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\\rangle",[21,1049,1051],{"className":1050,"ariaHidden":62},[61],[21,1052,1054,1057,1060],{"className":1053},[66],[21,1055],{"className":1056,"style":71},[70],[21,1058,357],{"className":1059},[75],[21,1061,52],{"className":1062},[80],[196,1064,1065],{},[21,1066,1068,1085],{"className":1067},[24],[21,1069,1071],{"className":1070},[28],[30,1072,1073],{"xmlns":32},[34,1074,1075,1083],{},[37,1076,1077,1079,1081],{},[40,1078,43],{"mathvariant":42},[45,1080,311],{},[49,1082,52],{"stretchy":51},[54,1084,1047],{"encoding":56},[21,1086,1088],{"className":1087,"ariaHidden":62},[61],[21,1089,1091,1094,1097],{"className":1090},[66],[21,1092],{"className":1093,"style":71},[70],[21,1095,357],{"className":1096},[75],[21,1098,52],{"className":1099},[80],[182,1101,1102,1140],{},[196,1103,1104],{},[21,1105,1107,1125],{"className":1106},[24],[21,1108,1110],{"className":1109},[28],[30,1111,1112],{"xmlns":32},[34,1113,1114,1122],{},[37,1115,1116,1118,1120],{},[40,1117,43],{"mathvariant":42},[45,1119,321],{},[49,1121,52],{"stretchy":51},[54,1123,1124],{"encoding":56},"\\vert 01 \\rangle",[21,1126,1128],{"className":1127,"ariaHidden":62},[61],[21,1129,1131,1134,1137],{"className":1130},[66],[21,1132],{"className":1133,"style":71},[70],[21,1135,372],{"className":1136},[75],[21,1138,52],{"className":1139},[80],[196,1141,1142],{},[21,1143,1145,1162],{"className":1144},[24],[21,1146,1148],{"className":1147},[28],[30,1149,1150],{"xmlns":32},[34,1151,1152,1160],{},[37,1153,1154,1156,1158],{},[40,1155,43],{"mathvariant":42},[45,1157,321],{},[49,1159,52],{"stretchy":51},[54,1161,1124],{"encoding":56},[21,1163,1165],{"className":1164,"ariaHidden":62},[61],[21,1166,1168,1171,1174],{"className":1167},[66],[21,1169],{"className":1170,"style":71},[70],[21,1172,372],{"className":1173},[75],[21,1175,52],{"className":1176},[80],[182,1178,1179,1217],{},[196,1180,1181],{},[21,1182,1184,1202],{"className":1183},[24],[21,1185,1187],{"className":1186},[28],[30,1188,1189],{"xmlns":32},[34,1190,1191,1199],{},[37,1192,1193,1195,1197],{},[40,1194,43],{"mathvariant":42},[45,1196,330],{},[49,1198,52],{"stretchy":51},[54,1200,1201],{"encoding":56},"\\vert 10 \\rangle",[21,1203,1205],{"className":1204,"ariaHidden":62},[61],[21,1206,1208,1211,1214],{"className":1207},[66],[21,1209],{"className":1210,"style":71},[70],[21,1212,385],{"className":1213},[75],[21,1215,52],{"className":1216},[80],[196,1218,1219],{},[21,1220,1222,1242],{"className":1221},[24],[21,1223,1225],{"className":1224},[28],[30,1226,1227],{"xmlns":32},[34,1228,1229,1239],{},[37,1230,1231,1233,1235,1237],{},[40,1232,525],{},[40,1234,43],{"mathvariant":42},[45,1236,339],{},[49,1238,52],{"stretchy":51},[54,1240,1241],{"encoding":56},"i\\vert 11 \\rangle",[21,1243,1245],{"className":1244,"ariaHidden":62},[61],[21,1246,1248,1251,1254,1257],{"className":1247},[66],[21,1249],{"className":1250,"style":71},[70],[21,1252,525],{"className":1253},[75,571],[21,1255,398],{"className":1256},[75],[21,1258,52],{"className":1259},[80],[182,1261,1262,1300],{},[196,1263,1264],{},[21,1265,1267,1285],{"className":1266},[24],[21,1268,1270],{"className":1269},[28],[30,1271,1272],{"xmlns":32},[34,1273,1274,1282],{},[37,1275,1276,1278,1280],{},[40,1277,43],{"mathvariant":42},[45,1279,339],{},[49,1281,52],{"stretchy":51},[54,1283,1284],{"encoding":56},"\\vert 11 \\rangle",[21,1286,1288],{"className":1287,"ariaHidden":62},[61],[21,1289,1291,1294,1297],{"className":1290},[66],[21,1292],{"className":1293,"style":71},[70],[21,1295,398],{"className":1296},[75],[21,1298,52],{"className":1299},[80],[196,1301,1302],{},[21,1303,1305,1327],{"className":1304},[24],[21,1306,1308],{"className":1307},[28],[30,1309,1310],{"xmlns":32},[34,1311,1312,1324],{},[37,1313,1314,1316,1318,1320,1322],{},[49,1315,522],{},[40,1317,525],{},[40,1319,43],{"mathvariant":42},[45,1321,330],{},[49,1323,52],{"stretchy":51},[54,1325,1326],{"encoding":56},"-i\\vert 10 \\rangle",[21,1328,1330],{"className":1329,"ariaHidden":62},[61],[21,1331,1333,1336,1339,1342,1345],{"className":1332},[66],[21,1334],{"className":1335,"style":71},[70],[21,1337,522],{"className":1338},[75],[21,1340,525],{"className":1341},[75,571],[21,1343,385],{"className":1344},[75],[21,1346,52],{"className":1347},[80],[11,1349,1350,1351,1355,1356,1396,1397,1432,1433,402],{},"Measured straight away, CY flips the target exactly as ",[15,1352,1354],{"href":1353},"\u002Flearn\u002Fdocs\u002Fcx-gate","CX"," does; the phases only matter once the qubits meet other gates. With the control in ",[21,1357,1359,1378],{"className":1358},[24],[21,1360,1362],{"className":1361},[28],[30,1363,1364],{"xmlns":32},[34,1365,1366,1375],{},[37,1367,1368,1370,1373],{},[40,1369,43],{"mathvariant":42},[49,1371,1372],{},"+",[49,1374,52],{"stretchy":51},[54,1376,1377],{"encoding":56},"\\vert + \\rangle",[21,1379,1381],{"className":1380,"ariaHidden":62},[61],[21,1382,1384,1387,1390,1393],{"className":1383},[66],[21,1385],{"className":1386,"style":71},[70],[21,1388,43],{"className":1389},[75],[21,1391,1372],{"className":1392},[75],[21,1394,52],{"className":1395},[80]," and the target in ",[21,1398,1400,1417],{"className":1399},[24],[21,1401,1403],{"className":1402},[28],[30,1404,1405],{"xmlns":32},[34,1406,1407,1415],{},[37,1408,1409,1411,1413],{},[40,1410,43],{"mathvariant":42},[45,1412,98],{},[49,1414,52],{"stretchy":51},[54,1416,103],{"encoding":56},[21,1418,1420],{"className":1419,"ariaHidden":62},[61],[21,1421,1423,1426,1429],{"className":1422},[66],[21,1424],{"className":1425,"style":71},[70],[21,1427,116],{"className":1428},[75],[21,1430,52],{"className":1431},[80],", CY produces the entangled state ",[21,1434,1436,1481],{"className":1435},[24],[21,1437,1439],{"className":1438},[28],[30,1440,1441],{"xmlns":32},[34,1442,1443,1478],{},[37,1444,1445,1458,1460,1462,1464,1466,1468,1470,1472,1474,1476],{},[446,1446,1447],{"scriptlevel":98,"displaystyle":51},[1448,1449,1450,1452],"mfrac",{},[45,1451,47],{},[1453,1454,1455],"msqrt",{},[45,1456,1457],{},"2",[49,1459,432],{"stretchy":51},[40,1461,43],{"mathvariant":42},[45,1463,311],{},[49,1465,52],{"stretchy":51},[49,1467,1372],{},[40,1469,525],{},[40,1471,43],{"mathvariant":42},[45,1473,339],{},[49,1475,52],{"stretchy":51},[49,1477,554],{"stretchy":51},[54,1479,1480],{"encoding":56},"\\tfrac{1}{\\sqrt{2}}(\\vert 00 \\rangle + i\\vert 11 \\rangle)",[21,1482,1484,1648],{"className":1483,"ariaHidden":62},[61],[21,1485,1487,1491,1629,1632,1635,1638,1641,1645],{"className":1486},[66],[21,1488],{"className":1489,"style":1490},[70],"height:1.3831em;vertical-align:-0.538em;",[21,1492,1494,1498,1626],{"className":1493},[75],[21,1495],{"className":1496},[601,1497],"nulldelimiter",[21,1499,1501],{"className":1500},[1448],[21,1502,1504,1617],{"className":1503},[610,611],[21,1505,1507,1614],{"className":1506},[615],[21,1508,1511,1588,1599],{"className":1509,"style":1510},[619],"height:0.8451em;",[21,1512,1514,1517],{"style":1513},"top:-2.551em;",[21,1515],{"className":1516,"style":682},[627],[21,1518,1524],{"className":1519},[1520,1521,1522,1523],"sizing","reset-size6","size3","mtight",[21,1525,1527],{"className":1526},[75,1523],[21,1528,1531],{"className":1529},[75,1530,1523],"sqrt",[21,1532,1534,1579],{"className":1533},[610,611],[21,1535,1537,1576],{"className":1536},[615],[21,1538,1541,1556],{"className":1539,"style":1540},[619],"height:0.9128em;",[21,1542,1546,1549],{"className":1543,"style":1545},[1544],"svg-align","top:-3em;",[21,1547],{"className":1548,"style":682},[627],[21,1550,1553],{"className":1551,"style":1552},[75,1523],"padding-left:0.833em;",[21,1554,1457],{"className":1555},[75,1523],[21,1557,1559,1562],{"style":1558},"top:-2.8728em;",[21,1560],{"className":1561,"style":682},[627],[21,1563,1567],{"className":1564,"style":1566},[1565,1523],"hide-tail","min-width:0.853em;height:1.08em;",[633,1568,1573],{"xmlns":635,"width":1569,"height":1570,"viewBox":1571,"preserveAspectRatio":1572},"400em","1.08em","0 0 400000 1080","xMinYMin slice",[640,1574],{"d":1575},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[21,1577,647],{"className":1578},[646],[21,1580,1582],{"className":1581},[615],[21,1583,1586],{"className":1584,"style":1585},[619],"height:0.1272em;",[21,1587],{},[21,1589,1591,1594],{"style":1590},"top:-3.23em;",[21,1592],{"className":1593,"style":682},[627],[21,1595],{"className":1596,"style":1598},[1597],"frac-line","border-bottom-width:0.04em;",[21,1600,1602,1605],{"style":1601},"top:-3.394em;",[21,1603],{"className":1604,"style":682},[627],[21,1606,1608],{"className":1607},[1520,1521,1522,1523],[21,1609,1611],{"className":1610},[75,1523],[21,1612,47],{"className":1613},[75,1523],[21,1615,647],{"className":1616},[646],[21,1618,1620],{"className":1619},[615],[21,1621,1624],{"className":1622,"style":1623},[619],"height:0.538em;",[21,1625],{},[21,1627],{"className":1628},[80,1497],[21,1630,432],{"className":1631},[601],[21,1633,357],{"className":1634},[75],[21,1636,52],{"className":1637},[80],[21,1639],{"className":1640,"style":576},[283],[21,1642,1372],{"className":1643},[1644],"mbin",[21,1646],{"className":1647,"style":576},[283],[21,1649,1651,1654,1657,1660],{"className":1650},[66],[21,1652],{"className":1653,"style":71},[70],[21,1655,525],{"className":1656},[75,571],[21,1658,398],{"className":1659},[75],[21,1661,1663],{"className":1662},[80],"⟩)",[171,1665,1667],{"id":1666},"inverse","Inverse",[11,1669,1670],{},"CY is its own inverse. Two CY gates in a row on the same control and target cancel.",[171,1672,1674],{"id":1673},"usage","Usage",[1676,1677,1682],"pre",{"className":1678,"code":1679,"language":1680,"meta":1681,"style":1681},"language-python shiki shiki-themes one-dark-pro","from qiskit import QuantumCircuit\n\nqc = QuantumCircuit(2, 2)\nqc.h(0)\nqc.cy(0, 1)\nqc.measure([0, 1], [0, 1])\n","python","",[202,1683,1684,1702,1709,1735,1750,1768],{"__ignoreMap":1681},[21,1685,1688,1692,1696,1699],{"class":1686,"line":1687},"line",1,[21,1689,1691],{"class":1690},"seHd6","from",[21,1693,1695],{"class":1694},"sn6KH"," qiskit ",[21,1697,1698],{"class":1690},"import",[21,1700,1701],{"class":1694}," QuantumCircuit\n",[21,1703,1705],{"class":1686,"line":1704},2,[21,1706,1708],{"emptyLinePlaceholder":1707},true,"\n",[21,1710,1712,1715,1718,1722,1724,1727,1730,1732],{"class":1686,"line":1711},3,[21,1713,1714],{"class":1694},"qc ",[21,1716,427],{"class":1717},"sjrmR",[21,1719,1721],{"class":1720},"sVbv2"," QuantumCircuit",[21,1723,432],{"class":1694},[21,1725,1457],{"class":1726},"sVC51",[21,1728,1729],{"class":1694},", ",[21,1731,1457],{"class":1726},[21,1733,1734],{"class":1694},")\n",[21,1736,1738,1741,1744,1746,1748],{"class":1686,"line":1737},4,[21,1739,1740],{"class":1694},"qc.",[21,1742,1743],{"class":1720},"h",[21,1745,432],{"class":1694},[21,1747,98],{"class":1726},[21,1749,1734],{"class":1694},[21,1751,1753,1755,1758,1760,1762,1764,1766],{"class":1686,"line":1752},5,[21,1754,1740],{"class":1694},[21,1756,1757],{"class":1720},"cy",[21,1759,432],{"class":1694},[21,1761,98],{"class":1726},[21,1763,1729],{"class":1694},[21,1765,47],{"class":1726},[21,1767,1734],{"class":1694},[21,1769,1771,1773,1776,1779,1781,1783,1785,1788,1790,1792,1794],{"class":1686,"line":1770},6,[21,1772,1740],{"class":1694},[21,1774,1775],{"class":1720},"measure",[21,1777,1778],{"class":1694},"([",[21,1780,98],{"class":1726},[21,1782,1729],{"class":1694},[21,1784,47],{"class":1726},[21,1786,1787],{"class":1694},"], [",[21,1789,98],{"class":1726},[21,1791,1729],{"class":1694},[21,1793,47],{"class":1726},[21,1795,1796],{"class":1694},"])\n",[1676,1798,1802],{"className":1799,"code":1800,"language":1801,"meta":1681,"style":1681},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\n\nconst circuit = QuantumCircuit(2, 2);\ncircuit.h(0);\ncircuit.cy(0, 1);\ncircuit.measure([0, 1], [0, 1]);\n","js",[202,1803,1804,1827,1831,1856,1871,1889],{"__ignoreMap":1681},[21,1805,1806,1808,1811,1815,1818,1820,1824],{"class":1686,"line":1687},[21,1807,1698],{"class":1690},[21,1809,1810],{"class":1694}," { ",[21,1812,1814],{"class":1813},"sVyAn","QuantumCircuit",[21,1816,1817],{"class":1694}," } ",[21,1819,1691],{"class":1690},[21,1821,1823],{"class":1822},"subq3"," 'qiskit'",[21,1825,1826],{"class":1694},";\n",[21,1828,1829],{"class":1686,"line":1704},[21,1830,1708],{"emptyLinePlaceholder":1707},[21,1832,1833,1836,1840,1843,1845,1847,1849,1851,1853],{"class":1686,"line":1711},[21,1834,1835],{"class":1690},"const",[21,1837,1839],{"class":1838},"sU0A5"," circuit",[21,1841,1842],{"class":1717}," =",[21,1844,1721],{"class":1720},[21,1846,432],{"class":1694},[21,1848,1457],{"class":1726},[21,1850,1729],{"class":1694},[21,1852,1457],{"class":1726},[21,1854,1855],{"class":1694},");\n",[21,1857,1858,1861,1863,1865,1867,1869],{"class":1686,"line":1737},[21,1859,1860],{"class":1838},"circuit",[21,1862,402],{"class":1694},[21,1864,1743],{"class":1720},[21,1866,432],{"class":1694},[21,1868,98],{"class":1726},[21,1870,1855],{"class":1694},[21,1872,1873,1875,1877,1879,1881,1883,1885,1887],{"class":1686,"line":1752},[21,1874,1860],{"class":1838},[21,1876,402],{"class":1694},[21,1878,1757],{"class":1720},[21,1880,432],{"class":1694},[21,1882,98],{"class":1726},[21,1884,1729],{"class":1694},[21,1886,47],{"class":1726},[21,1888,1855],{"class":1694},[21,1890,1891,1893,1895,1897,1899,1901,1903,1905,1907,1909,1911,1913],{"class":1686,"line":1770},[21,1892,1860],{"class":1838},[21,1894,402],{"class":1694},[21,1896,1775],{"class":1720},[21,1898,1778],{"class":1694},[21,1900,98],{"class":1726},[21,1902,1729],{"class":1694},[21,1904,47],{"class":1726},[21,1906,1787],{"class":1694},[21,1908,98],{"class":1726},[21,1910,1729],{"class":1694},[21,1912,47],{"class":1726},[21,1914,1915],{"class":1694},"]);\n",[11,1917,1918,1919,1921,1922,1924],{},"On a noiseless simulator every shot reads ",[202,1920,311],{}," or ",[202,1923,339],{},", in close to equal numbers.",[171,1926,1928],{"id":1927},"on-ionq-hardware","On IonQ hardware",[11,1930,1931,1932,1934,1935,1939,1940,1944,1945,1948,1949,1952,1953,402],{},"CY is not a native gate. It is a ",[15,1933,1354],{"href":1353}," with an ",[15,1936,1938],{"href":1937},"\u002Flearn\u002Fdocs\u002Fsdg-gate","Sdg"," before it and an ",[15,1941,1943],{"href":1942},"\u002Flearn\u002Fdocs\u002Fs-gate","S"," after it on the target, and those two are virtual Z rotations, so CY costs the same as CX: one entangling gate (",[202,1946,1947],{},"MS"," on Aria, ",[202,1950,1951],{},"ZZ"," on Forte) plus single-qubit pulses, before IonQ's optimiser runs. See ",[15,1954,1956],{"href":1955},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",[171,1958,1960],{"id":1959},"related","Related",[1962,1963,1964,1970,1974,1980],"ul",{},[1965,1966,1967],"li",{},[15,1968,1969],{"href":1353},"CX gate",[1965,1971,1972],{},[15,1973,18],{"href":17},[1965,1975,1976],{},[15,1977,1979],{"href":1978},"\u002Flearn\u002Fdocs\u002Fcz-gate","CZ gate",[1965,1981,1982],{},[15,1983,1985],{"href":1984},"\u002Flearn\u002Fdocs\u002Fgates","Gate reference",[1987,1988,1989],"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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