[{"data":1,"prerenderedAt":3540},["ShallowReactive",2],{"blog-post-docs\u002Fms-gate":3,"sibling-dives-docs\u002Fms-gate":3376,"learn-track-docs\u002Fms-gate":3377,"learn-docs-groups":3378},{"id":4,"title":5,"authors":6,"body":7,"breadcrumb":6,"builders":6,"byline":6,"category":3357,"categoryName":3358,"challenge":6,"courseAuthor":6,"courseLead":6,"dek":6,"description":3359,"draft":3360,"extension":3361,"eyebrow":6,"featured":3360,"finish":6,"fork":6,"group":3362,"groupName":3363,"hero":6,"heroAlt":6,"heroCta":6,"heroImage":6,"homepageFeatured":3360,"kind":3364,"lessonCount":6,"meta":3365,"navigation":3085,"newsItems":6,"next":6,"ogImage":6,"order":3366,"outcomes":6,"path":3367,"publishDate":3368,"readingTime":6,"related":3369,"relatedProjects":6,"seo":3370,"stem":3373,"tags":3374,"track":6,"trackName":6,"__hash__":3375},"blog\u002Fblog\u002Flearn\u002Fdocs\u002Fms-gate.md","MS gate",null,{"type":8,"value":9,"toc":3348},"minimark",[10,364,416,421,447,451,508,512,1180,2331,2353,2357,2360,2862,3022,3026,3036,3040,3173,3307,3316,3320,3344],[11,12,13,14,121,122,193,194,226,227,255,256,261,262,304,305,363],"p",{},"The MS gate, the Mølmer-Sørensen gate, is the native two-qubit entangling gate of IonQ's Aria systems. It rotates a pair of qubits together about an axis in the XY plane of each, with the two axes set by phases ",[15,16,19,49],"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",[28,29,30,44],"semantics",{},[31,32,33],"mrow",{},[34,35,36,40],"msub",{},[37,38,39],"mi",{},"ϕ",[41,42,43],"mn",{},"0",[45,46,48],"annotation",{"encoding":47},"application\u002Fx-tex","\\phi_0",[15,50,54],{"className":51,"ariaHidden":53},[52],"katex-html","true",[15,55,58,63],{"className":56},[57],"base",[15,59],{"className":60,"style":62},[61],"strut","height:0.8889em;vertical-align:-0.1944em;",[15,64,67,71],{"className":65},[66],"mord",[15,68,39],{"className":69},[66,70],"mathnormal",[15,72,75],{"className":73},[74],"msupsub",[15,76,80,112],{"className":77},[78,79],"vlist-t","vlist-t2",[15,81,84,107],{"className":82},[83],"vlist-r",[15,85,89],{"className":86,"style":88},[87],"vlist","height:0.3011em;",[15,90,92,97],{"style":91},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[15,93],{"className":94,"style":96},[95],"pstrut","height:2.7em;",[15,98,104],{"className":99},[100,101,102,103],"sizing","reset-size6","size3","mtight",[15,105,43],{"className":106},[66,103],[15,108,111],{"className":109},[110],"vlist-s","​",[15,113,115],{"className":114},[83],[15,116,119],{"className":117,"style":118},[87],"height:0.15em;",[15,120],{}," and ",[15,123,125,144],{"className":124},[18],[15,126,128],{"className":127},[22],[24,129,130],{"xmlns":26},[28,131,132,141],{},[31,133,134],{},[34,135,136,138],{},[37,137,39],{},[41,139,140],{},"1",[45,142,143],{"encoding":47},"\\phi_1",[15,145,147],{"className":146,"ariaHidden":53},[52],[15,148,150,153],{"className":149},[57],[15,151],{"className":152,"style":62},[61],[15,154,156,159],{"className":155},[66],[15,157,39],{"className":158},[66,70],[15,160,162],{"className":161},[74],[15,163,165,185],{"className":164},[78,79],[15,166,168,182],{"className":167},[83],[15,169,171],{"className":170,"style":88},[87],[15,172,173,176],{"style":91},[15,174],{"className":175,"style":96},[95],[15,177,179],{"className":178},[100,101,102,103],[15,180,140],{"className":181},[66,103],[15,183,111],{"className":184},[110],[15,186,188],{"className":187},[83],[15,189,191],{"className":190,"style":118},[87],[15,192],{}," and the amount of entanglement set by an angle ",[15,195,197,212],{"className":196},[18],[15,198,200],{"className":199},[22],[24,201,202],{"xmlns":26},[28,203,204,209],{},[31,205,206],{},[37,207,208],{},"θ",[45,210,211],{"encoding":47},"\\theta",[15,213,215],{"className":214,"ariaHidden":53},[52],[15,216,218,222],{"className":217},[57],[15,219],{"className":220,"style":221},[61],"height:0.6944em;",[15,223,208],{"className":224,"style":225},[66,70],"margin-right:0.0278em;",". All three are in turns: ",[15,228,230,243],{"className":229},[18],[15,231,233],{"className":232},[22],[24,234,235],{"xmlns":26},[28,236,237,241],{},[31,238,239],{},[37,240,208],{},[45,242,211],{"encoding":47},[15,244,246],{"className":245,"ariaHidden":53},[52],[15,247,249,252],{"className":248},[57],[15,250],{"className":251,"style":221},[61],[15,253,208],{"className":254,"style":225},[66,70]," runs from 0, the identity, to 0.25, fully entangling, which is the default. With both phases at 0 it is an ",[257,258,260],"a",{"href":259},"\u002Flearn\u002Fdocs\u002Frxx-gate","RXX gate"," of angle ",[15,263,265,285],{"className":264},[18],[15,266,268],{"className":267},[22],[24,269,270],{"xmlns":26},[28,271,272,282],{},[31,273,274,277,280],{},[41,275,276],{},"2",[37,278,279],{},"π",[37,281,208],{},[45,283,284],{"encoding":47},"2\\pi\\theta",[15,286,288],{"className":287,"ariaHidden":53},[52],[15,289,291,294,297,301],{"className":290},[57],[15,292],{"className":293,"style":221},[61],[15,295,276],{"className":296},[66],[15,298,279],{"className":299,"style":300},[66,70],"margin-right:0.0359em;",[15,302,208],{"className":303,"style":225},[66,70],". At ",[15,306,308,329],{"className":307},[18],[15,309,311],{"className":310},[22],[24,312,313],{"xmlns":26},[28,314,315,326],{},[31,316,317,319,323],{},[37,318,208],{},[320,321,322],"mo",{},"=",[41,324,325],{},"0.25",[45,327,328],{"encoding":47},"\\theta = 0.25",[15,330,332,353],{"className":331,"ariaHidden":53},[52],[15,333,335,338,341,346,350],{"className":334},[57],[15,336],{"className":337,"style":221},[61],[15,339,208],{"className":340,"style":225},[66,70],[15,342],{"className":343,"style":345},[344],"mspace","margin-right:0.2778em;",[15,347,322],{"className":348},[349],"mrel",[15,351],{"className":352,"style":345},[344],[15,354,356,360],{"className":355},[57],[15,357],{"className":358,"style":359},[61],"height:0.6444em;",[15,361,325],{"className":362},[66]," on two fresh qubits, the pair reads 00 or 11 with equal probability and never 01 or 10.",[11,365,366,367,410,411,415],{},"Kets such as ",[15,368,370,392],{"className":369},[18],[15,371,373],{"className":372},[22],[24,374,375],{"xmlns":26},[28,376,377,389],{},[31,378,379,383,385],{},[37,380,382],{"mathvariant":381},"normal","∣",[41,384,43],{},[320,386,388],{"stretchy":387},"false","⟩",[45,390,391],{"encoding":47},"\\vert 0 \\rangle",[15,393,395],{"className":394,"ariaHidden":53},[52],[15,396,398,402,406],{"className":397},[57],[15,399],{"className":400,"style":401},[61],"height:1em;vertical-align:-0.25em;",[15,403,405],{"className":404},[66],"∣0",[15,407,388],{"className":408},[409],"mclose"," name the basis states and rotations are described on the Bloch sphere; the ",[257,412,414],{"href":413},"\u002Flearn\u002Fquantum-foundations\u002Fqubits","qubits lesson"," introduces both.",[417,418,420],"h2",{"id":419},"before-you-use-a-native-gate","Before you use a native gate",[11,422,423,424,428,429,432,433,436,437,441,442,446],{},"Native gates only run in a native-gate circuit, and a circuit cannot mix native and standard gates. In ",[425,426,427],"code",{},"qiskit-ionq"," a backend is created for one gateset, ",[425,430,431],{},"provider.get_backend(name, gateset=\"native\")","; the pre-created ",[425,434,435],{},"backend"," on Qollab uses the standard gateset. MS is the entangler of Aria, which on Qollab means the Aria noise-model simulators; Forte, the hardware behind Qollab's QPU backends, uses the ",[257,438,440],{"href":439},"\u002Flearn\u002Fdocs\u002Fzz-gate","ZZ gate"," instead. Submitting native gates bypasses IonQ's compiler and optimiser and turns error mitigation off by default. See ",[257,443,445],{"href":444},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",".",[417,448,450],{"id":449},"call","Call",[452,453,454,466],"table",{},[455,456,457],"thead",{},[458,459,460,464],"tr",{},[461,462,463],"th",{},"Where",[461,465,450],{},[467,468,469,480,490],"tbody",{},[458,470,471,475],{},[472,473,474],"td",{},"Python",[472,476,477],{},[425,478,479],{},"qc.append(MSGate(φ0, φ1, θ), [qubit0, qubit1])",[458,481,482,485],{},[472,483,484],{},"JS",[472,486,487],{},[425,488,489],{},"circuit.append(MSGate(φ0, φ1, θ), [qubit0, qubit1])",[458,491,492,495],{},[472,493,494],{},"Class",[472,496,497,500,501,504,505,507],{},[425,498,499],{},"MSGate",", from ",[425,502,503],{},"qiskit_ionq","; ",[425,506,208],{}," defaults to 0.25",[417,509,511],{"id":510},"matrix","Matrix",[11,513,514,515,622,623,704,705,780,781,121,983,446],{},"The matrix uses the basis order ",[15,516,518,565],{"className":517},[18],[15,519,521],{"className":520},[22],[24,522,523],{"xmlns":26},[28,524,525,562],{},[31,526,527,529,532,534,537,539,542,544,546,548,551,553,555,557,560],{},[37,528,382],{"mathvariant":381},[41,530,531],{},"00",[320,533,388],{"stretchy":387},[320,535,536],{"separator":53},",",[37,538,382],{"mathvariant":381},[41,540,541],{},"01",[320,543,388],{"stretchy":387},[320,545,536],{"separator":53},[37,547,382],{"mathvariant":381},[41,549,550],{},"10",[320,552,388],{"stretchy":387},[320,554,536],{"separator":53},[37,556,382],{"mathvariant":381},[41,558,559],{},"11",[320,561,388],{"stretchy":387},[45,563,564],{"encoding":47},"\\vert 00 \\rangle, \\vert 01 \\rangle, \\vert 10 \\rangle, \\vert 11 \\rangle",[15,566,568],{"className":567,"ariaHidden":53},[52],[15,569,571,574,578,581,585,589,593,596,599,602,606,609,612,615,619],{"className":570},[57],[15,572],{"className":573,"style":401},[61],[15,575,577],{"className":576},[66],"∣00",[15,579,388],{"className":580},[409],[15,582,536],{"className":583},[584],"mpunct",[15,586],{"className":587,"style":588},[344],"margin-right:0.1667em;",[15,590,592],{"className":591},[66],"∣01",[15,594,388],{"className":595},[409],[15,597,536],{"className":598},[584],[15,600],{"className":601,"style":588},[344],[15,603,605],{"className":604},[66],"∣10",[15,607,388],{"className":608},[409],[15,610,536],{"className":611},[584],[15,613],{"className":614,"style":588},[344],[15,616,618],{"className":617},[66],"∣11",[15,620,388],{"className":621},[409],", with ",[15,624,626,659],{"className":625},[18],[15,627,629],{"className":628},[22],[24,630,631],{"xmlns":26},[28,632,633,656],{},[31,634,635,638,640,643,646,649,651,653],{},[37,636,637],{},"c",[320,639,322],{},[37,641,642],{},"cos",[320,644,645],{},"⁡",[320,647,648],{"stretchy":387},"(",[37,650,279],{},[37,652,208],{},[320,654,655],{"stretchy":387},")",[45,657,658],{"encoding":47},"c = \\cos(\\pi\\theta)",[15,660,662,681],{"className":661,"ariaHidden":53},[52],[15,663,665,669,672,675,678],{"className":664},[57],[15,666],{"className":667,"style":668},[61],"height:0.4306em;",[15,670,637],{"className":671},[66,70],[15,673],{"className":674,"style":345},[344],[15,676,322],{"className":677},[349],[15,679],{"className":680,"style":345},[344],[15,682,684,687,691,695,698,701],{"className":683},[57],[15,685],{"className":686,"style":401},[61],[15,688,642],{"className":689},[690],"mop",[15,692,648],{"className":693},[694],"mopen",[15,696,279],{"className":697,"style":300},[66,70],[15,699,208],{"className":700,"style":225},[66,70],[15,702,655],{"className":703},[409],", ",[15,706,708,738],{"className":707},[18],[15,709,711],{"className":710},[22],[24,712,713],{"xmlns":26},[28,714,715,735],{},[31,716,717,720,722,725,727,729,731,733],{},[37,718,719],{},"s",[320,721,322],{},[37,723,724],{},"sin",[320,726,645],{},[320,728,648],{"stretchy":387},[37,730,279],{},[37,732,208],{},[320,734,655],{"stretchy":387},[45,736,737],{"encoding":47},"s = \\sin(\\pi\\theta)",[15,739,741,759],{"className":740,"ariaHidden":53},[52],[15,742,744,747,750,753,756],{"className":743},[57],[15,745],{"className":746,"style":668},[61],[15,748,719],{"className":749},[66,70],[15,751],{"className":752,"style":345},[344],[15,754,322],{"className":755},[349],[15,757],{"className":758,"style":345},[344],[15,760,762,765,768,771,774,777],{"className":761},[57],[15,763],{"className":764,"style":401},[61],[15,766,724],{"className":767},[690],[15,769,648],{"className":770},[694],[15,772,279],{"className":773,"style":300},[66,70],[15,775,208],{"className":776,"style":225},[66,70],[15,778,655],{"className":779},[409]," , ",[15,782,784,819],{"className":783},[18],[15,785,787],{"className":786},[22],[24,788,789],{"xmlns":26},[28,790,791,816],{},[31,792,793,800,802,808,810],{},[34,794,795,797],{},[37,796,39],{},[320,798,799],{},"+",[320,801,322],{},[34,803,804,806],{},[37,805,39],{},[41,807,43],{},[320,809,799],{},[34,811,812,814],{},[37,813,39],{},[41,815,140],{},[45,817,818],{"encoding":47},"\\phi_+ = \\phi_0 + \\phi_1",[15,820,822,881,937],{"className":821,"ariaHidden":53},[52],[15,823,825,829,872,875,878],{"className":824},[57],[15,826],{"className":827,"style":828},[61],"height:0.9028em;vertical-align:-0.2083em;",[15,830,832,835],{"className":831},[66],[15,833,39],{"className":834},[66,70],[15,836,838],{"className":837},[74],[15,839,841,863],{"className":840},[78,79],[15,842,844,860],{"className":843},[83],[15,845,848],{"className":846,"style":847},[87],"height:0.2583em;",[15,849,850,853],{"style":91},[15,851],{"className":852,"style":96},[95],[15,854,856],{"className":855},[100,101,102,103],[15,857,799],{"className":858},[859,103],"mbin",[15,861,111],{"className":862},[110],[15,864,866],{"className":865},[83],[15,867,870],{"className":868,"style":869},[87],"height:0.2083em;",[15,871],{},[15,873],{"className":874,"style":345},[344],[15,876,322],{"className":877},[349],[15,879],{"className":880,"style":345},[344],[15,882,884,887,927,931,934],{"className":883},[57],[15,885],{"className":886,"style":62},[61],[15,888,890,893],{"className":889},[66],[15,891,39],{"className":892},[66,70],[15,894,896],{"className":895},[74],[15,897,899,919],{"className":898},[78,79],[15,900,902,916],{"className":901},[83],[15,903,905],{"className":904,"style":88},[87],[15,906,907,910],{"style":91},[15,908],{"className":909,"style":96},[95],[15,911,913],{"className":912},[100,101,102,103],[15,914,43],{"className":915},[66,103],[15,917,111],{"className":918},[110],[15,920,922],{"className":921},[83],[15,923,925],{"className":924,"style":118},[87],[15,926],{},[15,928],{"className":929,"style":930},[344],"margin-right:0.2222em;",[15,932,799],{"className":933},[859],[15,935],{"className":936,"style":930},[344],[15,938,940,943],{"className":939},[57],[15,941],{"className":942,"style":62},[61],[15,944,946,949],{"className":945},[66],[15,947,39],{"className":948},[66,70],[15,950,952],{"className":951},[74],[15,953,955,975],{"className":954},[78,79],[15,956,958,972],{"className":957},[83],[15,959,961],{"className":960,"style":88},[87],[15,962,963,966],{"style":91},[15,964],{"className":965,"style":96},[95],[15,967,969],{"className":968},[100,101,102,103],[15,970,140],{"className":971},[66,103],[15,973,111],{"className":974},[110],[15,976,978],{"className":977},[83],[15,979,981],{"className":980,"style":118},[87],[15,982],{},[15,984,986,1021],{"className":985},[18],[15,987,989],{"className":988},[22],[24,990,991],{"xmlns":26},[28,992,993,1018],{},[31,994,995,1002,1004,1010,1012],{},[34,996,997,999],{},[37,998,39],{},[320,1000,1001],{},"−",[320,1003,322],{},[34,1005,1006,1008],{},[37,1007,39],{},[41,1009,140],{},[320,1011,1001],{},[34,1013,1014,1016],{},[37,1015,39],{},[41,1017,43],{},[45,1019,1020],{"encoding":47},"\\phi_- = \\phi_1 - 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\\rangle",[15,2574,2576,2600],{"className":2575,"ariaHidden":53},[52],[15,2577,2579,2582,2585,2588,2591,2594,2597],{"className":2578},[57],[15,2580],{"className":2581,"style":401},[61],[15,2583,637],{"className":2584},[66,70],[15,2586,592],{"className":2587},[66],[15,2589,388],{"className":2590},[409],[15,2592],{"className":2593,"style":930},[344],[15,2595,1001],{"className":2596},[859],[15,2598],{"className":2599,"style":930},[344],[15,2601,2603,2606,2609,2612,2615],{"className":2602},[57],[15,2604],{"className":2605,"style":401},[61],[15,2607,1270],{"className":2608},[66,70],[15,2610,719],{"className":2611},[66,70],[15,2613,605],{"className":2614},[66],[15,2616,388],{"className":2617},[409],[458,2619,2620,2658],{},[472,2621,2622],{},[15,2623,2625,2643],{"className":2624},[18],[15,2626,2628],{"className":2627},[22],[24,2629,2630],{"xmlns":26},[28,2631,2632,2640],{},[31,2633,2634,2636,2638],{},[37,2635,382],{"mathvariant":381},[41,2637,550],{},[320,2639,388],{"stretchy":387},[45,2641,2642],{"encoding":47},"\\vert 10 \\rangle",[15,2644,2646],{"className":2645,"ariaHidden":53},[52],[15,2647,2649,2652,2655],{"className":2648},[57],[15,2650],{"className":2651,"style":401},[61],[15,2653,605],{"className":2654},[66],[15,2656,388],{"className":2657},[409],[472,2659,2660],{},[15,2661,2663,2695],{"className":2662},[18],[15,2664,2666],{"className":2665},[22],[24,2667,2668],{"xmlns":26},[28,2669,2670,2692],{},[31,2671,2672,2674,2676,2678,2680,2682,2684,2686,2688,2690],{},[37,2673,637],{},[37,2675,382],{"mathvariant":381},[41,2677,550],{},[320,2679,388],{"stretchy":387},[320,2681,1001],{},[37,2683,1270],{},[37,2685,719],{},[37,2687,382],{"mathvariant":381},[41,2689,541],{},[320,2691,388],{"stretchy":387},[45,2693,2694],{"encoding":47},"c\\vert 10 \\rangle - is\\vert 01 \\rangle",[15,2696,2698,2722],{"className":2697,"ariaHidden":53},[52],[15,2699,2701,2704,2707,2710,2713,2716,2719],{"className":2700},[57],[15,2702],{"className":2703,"style":401},[61],[15,2705,637],{"className":2706},[66,70],[15,2708,605],{"className":2709},[66],[15,2711,388],{"className":2712},[409],[15,2714],{"className":2715,"style":930},[344],[15,2717,1001],{"className":2718},[859],[15,2720],{"className":2721,"style":930},[344],[15,2723,2725,2728,2731,2734,2737],{"className":2724},[57],[15,2726],{"className":2727,"style":401},[61],[15,2729,1270],{"className":2730},[66,70],[15,2732,719],{"className":2733},[66,70],[15,2735,592],{"className":2736},[66],[15,2738,388],{"className":2739},[409],[458,2741,2742,2780],{},[472,2743,2744],{},[15,2745,2747,2765],{"className":2746},[18],[15,2748,2750],{"className":2749},[22],[24,2751,2752],{"xmlns":26},[28,2753,2754,2762],{},[31,2755,2756,2758,2760],{},[37,2757,382],{"mathvariant":381},[41,2759,559],{},[320,2761,388],{"stretchy":387},[45,2763,2764],{"encoding":47},"\\vert 11 \\rangle",[15,2766,2768],{"className":2767,"ariaHidden":53},[52],[15,2769,2771,2774,2777],{"className":2770},[57],[15,2772],{"className":2773,"style":401},[61],[15,2775,618],{"className":2776},[66],[15,2778,388],{"className":2779},[409],[472,2781,2782],{},[15,2783,2785,2817],{"className":2784},[18],[15,2786,2788],{"className":2787},[22],[24,2789,2790],{"xmlns":26},[28,2791,2792,2814],{},[31,2793,2794,2796,2798,2800,2802,2804,2806,2808,2810,2812],{},[37,2795,637],{},[37,2797,382],{"mathvariant":381},[41,2799,559],{},[320,2801,388],{"stretchy":387},[320,2803,1001],{},[37,2805,1270],{},[37,2807,719],{},[37,2809,382],{"mathvariant":381},[41,2811,531],{},[320,2813,388],{"stretchy":387},[45,2815,2816],{"encoding":47},"c\\vert 11 \\rangle - is\\vert 00 \\rangle",[15,2818,2820,2844],{"className":2819,"ariaHidden":53},[52],[15,2821,2823,2826,2829,2832,2835,2838,2841],{"className":2822},[57],[15,2824],{"className":2825,"style":401},[61],[15,2827,637],{"className":2828},[66,70],[15,2830,618],{"className":2831},[66],[15,2833,388],{"className":2834},[409],[15,2836],{"className":2837,"style":930},[344],[15,2839,1001],{"className":2840},[859],[15,2842],{"className":2843,"style":930},[344],[15,2845,2847,2850,2853,2856,2859],{"className":2846},[57],[15,2848],{"className":2849,"style":401},[61],[15,2851,1270],{"className":2852},[66,70],[15,2854,719],{"className":2855},[66,70],[15,2857,577],{"className":2858},[66],[15,2860,388],{"className":2861},[409],[11,2863,2864,2865,500,2915,2950,2951,121,2986,3021],{},"At ",[15,2866,2868,2885],{"className":2867},[18],[15,2869,2871],{"className":2870},[22],[24,2872,2873],{"xmlns":26},[28,2874,2875,2883],{},[31,2876,2877,2879,2881],{},[37,2878,208],{},[320,2880,322],{},[41,2882,325],{},[45,2884,328],{"encoding":47},[15,2886,2888,2906],{"className":2887,"ariaHidden":53},[52],[15,2889,2891,2894,2897,2900,2903],{"className":2890},[57],[15,2892],{"className":2893,"style":221},[61],[15,2895,208],{"className":2896,"style":225},[66,70],[15,2898],{"className":2899,"style":345},[344],[15,2901,322],{"className":2902},[349],[15,2904],{"className":2905,"style":345},[344],[15,2907,2909,2912],{"className":2908},[57],[15,2910],{"className":2911,"style":359},[61],[15,2913,325],{"className":2914},[66],[15,2916,2918,2935],{"className":2917},[18],[15,2919,2921],{"className":2920},[22],[24,2922,2923],{"xmlns":26},[28,2924,2925,2933],{},[31,2926,2927,2929,2931],{},[37,2928,382],{"mathvariant":381},[41,2930,531],{},[320,2932,388],{"stretchy":387},[45,2934,2398],{"encoding":47},[15,2936,2938],{"className":2937,"ariaHidden":53},[52],[15,2939,2941,2944,2947],{"className":2940},[57],[15,2942],{"className":2943,"style":401},[61],[15,2945,577],{"className":2946},[66],[15,2948,388],{"className":2949},[409]," the gate produces an equal superposition of ",[15,2952,2954,2971],{"className":2953},[18],[15,2955,2957],{"className":2956},[22],[24,2958,2959],{"xmlns":26},[28,2960,2961,2969],{},[31,2962,2963,2965,2967],{},[37,2964,382],{"mathvariant":381},[41,2966,531],{},[320,2968,388],{"stretchy":387},[45,2970,2398],{"encoding":47},[15,2972,2974],{"className":2973,"ariaHidden":53},[52],[15,2975,2977,2980,2983],{"className":2976},[57],[15,2978],{"className":2979,"style":401},[61],[15,2981,577],{"className":2982},[66],[15,2984,388],{"className":2985},[409],[15,2987,2989,3006],{"className":2988},[18],[15,2990,2992],{"className":2991},[22],[24,2993,2994],{"xmlns":26},[28,2995,2996,3004],{},[31,2997,2998,3000,3002],{},[37,2999,382],{"mathvariant":381},[41,3001,559],{},[320,3003,388],{"stretchy":387},[45,3005,2764],{"encoding":47},[15,3007,3009],{"className":3008,"ariaHidden":53},[52],[15,3010,3012,3015,3018],{"className":3011},[57],[15,3013],{"className":3014,"style":401},[61],[15,3016,618],{"className":3017},[66],[15,3019,388],{"className":3020},[409],", a Bell state up to a phase. Smaller angles entangle partially, which is what makes arbitrary-angle MS gates cheaper than building the same rotation from fully entangling ones.",[417,3023,3025],{"id":3024},"inverse","Inverse",[11,3027,3028,3029,2336,3032,3035],{},"The inverse of ",[425,3030,3031],{},"MS(φ0, φ1, θ)",[425,3033,3034],{},"MS(φ0 + 0.5, φ1, θ)",": the same gate with one axis turned half a turn round, since the angle cannot go negative.",[417,3037,3039],{"id":3038},"usage","Usage",[3041,3042,3047],"pre",{"className":3043,"code":3044,"language":3045,"meta":3046,"style":3046},"language-python shiki shiki-themes one-dark-pro","from qiskit import QuantumCircuit\nfrom qiskit_ionq import MSGate\n\nqc = QuantumCircuit(2, 2)\nqc.append(MSGate(0, 0), [0, 1])\nqc.measure([0, 1], [0, 1])\n","python","",[425,3048,3049,3067,3080,3087,3112,3145],{"__ignoreMap":3046},[15,3050,3053,3057,3061,3064],{"class":3051,"line":3052},"line",1,[15,3054,3056],{"class":3055},"seHd6","from",[15,3058,3060],{"class":3059},"sn6KH"," qiskit ",[15,3062,3063],{"class":3055},"import",[15,3065,3066],{"class":3059}," QuantumCircuit\n",[15,3068,3070,3072,3075,3077],{"class":3051,"line":3069},2,[15,3071,3056],{"class":3055},[15,3073,3074],{"class":3059}," qiskit_ionq ",[15,3076,3063],{"class":3055},[15,3078,3079],{"class":3059}," MSGate\n",[15,3081,3083],{"class":3051,"line":3082},3,[15,3084,3086],{"emptyLinePlaceholder":3085},true,"\n",[15,3088,3090,3093,3096,3100,3102,3105,3107,3109],{"class":3051,"line":3089},4,[15,3091,3092],{"class":3059},"qc ",[15,3094,322],{"class":3095},"sjrmR",[15,3097,3099],{"class":3098},"sVbv2"," QuantumCircuit",[15,3101,648],{"class":3059},[15,3103,276],{"class":3104},"sVC51",[15,3106,704],{"class":3059},[15,3108,276],{"class":3104},[15,3110,3111],{"class":3059},")\n",[15,3113,3115,3118,3121,3123,3125,3127,3129,3131,3133,3136,3138,3140,3142],{"class":3051,"line":3114},5,[15,3116,3117],{"class":3059},"qc.",[15,3119,3120],{"class":3098},"append",[15,3122,648],{"class":3059},[15,3124,499],{"class":3098},[15,3126,648],{"class":3059},[15,3128,43],{"class":3104},[15,3130,704],{"class":3059},[15,3132,43],{"class":3104},[15,3134,3135],{"class":3059},"), [",[15,3137,43],{"class":3104},[15,3139,704],{"class":3059},[15,3141,140],{"class":3104},[15,3143,3144],{"class":3059},"])\n",[15,3146,3148,3150,3153,3156,3158,3160,3162,3165,3167,3169,3171],{"class":3051,"line":3147},6,[15,3149,3117],{"class":3059},[15,3151,3152],{"class":3098},"measure",[15,3154,3155],{"class":3059},"([",[15,3157,43],{"class":3104},[15,3159,704],{"class":3059},[15,3161,140],{"class":3104},[15,3163,3164],{"class":3059},"], [",[15,3166,43],{"class":3104},[15,3168,704],{"class":3059},[15,3170,140],{"class":3104},[15,3172,3144],{"class":3059},[3041,3174,3178],{"className":3175,"code":3176,"language":3177,"meta":3046,"style":3046},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\nimport { MSGate } from 'qiskit_ionq';\n\nconst circuit = QuantumCircuit(2, 2);\ncircuit.append(MSGate(0, 0), [0, 1]);\ncircuit.measure([0, 1], [0, 1]);\n","js",[425,3179,3180,3203,3220,3224,3249,3281],{"__ignoreMap":3046},[15,3181,3182,3184,3187,3191,3194,3196,3200],{"class":3051,"line":3052},[15,3183,3063],{"class":3055},[15,3185,3186],{"class":3059}," { ",[15,3188,3190],{"class":3189},"sVyAn","QuantumCircuit",[15,3192,3193],{"class":3059}," } ",[15,3195,3056],{"class":3055},[15,3197,3199],{"class":3198},"subq3"," 'qiskit'",[15,3201,3202],{"class":3059},";\n",[15,3204,3205,3207,3209,3211,3213,3215,3218],{"class":3051,"line":3069},[15,3206,3063],{"class":3055},[15,3208,3186],{"class":3059},[15,3210,499],{"class":3189},[15,3212,3193],{"class":3059},[15,3214,3056],{"class":3055},[15,3216,3217],{"class":3198}," 'qiskit_ionq'",[15,3219,3202],{"class":3059},[15,3221,3222],{"class":3051,"line":3082},[15,3223,3086],{"emptyLinePlaceholder":3085},[15,3225,3226,3229,3233,3236,3238,3240,3242,3244,3246],{"class":3051,"line":3089},[15,3227,3228],{"class":3055},"const",[15,3230,3232],{"class":3231},"sU0A5"," circuit",[15,3234,3235],{"class":3095}," =",[15,3237,3099],{"class":3098},[15,3239,648],{"class":3059},[15,3241,276],{"class":3104},[15,3243,704],{"class":3059},[15,3245,276],{"class":3104},[15,3247,3248],{"class":3059},");\n",[15,3250,3251,3254,3256,3258,3260,3262,3264,3266,3268,3270,3272,3274,3276,3278],{"class":3051,"line":3114},[15,3252,3253],{"class":3231},"circuit",[15,3255,446],{"class":3059},[15,3257,3120],{"class":3098},[15,3259,648],{"class":3059},[15,3261,499],{"class":3098},[15,3263,648],{"class":3059},[15,3265,43],{"class":3104},[15,3267,704],{"class":3059},[15,3269,43],{"class":3104},[15,3271,3135],{"class":3059},[15,3273,43],{"class":3104},[15,3275,704],{"class":3059},[15,3277,140],{"class":3104},[15,3279,3280],{"class":3059},"]);\n",[15,3282,3283,3285,3287,3289,3291,3293,3295,3297,3299,3301,3303,3305],{"class":3051,"line":3147},[15,3284,3253],{"class":3231},[15,3286,446],{"class":3059},[15,3288,3152],{"class":3098},[15,3290,3155],{"class":3059},[15,3292,43],{"class":3104},[15,3294,704],{"class":3059},[15,3296,140],{"class":3104},[15,3298,3164],{"class":3059},[15,3300,43],{"class":3104},[15,3302,704],{"class":3059},[15,3304,140],{"class":3104},[15,3306,3280],{"class":3059},[11,3308,3309,3310,3312,3313,3315],{},"On a noiseless simulator every shot reads ",[425,3311,531],{}," or ",[425,3314,559],{},", in close to equal numbers.",[417,3317,3319],{"id":3318},"related","Related",[3321,3322,3323,3328,3332,3338],"ul",{},[3324,3325,3326],"li",{},[257,3327,440],{"href":439},[3324,3329,3330],{},[257,3331,260],{"href":259},[3324,3333,3334],{},[257,3335,3337],{"href":3336},"\u002Flearn\u002Fdocs\u002Fryy-gate","RYY gate",[3324,3339,3340],{},[257,3341,3343],{"href":3342},"\u002Flearn\u002Fdocs\u002Fgates","Gate reference",[3345,3346,3347],"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: 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