[{"data":1,"prerenderedAt":1081},["ShallowReactive",2],{"blog-post-docs\u002Fgates":3,"sibling-dives-docs\u002Fgates":967,"learn-track-docs\u002Fgates":968,"learn-docs-groups":969},{"id":4,"title":5,"authors":6,"body":7,"breadcrumb":6,"builders":6,"byline":6,"category":949,"categoryName":950,"challenge":6,"courseAuthor":6,"courseLead":6,"dek":6,"description":951,"draft":952,"extension":953,"eyebrow":6,"featured":952,"finish":6,"fork":6,"group":6,"groupName":6,"hero":6,"heroAlt":6,"heroCta":6,"heroImage":6,"homepageFeatured":952,"kind":954,"lessonCount":6,"meta":955,"navigation":956,"newsItems":6,"next":6,"ogImage":6,"order":957,"outcomes":6,"path":958,"publishDate":959,"readingTime":6,"related":960,"relatedProjects":6,"seo":961,"stem":964,"tags":965,"track":6,"trackName":6,"__hash__":966},"blog\u002Fblog\u002Flearn\u002Fdocs\u002Fgates.md","Gate reference",null,{"type":8,"value":9,"toc":939},"minimark",[10,48,51,56,422,487,491,652,656,728,736,740,774,800,804,820,911,915],[11,12,13,14,18,19,22,23,26,27,30,31,34,35,30,38,30,41,30,44,47],"p",{},"Qollab circuits use Qiskit's gate methods, called the same way in Python and JS: ",[15,16,17],"code",{},"qc.h(0)"," in one, ",[15,20,21],{},"circuit.h(0)"," in the other. Angles are in radians. The standard gates run on every backend, with two cases that need ",[15,24,25],{},"transpile()"," first: the built-in simulator for the multi-controlled gates (",[15,28,29],{},"mcx",", ",[15,32,33],{},"mcp",") and for Pauli evolution, and the IBM noise models for Pauli evolution. The native gates need a native-gateset backend. The local simulators also take some of Qiskit's rarer gates (",[15,36,37],{},"iswap",[15,39,40],{},"ecr",[15,42,43],{},"cswap",[15,45,46],{},"rzx","), which have no page here.",[11,49,50],{},"On an IonQ run the Circuit panel on the Run tab draws the circuit as it was submitted, one box per gate, with a dot on each control wire. Local and IBM noise-model runs show no circuit panel.",[52,53,55],"h2",{"id":54},"single-qubit-gates","Single-qubit gates",[57,58,59,81],"table",{},[60,61,62],"thead",{},[63,64,65,69,72,75,78],"tr",{},[66,67,68],"th",{},"Panel",[66,70,71],{},"Gate",[66,73,74],{},"Does",[66,76,77],{},"Call",[66,79,80],{},"Controlled form",[82,83,84,111,139,166,193,214,235,256,277,301,322,350,374,398],"tbody",{},[63,85,86,90,98,101,106],{},[87,88,89],"td",{},"H",[87,91,92,97],{},[93,94,96],"a",{"href":95},"\u002Flearn\u002Fdocs\u002Fh-gate","H gate"," (Hadamard)",[87,99,100],{},"Equal superposition of 0 and 1",[87,102,103],{},[15,104,105],{},"h(q)",[87,107,108],{},[15,109,110],{},"ch(control, target)",[63,112,113,116,123,126,131],{},[87,114,115],{},"X",[87,117,118,122],{},[93,119,121],{"href":120},"\u002Flearn\u002Fdocs\u002Fx-gate","X gate"," (NOT)",[87,124,125],{},"Flips 0 and 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gate",[87,205,206],{},"Quarter-turn phase on 1",[87,208,209],{},[15,210,211],{},"s(q)",[87,213],{},[63,215,216,219,225,228,233],{},[87,217,218],{},"Sdg",[87,220,221],{},[93,222,224],{"href":223},"\u002Flearn\u002Fdocs\u002Fsdg-gate","S† gate",[87,226,227],{},"Undoes S",[87,229,230],{},[15,231,232],{},"sdg(q)",[87,234],{},[63,236,237,240,246,249,254],{},[87,238,239],{},"T",[87,241,242],{},[93,243,245],{"href":244},"\u002Flearn\u002Fdocs\u002Ft-gate","T gate",[87,247,248],{},"Eighth-turn phase on 1",[87,250,251],{},[15,252,253],{},"t(q)",[87,255],{},[63,257,258,261,267,270,275],{},[87,259,260],{},"Tdg",[87,262,263],{},[93,264,266],{"href":265},"\u002Flearn\u002Fdocs\u002Ftdg-gate","T† gate",[87,268,269],{},"Undoes T",[87,271,272],{},[15,273,274],{},"tdg(q)",[87,276],{},[63,278,279,282,288,291,296],{},[87,280,281],{},"√X",[87,283,284],{},[93,285,287],{"href":286},"\u002Flearn\u002Fdocs\u002Fsx-gate","√X gate",[87,289,290],{},"Half of an X",[87,292,293],{},[15,294,295],{},"sx(q)",[87,297,298],{},[15,299,300],{},"csx(control, target)",[63,302,303,306,312,315,320],{},[87,304,305],{},"√X†",[87,307,308],{},[93,309,311],{"href":310},"\u002Flearn\u002Fdocs\u002Fsxdg-gate","√X† gate",[87,313,314],{},"Undoes √X",[87,316,317],{},[15,318,319],{},"sxdg(q)",[87,321],{},[63,323,324,327,334,337,342],{},[87,325,326],{},"P(λ)",[87,328,329,333],{},[93,330,332],{"href":331},"\u002Flearn\u002Fdocs\u002Fp-gate","P gate"," (phase)",[87,335,336],{},"Phase λ on 1",[87,338,339],{},[15,340,341],{},"p(λ, q)",[87,343,344],{},[93,345,347],{"href":346},"\u002Flearn\u002Fdocs\u002Fcp-gate",[15,348,349],{},"cp(λ, control, target)",[63,351,352,355,361,364,369],{},[87,353,354],{},"Rx(θ)",[87,356,357],{},[93,358,360],{"href":359},"\u002Flearn\u002Fdocs\u002Frx-gate","RX gate",[87,362,363],{},"Rotation about X by θ",[87,365,366],{},[15,367,368],{},"rx(θ, q)",[87,370,371],{},[15,372,373],{},"crx(θ, control, target)",[63,375,376,379,385,388,393],{},[87,377,378],{},"Ry(θ)",[87,380,381],{},[93,382,384],{"href":383},"\u002Flearn\u002Fdocs\u002Fry-gate","RY gate",[87,386,387],{},"Rotation about Y by θ",[87,389,390],{},[15,391,392],{},"ry(θ, q)",[87,394,395],{},[15,396,397],{},"cry(θ, control, target)",[63,399,400,403,409,412,417],{},[87,401,402],{},"Rz(θ)",[87,404,405],{},[93,406,408],{"href":407},"\u002Flearn\u002Fdocs\u002Frz-gate","RZ gate",[87,410,411],{},"Rotation about Z by θ",[87,413,414],{},[15,415,416],{},"rz(θ, q)",[87,418,419],{},[15,420,421],{},"crz(θ, control, target)",[11,423,424,425,486],{},"A controlled form applies the gate to the target only when the control is 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The panel draws it as the base gate's box with a dot on the control wire.",[52,488,490],{"id":489},"two-qubit-gates","Two-qubit gates",[57,492,493,505],{},[60,494,495],{},[63,496,497,499,501,503],{},[66,498,68],{},[66,500,71],{},[66,502,74],{},[66,504,77],{},[82,506,507,525,542,559,576,595,614,633],{},[63,508,509,512,518,521],{},[87,510,511],{},"● X",[87,513,514,517],{},[93,515,516],{"href":135},"CX gate"," (CNOT)",[87,519,520],{},"Flips the target when the control is 1",[87,522,523],{},[15,524,138],{},[63,526,527,530,535,538],{},[87,528,529],{},"● Y",[87,531,532],{},[93,533,534],{"href":162},"CY gate",[87,536,537],{},"Y on the target when the control is 1",[87,539,540],{},[15,541,165],{},[63,543,544,547,552,555],{},[87,545,546],{},"● Z",[87,548,549],{},[93,550,551],{"href":189},"CZ gate",[87,553,554],{},"Flips the sign of 11",[87,556,557],{},[15,558,192],{},[63,560,561,564,569,572],{},[87,562,563],{},"● P(λ)",[87,565,566],{},[93,567,568],{"href":346},"CP gate",[87,570,571],{},"Phase λ on 11",[87,573,574],{},[15,575,349],{},[63,577,578,581,587,590],{},[87,579,580],{},"Swap",[87,582,583],{},[93,584,586],{"href":585},"\u002Flearn\u002Fdocs\u002Fswap-gate","Swap gate",[87,588,589],{},"Exchanges two qubits",[87,591,592],{},[15,593,594],{},"swap(a, b)",[63,596,597,600,606,609],{},[87,598,599],{},"Xx(θ)",[87,601,602],{},[93,603,605],{"href":604},"\u002Flearn\u002Fdocs\u002Frxx-gate","RXX gate",[87,607,608],{},"Rotates the pair about X⊗X by θ",[87,610,611],{},[15,612,613],{},"rxx(θ, a, b)",[63,615,616,619,625,628],{},[87,617,618],{},"Yy(θ)",[87,620,621],{},[93,622,624],{"href":623},"\u002Flearn\u002Fdocs\u002Fryy-gate","RYY gate",[87,626,627],{},"Rotates the pair about Y⊗Y by θ",[87,629,630],{},[15,631,632],{},"ryy(θ, a, b)",[63,634,635,638,644,647],{},[87,636,637],{},"Zz(θ)",[87,639,640],{},[93,641,643],{"href":642},"\u002Flearn\u002Fdocs\u002Frzz-gate","RZZ gate",[87,645,646],{},"Phase that depends on whether the pair agrees",[87,648,649],{},[15,650,651],{},"rzz(θ, a, b)",[52,653,655],{"id":654},"three-or-more-qubits","Three or more qubits",[57,657,658,670],{},[60,659,660],{},[63,661,662,664,666,668],{},[66,663,68],{},[66,665,71],{},[66,667,74],{},[66,669,77],{},[82,671,672,692,710],{},[63,673,674,677,684,687],{},[87,675,676],{},"● ● X",[87,678,679,683],{},[93,680,682],{"href":681},"\u002Flearn\u002Fdocs\u002Fccx-gate","CCX gate"," (Toffoli)",[87,685,686],{},"Flips the target when both controls are 1",[87,688,689],{},[15,690,691],{},"ccx(control1, control2, target)",[63,693,694,697,702,705],{},[87,695,696],{},"● … X",[87,698,699],{},[93,700,701],{"href":681},"Multi-controlled X",[87,703,704],{},"Flips the target when every control is 1",[87,706,707],{},[15,708,709],{},"mcx([controls], target)",[63,711,712,715,720,723],{},[87,713,714],{},"● … P(λ)",[87,716,717],{},[93,718,719],{"href":346},"Multi-controlled phase",[87,721,722],{},"Phase λ when every control and the target are 1",[87,724,725],{},[15,726,727],{},"mcp(λ, [controls], target)",[11,729,730,731,735],{},"A multi-controlled gate can carry up to 7 control qubits on IonQ backends; more than that fails at submission with the entry in the ",[93,732,734],{"href":733},"\u002Flearn\u002Fdocs\u002Ferror-reference","Error reference",".",[52,737,739],{"id":738},"pauli-evolution","Pauli evolution",[57,741,742,754],{},[60,743,744],{},[63,745,746,748,750,752],{},[66,747,68],{},[66,749,71],{},[66,751,74],{},[66,753,77],{},[82,755,756],{},[63,757,758,761,766,769],{},[87,759,760],{},"exp(…)(t)",[87,762,763],{},[93,764,739],{"href":765},"\u002Flearn\u002Fdocs\u002Fpauli-evolution-gate",[87,767,768],{},"Evolves the qubits under a Hamiltonian for time t",[87,770,771],{},[15,772,773],{},"qc.append(PauliEvolutionGate(op, time=t), qubits)",[11,775,776,779,780,783,784,787,788,791,792,794,795,799],{},[15,777,778],{},"PauliEvolutionGate"," is in ",[15,781,782],{},"qiskit.circuit.library",". The panel prints the weighted Pauli terms inside ",[15,785,786],{},"exp(…)"," and the time after them. IonQ backends take the gate as submitted when its terms commute with each other (the ",[93,789,790],{"href":765},"gate page"," covers the option for terms that do not); the built-in simulator and the IBM noise models reject it untranspiled, so run ",[15,793,25],{}," first there (see ",[93,796,798],{"href":797},"\u002Flearn\u002Fdocs\u002Ftranspilation","Transpilation",").",[52,801,803],{"id":802},"ionq-native-gates","IonQ native gates",[11,805,806,807,811,812,815,816,819],{},"Native gates are what IonQ hardware physically executes. They appear in your circuit only when you write a native-gate circuit yourself, which turns IonQ's compiler off; see ",[93,808,810],{"href":809},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",". They come from ",[15,813,814],{},"qiskit_ionq"," rather than ",[15,817,818],{},"qiskit",", and their angles are in turns (a fraction of a full rotation), not radians.",[57,821,822,835],{},[60,823,824],{},[63,825,826,828,830,832],{},[66,827,71],{},[66,829,74],{},[66,831,77],{},[66,833,834],{},"Systems",[82,836,837,856,874,893],{},[63,838,839,845,848,853],{},[87,840,841],{},[93,842,844],{"href":843},"\u002Flearn\u002Fdocs\u002Fgpi-gate","GPi",[87,846,847],{},"Half-turn about an axis at phase φ",[87,849,850],{},[15,851,852],{},"qc.append(GPIGate(φ), [q])",[87,854,855],{},"Aria and Forte",[63,857,858,864,867,872],{},[87,859,860],{},[93,861,863],{"href":862},"\u002Flearn\u002Fdocs\u002Fgpi2-gate","GPi2",[87,865,866],{},"Quarter-turn about an axis at phase φ",[87,868,869],{},[15,870,871],{},"qc.append(GPI2Gate(φ), [q])",[87,873,855],{},[63,875,876,882,885,890],{},[87,877,878],{},[93,879,881],{"href":880},"\u002Flearn\u002Fdocs\u002Fms-gate","MS",[87,883,884],{},"Entangles the pair by θ, from 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