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i)\\vert 1 \\rangle\\big)",[34,1073,1075,1170,1197,1218],{"className":1074,"ariaHidden":75},[74],[34,1076,1078,1081,1149,1155,1158,1161,1164,1167],{"className":1077},[79],[34,1079],{"className":1080,"style":801},[83],[34,1082,1084,1087,1146],{"className":1083},[88],[34,1085],{"className":1086},[418,419],[34,1088,1090],{"className":1089},[191],[34,1091,1093,1138],{"className":1092},[294,295],[34,1094,1096,1135],{"className":1095},[299],[34,1097,1099,1113,1121],{"className":1098,"style":820},[303],[34,1100,1101,1104],{"style":823},[34,1102],{"className":1103,"style":314},[313],[34,1105,1107],{"className":1106},[385,386,387,388],[34,1108,1110],{"className":1109},[88,388],[34,1111,198],{"className":1112},[88,388],[34,1114,1115,1118],{"style":447},[34,1116],{"className":1117,"style":314},[313],[34,1119],{"className":1120,"style":455},[454],[34,1122,1123,1126],{"style":846},[34,1124],{"className":1125,"style":314},[313],[34,1127,1129],{"className":1128},[385,386,387,388],[34,1130,1132],{"className":1131},[88,388],[34,1133,195],{"className":1134},[88,388],[34,1136,351],{"className":1137},[350],[34,1139,1141],{"className":1140},[299],[34,1142,1144],{"className":1143,"style":868},[303],[34,1145],{},[34,1147],{"className":1148},[93,419],[34,1150,1152],{"className":1151},[88],[34,1153,203],{"className":1154},[499,880],[34,1156,203],{"className":1157},[418],[34,1159,195],{"className":1160},[88],[34,1162],{"className":1163,"style":535},[396],[34,1165,239],{"className":1166},[392],[34,1168],{"className":1169,"style":535},[396],[34,1171,1173,1176,1179,1182,1185,1188,1191,1194],{"className":1172},[79],[34,1174],{"className":1175,"style":84},[83],[34,1177,228],{"className":1178},[88,322],[34,1180,270],{"className":1181},[93],[34,1183,89],{"className":1184},[88],[34,1186,65],{"className":1187},[93],[34,1189],{"className":1190,"style":535},[396],[34,1192,239],{"className":1193},[392],[34,1195],{"className":1196,"style":535},[396],[34,1198,1200,1203,1206,1209,1212,1215],{"className":1199},[79],[34,1201],{"className":1202,"style":84},[83],[34,1204,203],{"className":1205},[418],[34,1207,195],{"className":1208},[88],[34,1210],{"className":1211,"style":535},[396],[34,1213,225],{"className":1214},[392],[34,1216],{"className":1217,"style":535},[396],[34,1219,1221,1224,1227,1230,1233,1236],{"className":1220},[79],[34,1222],{"className":1223,"style":801},[83],[34,1225,228],{"className":1226},[88,322],[34,1228,270],{"className":1229},[93],[34,1231,959],{"className":1232},[88],[34,1234,65],{"className":1235},[93],[34,1237,1239],{"className":1238},[88],[34,1240,270],{"className":1241},[499,880],[11,1243,1244,1245,1280,1281,1316],{},"Measured straight after √X†, a qubit that started in ",[34,1246,1248,1265],{"className":1247},[37],[34,1249,1251],{"className":1250},[41],[43,1252,1253],{"xmlns":45},[47,1254,1255,1263],{},[50,1256,1257,1259,1261],{},[53,1258,56],{"mathvariant":55},[58,1260,60],{},[62,1262,65],{"stretchy":64},[67,1264,70],{"encoding":69},[34,1266,1268],{"className":1267,"ariaHidden":75},[74],[34,1269,1271,1274,1277],{"className":1270},[79],[34,1272],{"className":1273,"style":84},[83],[34,1275,89],{"className":1276},[88],[34,1278,65],{"className":1279},[93]," or ",[34,1282,1284,1301],{"className":1283},[37],[34,1285,1287],{"className":1286},[41],[43,1288,1289],{"xmlns":45},[47,1290,1291,1299],{},[50,1292,1293,1295,1297],{},[53,1294,56],{"mathvariant":55},[58,1296,195],{},[62,1298,65],{"stretchy":64},[67,1300,993],{"encoding":69},[34,1302,1304],{"className":1303,"ariaHidden":75},[74],[34,1305,1307,1310,1313],{"className":1306},[79],[34,1308],{"className":1309,"style":84},[83],[34,1311,959],{"className":1312},[88],[34,1314,65],{"className":1315},[93]," reads 0 or 1 with equal probability.",[101,1318,1320],{"id":1319},"inverse","Inverse",[11,1322,1323,1324,1327],{},"The inverse of √X† is ",[15,1325,1326],{"href":17},"√X",". A √X followed by a √X† on the same qubit is the identity.",[101,1329,1331],{"id":1330},"usage","Usage",[1333,1334,1339],"pre",{"className":1335,"code":1336,"language":1337,"meta":1338,"style":1338},"language-python shiki shiki-themes one-dark-pro","from qiskit import QuantumCircuit\n\nqc = QuantumCircuit(1, 1)\nqc.sx(0)\nqc.sxdg(0)\nqc.measure(0, 0)\n","python","",[132,1340,1341,1359,1366,1392,1407,1421],{"__ignoreMap":1338},[34,1342,1345,1349,1353,1356],{"class":1343,"line":1344},"line",1,[34,1346,1348],{"class":1347},"seHd6","from",[34,1350,1352],{"class":1351},"sn6KH"," qiskit ",[34,1354,1355],{"class":1347},"import",[34,1357,1358],{"class":1351}," QuantumCircuit\n",[34,1360,1362],{"class":1343,"line":1361},2,[34,1363,1365],{"emptyLinePlaceholder":1364},true,"\n",[34,1367,1369,1372,1375,1379,1381,1384,1387,1389],{"class":1343,"line":1368},3,[34,1370,1371],{"class":1351},"qc ",[34,1373,189],{"class":1374},"sjrmR",[34,1376,1378],{"class":1377},"sVbv2"," QuantumCircuit",[34,1380,203],{"class":1351},[34,1382,195],{"class":1383},"sVC51",[34,1385,1386],{"class":1351},", ",[34,1388,195],{"class":1383},[34,1390,1391],{"class":1351},")\n",[34,1393,1395,1398,1401,1403,1405],{"class":1343,"line":1394},4,[34,1396,1397],{"class":1351},"qc.",[34,1399,1400],{"class":1377},"sx",[34,1402,203],{"class":1351},[34,1404,60],{"class":1383},[34,1406,1391],{"class":1351},[34,1408,1410,1412,1415,1417,1419],{"class":1343,"line":1409},5,[34,1411,1397],{"class":1351},[34,1413,1414],{"class":1377},"sxdg",[34,1416,203],{"class":1351},[34,1418,60],{"class":1383},[34,1420,1391],{"class":1351},[34,1422,1424,1426,1429,1431,1433,1435,1437],{"class":1343,"line":1423},6,[34,1425,1397],{"class":1351},[34,1427,1428],{"class":1377},"measure",[34,1430,203],{"class":1351},[34,1432,60],{"class":1383},[34,1434,1386],{"class":1351},[34,1436,60],{"class":1383},[34,1438,1391],{"class":1351},[1333,1440,1444],{"className":1441,"code":1442,"language":1443,"meta":1338,"style":1338},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\n\nconst circuit = QuantumCircuit(1, 1);\ncircuit.sx(0);\ncircuit.sxdg(0);\ncircuit.measure(0, 0);\n","js",[132,1445,1446,1469,1473,1498,1514,1528],{"__ignoreMap":1338},[34,1447,1448,1450,1453,1457,1460,1462,1466],{"class":1343,"line":1344},[34,1449,1355],{"class":1347},[34,1451,1452],{"class":1351}," { ",[34,1454,1456],{"class":1455},"sVyAn","QuantumCircuit",[34,1458,1459],{"class":1351}," } ",[34,1461,1348],{"class":1347},[34,1463,1465],{"class":1464},"subq3"," 'qiskit'",[34,1467,1468],{"class":1351},";\n",[34,1470,1471],{"class":1343,"line":1361},[34,1472,1365],{"emptyLinePlaceholder":1364},[34,1474,1475,1478,1482,1485,1487,1489,1491,1493,1495],{"class":1343,"line":1368},[34,1476,1477],{"class":1347},"const",[34,1479,1481],{"class":1480},"sU0A5"," circuit",[34,1483,1484],{"class":1374}," =",[34,1486,1378],{"class":1377},[34,1488,203],{"class":1351},[34,1490,195],{"class":1383},[34,1492,1386],{"class":1351},[34,1494,195],{"class":1383},[34,1496,1497],{"class":1351},");\n",[34,1499,1500,1503,1506,1508,1510,1512],{"class":1343,"line":1394},[34,1501,1502],{"class":1480},"circuit",[34,1504,1505],{"class":1351},".",[34,1507,1400],{"class":1377},[34,1509,203],{"class":1351},[34,1511,60],{"class":1383},[34,1513,1497],{"class":1351},[34,1515,1516,1518,1520,1522,1524,1526],{"class":1343,"line":1409},[34,1517,1502],{"class":1480},[34,1519,1505],{"class":1351},[34,1521,1414],{"class":1377},[34,1523,203],{"class":1351},[34,1525,60],{"class":1383},[34,1527,1497],{"class":1351},[34,1529,1530,1532,1534,1536,1538,1540,1542,1544],{"class":1343,"line":1423},[34,1531,1502],{"class":1480},[34,1533,1505],{"class":1351},[34,1535,1428],{"class":1377},[34,1537,203],{"class":1351},[34,1539,60],{"class":1383},[34,1541,1386],{"class":1351},[34,1543,60],{"class":1383},[34,1545,1497],{"class":1351},[11,1547,1548,1549,1551],{},"Every shot reads ",[132,1550,60],{},": the pair cancels.",[101,1553,1555],{"id":1554},"on-ionq-hardware","On IonQ hardware",[11,1557,1558,1559,1562,1563,1505],{},"√X† is ",[132,1560,1561],{},"GPi2(0.5)"," up to a global phase, a native gate with its phase half a turn from √X, so it costs one physical pulse. See ",[15,1564,1566],{"href":1565},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",[101,1568,1570],{"id":1569},"related","Related",[1572,1573,1574,1579,1585,1591],"ul",{},[1575,1576,1577],"li",{},[15,1578,18],{"href":17},[1575,1580,1581],{},[15,1582,1584],{"href":1583},"\u002Flearn\u002Fdocs\u002Frx-gate","RX gate",[1575,1586,1587],{},[15,1588,1590],{"href":1589},"\u002Flearn\u002Fdocs\u002Fgpi2-gate","GPi2 gate",[1575,1592,1593],{},[15,1594,1596],{"href":1595},"\u002Flearn\u002Fdocs\u002Fgates","Gate reference",[1598,1599,1600],"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: 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 .subq3, html code.shiki .subq3{--shiki-default:#98C379}html pre.shiki code .sU0A5, html code.shiki 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