs\u002Ftranspilation","Transpilation",[280,1506,392],{"id":1507},"on-ionq-hardware",[11,1509,1510,1511,1514,1515,1517],{},"Qollab submits the gate to IonQ as a single ",[311,1512,1513],{},"pauliexp"," operation carrying the Pauli strings, their coefficients and the time, rather than as Qiskit's synthesised gate sequence, and IonQ's compiler chooses the decomposition on its side. That path takes terms that all commute with each other, as in the example above. Terms that do not commute are refused before submission with ",[311,1516,382],{}," unless you opt in to IonQ's compiler synthesis first:",[1066,1519,1521],{"className":1068,"code":1520,"language":1070,"meta":1071,"style":1071},"backend.set_options(extra_metadata={\"ionq_compiler_synthesis\": True})\n",[311,1522,1523],{"__ignoreMap":1071},[15,1524,1525,1528,1531,1533,1536,1538,1541,1544,1546,1549],{"class":1076,"line":1077},[15,1526,1527],{"class":1084},"backend.",[15,1529,1530],{"class":1136},"set_options",[15,1532,419],{"class":1084},[15,1534,1535],{"class":1220},"extra_metadata",[15,1537,427],{"class":1133},[15,1539,1540],{"class":1084},"{",[15,1542,1543],{"class":1143},"\"ionq_compiler_synthesis\"",[15,1545,1431],{"class":1084},[15,1547,1548],{"class":1161},"True",[15,1550,1551],{"class":1084},"})\n",[11,1553,1554,1555,364],{},"With the option set, IonQ decomposes the non-commuting sum on its side as well. See ",[274,1556,1558],{"href":1557},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",[280,1560,1562],{"id":1561},"related","Related",[1564,1565,1566,1571,1575,1581],"ul",{},[1567,1568,1569],"li",{},[274,1570,948],{"href":947},[1567,1572,1573],{},[274,1574,902],{"href":901},[1567,1576,1577],{},[274,1578,1580],{"href":1579},"\u002Flearn\u002Fdocs\u002Fgates","Gate reference",[1567,1582,1583],{},[274,1584,1558],{"href":1557},[1586,1587,1588],"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 .subq3, html code.shiki .subq3{--shiki-default:#98C379}html pre.shiki code .sVC51, html code.shiki .sVC51{--shiki-default:#D19A66}html pre.shiki code .s_ZVi, html code.shiki .s_ZVi{--shiki-default:#E06C75;--shiki-default-font-style:italic}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 .sU0A5, html code.shiki .sU0A5{--shiki-default:#E5C07B}",{"title":1071,"searchDepth":1094,"depth":1094,"links":1590},[1591,1592,1593,1594,1595,1596,1597,1598],{"id":282,"depth":1094,"text":283},{"id":367,"depth":1094,"text":368},{"id":395,"depth":1094,"text":396},{"id":992,"depth":1094,"text":993},{"id":1063,"depth":1094,"text":1064},{"id":1479,"depth":1094,"text":387},{"id":1507,"depth":1094,"text":392},{"id":1561,"depth":1094,"text":1562},"gates","Gates","The Pauli evolution gate, exp(−itH) for a Pauli-sum Hamiltonian: parameters, the PauliEvolutionGate call in Python and JS, and how IonQ receives it.",false,"md","multi-qubit","Multi-qubit gates","doc",{},24,"\u002Fblog\u002Flearn\u002Fdocs\u002Fpauli-evolution-gate","2026-09-16",[],{"title":1613,"description":1614},"Pauli evolution gate · Qollab docs","Reference for Qiskit's PauliEvolutionGate on Qollab: what exp(−itH) means, the operator and time parameters, the call in Python and JS, and its IonQ form.","blog\u002Flearn\u002Fdocs\u002Fpauli-evolution-gate",[],"rnNl_X7hmEH-tKVjFE1Hjw2oMwHG8r7c_JF6aNl0GYA",[],[],[1621,1628,1644,1669,1757,1767],{"category":1622,"categoryName":1623,"articles":1624},"account","Account",[1625],{"title":1626,"href":1627},"Account and profile","\u002Flearn\u002Fdocs\u002Faccount-and-profile",{"category":1629,"categoryName":1630,"articles":1631},"projects","Projects",[1632,1635,1638,1641],{"title":1633,"href":1634},"The project page","\u002Flearn\u002Fdocs\u002Fproject-anatomy",{"title":1636,"href":1637},"Editing your project","\u002Flearn\u002Fdocs\u002Fwrite-your-project-page",{"title":1639,"href":1640},"Publishing and versions","\u002Flearn\u002Fdocs\u002Fpublish",{"title":1642,"href":1643},"Forking a project","\u002Flearn\u002Fdocs\u002Ffork-and-remix",{"category":1645,"categoryName":1646,"articles":1647},"running-code","Running code",[1648,1651,1654,1657,1658,1661,1662,1665,1666],{"title":1649,"href":1650},"Running your code","\u002Flearn\u002Fdocs\u002Frun-your-code",{"title":1652,"href":1653},"Compute backends","\u002Flearn\u002Fdocs\u002Fcompute-backends",{"title":1655,"href":1656},"The runtime environment","\u002Flearn\u002Fdocs\u002Fruntime-environment",{"title":363,"href":362},{"title":1659,"href":1660},"Python \u002F Qiskit projects","\u002Flearn\u002Fdocs\u002Fpython-qiskit-projects",{"title":1558,"href":1557},{"title":1663,"href":1664},"Error mitigation and debiasing","\u002Flearn\u002Fdocs\u002Ferror-mitigation",{"title":1504,"href":1503},{"title":1667,"href":1668},"Primitives","\u002Flearn\u002Fdocs\u002Fprimitives",{"category":1599,"categoryName":1600,"articles":1670},[1671,1672,1677,1680,1683,1686,1689,1692,1695,1698,1701,1704,1707,1710,1713,1714,1719,1722,1725,1728,1731,1734,1737,1738,1741,1743,1748,1751,1754],{"title":1580,"href":1579},{"title":1673,"href":1674,"group":1675,"groupName":1676},"H gate","\u002Flearn\u002Fdocs\u002Fh-gate","single-qubit","Single-qubit 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gate","\u002Flearn\u002Fdocs\u002Frxx-gate",{"title":1735,"href":1736,"group":1717,"groupName":1718},"RYY gate","\u002Flearn\u002Fdocs\u002Fryy-gate",{"title":948,"href":947,"group":1717,"groupName":1718},{"title":1739,"href":1740,"group":1604,"groupName":1605},"CCX gate","\u002Flearn\u002Fdocs\u002Fccx-gate",{"title":5,"href":1742,"group":1604,"groupName":1605},"\u002Flearn\u002Fdocs\u002Fpauli-evolution-gate",{"title":1744,"href":1745,"group":1746,"groupName":1747},"GPi gate","\u002Flearn\u002Fdocs\u002Fgpi-gate","native","IonQ native gates",{"title":1749,"href":1750,"group":1746,"groupName":1747},"GPi2 gate","\u002Flearn\u002Fdocs\u002Fgpi2-gate",{"title":1752,"href":1753,"group":1746,"groupName":1747},"MS gate","\u002Flearn\u002Fdocs\u002Fms-gate",{"title":1755,"href":1756,"group":1746,"groupName":1747},"ZZ gate","\u002Flearn\u002Fdocs\u002Fzz-gate",{"category":1758,"categoryName":1759,"articles":1760},"credits","Credits",[1761,1764],{"title":1762,"href":1763},"How credits work","\u002Flearn\u002Fdocs\u002Fhow-credits-work",{"title":1765,"href":1766},"Before you spend credits","\u002Flearn\u002Fdocs\u002Fbefore-you-spend-credits",{"category":1768,"categoryName":1769,"articles":1770},"troubleshooting","Troubleshooting",[1771,1774,1777],{"title":1772,"href":1773},"Troubleshooting and FAQ","\u002Flearn\u002Fdocs\u002Ffaq",{"title":1775,"href":1776},"Error reference","\u002Flearn\u002Fdocs\u002Ferror-reference",{"title":1778,"href":1779},"Why your results look wrong","\u002Flearn\u002Fdocs\u002Fwhy-your-results-look-wrong",1789652389880]