[{"data":1,"prerenderedAt":2103},["ShallowReactive",2],{"blog-post-docs\u002Fgpi2-gate":3,"sibling-dives-docs\u002Fgpi2-gate":1940,"learn-track-docs\u002Fgpi2-gate":1941,"learn-docs-groups":1942},{"id":4,"title":5,"authors":6,"body":7,"breadcrumb":6,"builders":6,"byline":6,"category":1921,"categoryName":1922,"challenge":6,"courseAuthor":6,"courseLead":6,"dek":6,"description":1923,"draft":1924,"extension":1925,"eyebrow":6,"featured":1924,"finish":6,"fork":6,"group":1926,"groupName":1927,"hero":6,"heroAlt":6,"heroCta":6,"heroImage":6,"homepageFeatured":1924,"kind":1928,"lessonCount":6,"meta":1929,"navigation":1633,"newsItems":6,"next":6,"ogImage":6,"order":1930,"outcomes":6,"path":1931,"publishDate":1932,"readingTime":6,"related":1933,"relatedProjects":6,"seo":1934,"stem":1937,"tags":1938,"track":6,"trackName":6,"__hash__":1939},"blog\u002Fblog\u002Flearn\u002Fdocs\u002Fgpi2-gate.md","GPi2 gate",null,{"type":8,"value":9,"toc":1912},"minimark",[10,118,173,178,198,202,255,259,818,830,834,1495,1570,1574,1584,1588,1725,1865,1878,1882,1908],[11,12,13,14,61,62,90,91,95,96,99,100,103,104,107,108,103,113,117],"p",{},"The GPi2 gate is an IonQ native gate: a quarter-turn (π\u002F2) rotation about an axis in the XY plane of the Bloch sphere, with the axis set by a phase ",[15,16,19,42],"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",[28,29,30,37],"semantics",{},[31,32,33],"mrow",{},[34,35,36],"mi",{},"ϕ",[38,39,41],"annotation",{"encoding":40},"application\u002Fx-tex","\\phi",[15,43,47],{"className":44,"ariaHidden":46},[45],"katex-html","true",[15,48,51,56],{"className":49},[50],"base",[15,52],{"className":53,"style":55},[54],"strut","height:0.8889em;vertical-align:-0.1944em;",[15,57,36],{"className":58},[59,60],"mord","mathnormal",". It acts on one qubit and takes one parameter, ",[15,63,65,78],{"className":64},[18],[15,66,68],{"className":67},[22],[24,69,70],{"xmlns":26},[28,71,72,76],{},[31,73,74],{},[34,75,36],{},[38,77,41],{"encoding":40},[15,79,81],{"className":80,"ariaHidden":46},[45],[15,82,84,87],{"className":83},[50],[15,85],{"className":86,"style":55},[54],[15,88,36],{"className":89},[59,60]," in turns: ",[92,93,94],"code",{},"GPi2(0.25)"," is exactly ",[92,97,98],{},"ry(π\u002F2)",", and ",[92,101,102],{},"GPi2(0)"," and ",[92,105,106],{},"GPi2(0.5)"," are the ",[109,110,112],"a",{"href":111},"\u002Flearn\u002Fdocs\u002Fsx-gate","√X",[109,114,116],{"href":115},"\u002Flearn\u002Fdocs\u002Fsxdg-gate","√X†"," gates up to a global phase. It runs on Aria and Forte, and it is the pulse most standard single-qubit gates compile into. Measured straight after it, a qubit that started as 0 reads 0 or 1 with equal probability, whatever the phase.",[11,119,120,121,167,168,172],{},"Kets such as ",[15,122,124,149],{"className":123},[18],[15,125,127],{"className":126},[22],[24,128,129],{"xmlns":26},[28,130,131,146],{},[31,132,133,137,141],{},[34,134,136],{"mathvariant":135},"normal","∣",[138,139,140],"mn",{},"0",[142,143,145],"mo",{"stretchy":144},"false","⟩",[38,147,148],{"encoding":40},"\\vert 0 \\rangle",[15,150,152],{"className":151,"ariaHidden":46},[45],[15,153,155,159,163],{"className":154},[50],[15,156],{"className":157,"style":158},[54],"height:1em;vertical-align:-0.25em;",[15,160,162],{"className":161},[59],"∣0",[15,164,145],{"className":165},[166],"mclose"," name the basis states and rotations are described on the Bloch sphere; the ",[109,169,171],{"href":170},"\u002Flearn\u002Fquantum-foundations\u002Fqubits","qubits lesson"," introduces both.",[174,175,177],"h2",{"id":176},"before-you-use-a-native-gate","Before you use a native gate",[11,179,180,181,184,185,188,189,192,193,197],{},"Native gates only run in a native-gate circuit, and a circuit cannot mix native and standard gates. In ",[92,182,183],{},"qiskit-ionq"," a backend is created for one gateset, ",[92,186,187],{},"provider.get_backend(name, gateset=\"native\")","; the pre-created ",[92,190,191],{},"backend"," on Qollab uses the standard gateset. Submitting native gates bypasses IonQ's compiler and optimiser and turns error mitigation off by default, which is why IonQ recommends them only for research work. See ",[109,194,196],{"href":195},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",".",[174,199,201],{"id":200},"call","Call",[203,204,205,217],"table",{},[206,207,208],"thead",{},[209,210,211,215],"tr",{},[212,213,214],"th",{},"Where",[212,216,201],{},[218,219,220,231,241],"tbody",{},[209,221,222,226],{},[223,224,225],"td",{},"Python",[223,227,228],{},[92,229,230],{},"qc.append(GPI2Gate(φ), [qubit])",[209,232,233,236],{},[223,234,235],{},"JS",[223,237,238],{},[92,239,240],{},"circuit.append(GPI2Gate(φ), [qubit])",[209,242,243,246],{},[223,244,245],{},"Class",[223,247,248,251,252],{},[92,249,250],{},"GPI2Gate",", from 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\\rangle",[15,1192,1194],{"className":1193,"ariaHidden":46},[45],[15,1195,1197,1200,1203],{"className":1196},[50],[15,1198],{"className":1199,"style":158},[54],[15,1201,1156],{"className":1202},[59],[15,1204,145],{"className":1205},[166],[223,1207,1208],{},[15,1209,1211,1272],{"className":1210},[18],[15,1212,1214],{"className":1213},[22],[24,1215,1216],{"xmlns":26},[28,1217,1218,1269],{},[31,1219,1220,1230,1232,1234,1236,1252,1254,1256,1258,1261,1263,1265,1267],{},[327,1221,1222],{"scriptlevel":140,"displaystyle":144},[300,1223,1224,1226],{},[138,1225,304],{},[306,1227,1228],{},[138,1229,287],{},[142,1231,290],{"fence":144,"stretchy":46,"minsize":913,"maxsize":913},[142,1233,339],{},[34,1235,284],{},[343,1237,1238,1240],{},[34,1239,347],{},[31,1241,1242,1244,1246,1248,1250],{},[142,1243,339],{},[138,1245,287],{},[34,1247,356],{},[34,1249,284],{},[34,1251,36],{},[34,1253,136],{"mathvariant":135},[138,1255,140],{},[142,1257,145],{"stretchy":144},[142,1259,1260],{},"+",[34,1262,136],{"mathvariant":135},[138,1264,304],{},[142,1266,145],{"stretchy":144},[142,1268,295],{"fence":144,"stretchy":46,"minsize":913,"maxsize":913},[38,1270,1271],{"encoding":40},"\\tfrac{1}{\\sqrt{2}}\\big(-ie^{-2\\pi i\\phi}\\vert 0 \\rangle + \\vert 1 \\rangle\\big)",[15,1273,1275,1408,1477],{"className":1274,"ariaHidden":46},[45],[15,1276,1278,1281,1393,1399,1402,1405],{"className":1277},[50],[15,1279],{"className":1280,"style":958},[54],[15,1282,1284,1287,1390],{"className":1283},[59],[15,1285],{"className":1286},[421,453],[15,1288,1290],{"className":1289},[300],[15,1291,1293,1382],{"className":1292},[460,461],[15,1294,1296,1379],{"className":1295},[465],[15,1297,1299,1357,1365],{"className":1298,"style":977},[469],[15,1300,1301,1304],{"style":980},[15,1302],{"className":1303,"style":478},[477],[15,1305,1307],{"className":1306},[681,682,603,683],[15,1308,1310],{"className":1309},[59,683],[15,1311,1313],{"className":1312},[59,485,683],[15,1314,1316,1349],{"className":1315},[460,461],[15,1317,1319,1346],{"className":1318},[465],[15,1320,1322,1334],{"className":1321,"style":1002},[469],[15,1323,1325,1328],{"className":1324,"style":500},[499],[15,1326],{"className":1327,"style":478},[477],[15,1329,1331],{"className":1330,"style":507},[59,683],[15,1332,287],{"className":1333},[59,683],[15,1335,1336,1339],{"style":1017},[15,1337],{"className":1338,"style":478},[477],[15,1340,1342],{"className":1341,"style":521},[520,683],[523,1343,1344],{"xmlns":525,"width":526,"height":527,"viewBox":528,"preserveAspectRatio":529},[531,1345],{"d":533},[15,1347,538],{"className":1348},[537],[15,1350,1352],{"className":1351},[465],[15,1353,1355],{"className":1354,"style":1037},[469],[15,1356],{},[15,1358,1359,1362],{"style":550},[15,1360],{"className":1361,"style":478},[477],[15,1363],{"className":1364,"style":558},[557],[15,1366,1367,1370],{"style":1050},[15,1368],{"className":1369,"style":478},[477],[15,1371,1373],{"className":1372},[681,682,603,683],[15,1374,1376],{"className":1375},[59,683],[15,1377,304],{"className":1378},[59,683],[15,1380,538],{"className":1381},[537],[15,1383,1385],{"className":1384},[465],[15,1386,1388],{"className":1387,"style":1072},[469],[15,1389],{},[15,1391],{"className":1392},[166,453],[15,1394,1396],{"className":1395},[59],[15,1397,290],{"className":1398},[602,1084],[15,1400],{"className":1401,"style":1094},[431],[15,1403,339],{"className":1404},[1098],[15,1406],{"className":1407,"style":1094},[431],[15,1409,1411,1415,1418,1462,1465,1468,1471,1474],{"className":1410},[50],[15,1412],{"className":1413,"style":1414},[54],"height:1.0991em;vertical-align:-0.25em;",[15,1416,284],{"className":1417},[59,60],[15,1419,1421,1424],{"className":1420},[59],[15,1422,347],{"className":1423},[59,60],[15,1425,1427],{"className":1426},[660],[15,1428,1430],{"className":1429},[460],[15,1431,1433],{"className":1432},[465],[15,1434,1436],{"className":1435,"style":670},[469],[15,1437,1438,1441],{"style":673},[15,1439],{"className":1440,"style":677},[477],[15,1442,1444],{"className":1443},[681,682,603,683],[15,1445,1447,1450,1453,1456,1459],{"className":1446},[59,683],[15,1448,339],{"className":1449},[59,683],[15,1451,287],{"className":1452},[59,683],[15,1454,356],{"className":1455,"style":693},[59,60,683],[15,1457,284],{"className":1458},[59,60,683],[15,1460,36],{"className":1461},[59,60,683],[15,1463,162],{"className":1464},[59],[15,1466,145],{"className":1467},[166],[15,1469],{"className":1470,"style":1094},[431],[15,1472,1260],{"className":1473},[1098],[15,1475],{"className":1476,"style":1094},[431],[15,1478,1480,1483,1486,1489],{"className":1479},[50],[15,1481],{"className":1482,"style":1108},[54],[15,1484,1156],{"className":1485},[59],[15,1487,145],{"className":1488},[166],[15,1490,1492],{"className":1491},[59],[15,1493,295],{"className":1494},[602,1084],[11,1496,1497,1498,1533,1534,1569],{},"Measured straight after GPi2, a qubit that started in ",[15,1499,1501,1518],{"className":1500},[18],[15,1502,1504],{"className":1503},[22],[24,1505,1506],{"xmlns":26},[28,1507,1508,1516],{},[31,1509,1510,1512,1514],{},[34,1511,136],{"mathvariant":135},[138,1513,140],{},[142,1515,145],{"stretchy":144},[38,1517,148],{"encoding":40},[15,1519,1521],{"className":1520,"ariaHidden":46},[45],[15,1522,1524,1527,1530],{"className":1523},[50],[15,1525],{"className":1526,"style":158},[54],[15,1528,162],{"className":1529},[59],[15,1531,145],{"className":1532},[166]," or ",[15,1535,1537,1554],{"className":1536},[18],[15,1538,1540],{"className":1539},[22],[24,1541,1542],{"xmlns":26},[28,1543,1544,1552],{},[31,1545,1546,1548,1550],{},[34,1547,136],{"mathvariant":135},[138,1549,304],{},[142,1551,145],{"stretchy":144},[38,1553,1190],{"encoding":40},[15,1555,1557],{"className":1556,"ariaHidden":46},[45],[15,1558,1560,1563,1566],{"className":1559},[50],[15,1561],{"className":1562,"style":158},[54],[15,1564,1156],{"className":1565},[59],[15,1567,145],{"className":1568},[166]," reads 0 or 1 with equal probability, whatever the phase.",[174,1571,1573],{"id":1572},"inverse","Inverse",[11,1575,1576,1577,1579,1580,1583],{},"The inverse of ",[92,1578,823],{}," is ",[92,1581,1582],{},"GPi2(φ + 0.5)",": the same pulse with its axis turned half a turn round.",[174,1585,1587],{"id":1586},"usage","Usage",[1589,1590,1595],"pre",{"className":1591,"code":1592,"language":1593,"meta":1594,"style":1594},"language-python shiki shiki-themes one-dark-pro","from qiskit import QuantumCircuit\nfrom qiskit_ionq import GPI2Gate\n\nqc = QuantumCircuit(1, 1)\nqc.append(GPI2Gate(0), [0])\nqc.append(GPI2Gate(0), [0])\nqc.measure(0, 0)\n","python","",[92,1596,1597,1615,1628,1635,1661,1686,1707],{"__ignoreMap":1594},[15,1598,1601,1605,1609,1612],{"class":1599,"line":1600},"line",1,[15,1602,1604],{"class":1603},"seHd6","from",[15,1606,1608],{"class":1607},"sn6KH"," qiskit ",[15,1610,1611],{"class":1603},"import",[15,1613,1614],{"class":1607}," QuantumCircuit\n",[15,1616,1618,1620,1623,1625],{"class":1599,"line":1617},2,[15,1619,1604],{"class":1603},[15,1621,1622],{"class":1607}," qiskit_ionq ",[15,1624,1611],{"class":1603},[15,1626,1627],{"class":1607}," GPI2Gate\n",[15,1629,1631],{"class":1599,"line":1630},3,[15,1632,1634],{"emptyLinePlaceholder":1633},true,"\n",[15,1636,1638,1641,1644,1648,1650,1653,1656,1658],{"class":1599,"line":1637},4,[15,1639,1640],{"class":1607},"qc ",[15,1642,298],{"class":1643},"sjrmR",[15,1645,1647],{"class":1646},"sVbv2"," QuantumCircuit",[15,1649,290],{"class":1607},[15,1651,304],{"class":1652},"sVC51",[15,1654,1655],{"class":1607},", ",[15,1657,304],{"class":1652},[15,1659,1660],{"class":1607},")\n",[15,1662,1664,1667,1670,1672,1674,1676,1678,1681,1683],{"class":1599,"line":1663},5,[15,1665,1666],{"class":1607},"qc.",[15,1668,1669],{"class":1646},"append",[15,1671,290],{"class":1607},[15,1673,250],{"class":1646},[15,1675,290],{"class":1607},[15,1677,140],{"class":1652},[15,1679,1680],{"class":1607},"), [",[15,1682,140],{"class":1652},[15,1684,1685],{"class":1607},"])\n",[15,1687,1689,1691,1693,1695,1697,1699,1701,1703,1705],{"class":1599,"line":1688},6,[15,1690,1666],{"class":1607},[15,1692,1669],{"class":1646},[15,1694,290],{"class":1607},[15,1696,250],{"class":1646},[15,1698,290],{"class":1607},[15,1700,140],{"class":1652},[15,1702,1680],{"class":1607},[15,1704,140],{"class":1652},[15,1706,1685],{"class":1607},[15,1708,1710,1712,1715,1717,1719,1721,1723],{"class":1599,"line":1709},7,[15,1711,1666],{"class":1607},[15,1713,1714],{"class":1646},"measure",[15,1716,290],{"class":1607},[15,1718,140],{"class":1652},[15,1720,1655],{"class":1607},[15,1722,140],{"class":1652},[15,1724,1660],{"class":1607},[1589,1726,1730],{"className":1727,"code":1728,"language":1729,"meta":1594,"style":1594},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\nimport { GPI2Gate } from 'qiskit_ionq';\n\nconst circuit = QuantumCircuit(1, 1);\ncircuit.append(GPI2Gate(0), [0]);\ncircuit.append(GPI2Gate(0), [0]);\ncircuit.measure(0, 0);\n","js",[92,1731,1732,1755,1772,1776,1801,1825,1847],{"__ignoreMap":1594},[15,1733,1734,1736,1739,1743,1746,1748,1752],{"class":1599,"line":1600},[15,1735,1611],{"class":1603},[15,1737,1738],{"class":1607}," { ",[15,1740,1742],{"class":1741},"sVyAn","QuantumCircuit",[15,1744,1745],{"class":1607}," } ",[15,1747,1604],{"class":1603},[15,1749,1751],{"class":1750},"subq3"," 'qiskit'",[15,1753,1754],{"class":1607},";\n",[15,1756,1757,1759,1761,1763,1765,1767,1770],{"class":1599,"line":1617},[15,1758,1611],{"class":1603},[15,1760,1738],{"class":1607},[15,1762,250],{"class":1741},[15,1764,1745],{"class":1607},[15,1766,1604],{"class":1603},[15,1768,1769],{"class":1750}," 'qiskit_ionq'",[15,1771,1754],{"class":1607},[15,1773,1774],{"class":1599,"line":1630},[15,1775,1634],{"emptyLinePlaceholder":1633},[15,1777,1778,1781,1785,1788,1790,1792,1794,1796,1798],{"class":1599,"line":1637},[15,1779,1780],{"class":1603},"const",[15,1782,1784],{"class":1783},"sU0A5"," circuit",[15,1786,1787],{"class":1643}," =",[15,1789,1647],{"class":1646},[15,1791,290],{"class":1607},[15,1793,304],{"class":1652},[15,1795,1655],{"class":1607},[15,1797,304],{"class":1652},[15,1799,1800],{"class":1607},");\n",[15,1802,1803,1806,1808,1810,1812,1814,1816,1818,1820,1822],{"class":1599,"line":1663},[15,1804,1805],{"class":1783},"circuit",[15,1807,197],{"class":1607},[15,1809,1669],{"class":1646},[15,1811,290],{"class":1607},[15,1813,250],{"class":1646},[15,1815,290],{"class":1607},[15,1817,140],{"class":1652},[15,1819,1680],{"class":1607},[15,1821,140],{"class":1652},[15,1823,1824],{"class":1607},"]);\n",[15,1826,1827,1829,1831,1833,1835,1837,1839,1841,1843,1845],{"class":1599,"line":1688},[15,1828,1805],{"class":1783},[15,1830,197],{"class":1607},[15,1832,1669],{"class":1646},[15,1834,290],{"class":1607},[15,1836,250],{"class":1646},[15,1838,290],{"class":1607},[15,1840,140],{"class":1652},[15,1842,1680],{"class":1607},[15,1844,140],{"class":1652},[15,1846,1824],{"class":1607},[15,1848,1849,1851,1853,1855,1857,1859,1861,1863],{"class":1599,"line":1709},[15,1850,1805],{"class":1783},[15,1852,197],{"class":1607},[15,1854,1714],{"class":1646},[15,1856,290],{"class":1607},[15,1858,140],{"class":1652},[15,1860,1655],{"class":1607},[15,1862,140],{"class":1652},[15,1864,1800],{"class":1607},[11,1866,1867,1868,1870,1871,1873,1874,1877],{},"Every shot reads ",[92,1869,304],{},": two ",[92,1872,102],{}," make a ",[92,1875,1876],{},"GPi(0)"," up to a global phase, which is an X.",[174,1879,1881],{"id":1880},"related","Related",[1883,1884,1885,1891,1896,1902],"ul",{},[1886,1887,1888],"li",{},[109,1889,1890],{"href":827},"GPi gate",[1886,1892,1893],{},[109,1894,1895],{"href":111},"√X gate",[1886,1897,1898],{},[109,1899,1901],{"href":1900},"\u002Flearn\u002Fdocs\u002Frx-gate","RX gate",[1886,1903,1904],{},[109,1905,1907],{"href":1906},"\u002Flearn\u002Fdocs\u002Fgates","Gate reference",[1909,1910,1911],"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: 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