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0 \\rangle - i\\sin\\frac{\\theta}{2}\\vert 1 \\rangle",[15,1248,1250,1348],{"className":1249,"ariaHidden":46},[45],[15,1251,1253,1257,1260,1263,1331,1334,1337,1341,1345],{"className":1252},[50],[15,1254],{"className":1255,"style":1256},[54],"height:1.2251em;vertical-align:-0.345em;",[15,1258,556],{"className":1259},[156],[15,1261],{"className":1262,"style":723},[249],[15,1264,1266,1269,1328],{"className":1265},[59],[15,1267],{"className":1268},[198,730],[15,1270,1272],{"className":1271},[560],[15,1273,1275,1320],{"className":1274},[167,699],[15,1276,1278,1317],{"className":1277},[171],[15,1279,1281,1295,1303],{"className":1280,"style":743},[175],[15,1282,1283,1286],{"style":746},[15,1284],{"className":1285,"style":713},[183],[15,1287,1289],{"className":1288},[188,189,190,191],[15,1290,1292],{"className":1291},[59,191],[15,1293,124],{"className":1294},[59,191],[15,1296,1297,1300],{"style":761},[15,1298],{"className":1299,"style":713},[183],[15,1301],{"className":1302,"style":769},[768],[15,1304,1305,1308],{"style":772},[15,1306],{"className":1307,"style":713},[183],[15,1309,1311],{"className":1310},[188,189,190,191],[15,1312,1314],{"className":1313},[59,191],[15,1315,36],{"className":1316,"style":61},[59,60,191],[15,1318,789],{"className":1319},[788],[15,1321,1323],{"className":1322},[171],[15,1324,1326],{"className":1325,"style":796},[175],[15,1327],{},[15,1329],{"className":1330},[209,730],[15,1332,422],{"className":1333},[59],[15,1335,406],{"className":1336},[209],[15,1338],{"className":1339,"style":1340},[249],"margin-right:0.2222em;",[15,1342,574],{"className":1343},[1344],"mbin",[15,1346],{"className":1347,"style":1340},[249],[15,1349,1351,1354,1357,1360,1363,1366,1434,1438],{"className":1350},[50],[15,1352],{"className":1353,"style":1256},[54],[15,1355,577],{"className":1356},[59,60],[15,1358],{"className":1359,"style":723},[249],[15,1361,116],{"className":1362},[156],[15,1364],{"className":1365,"style":723},[249],[15,1367,1369,1372,1431],{"className":1368},[59],[15,1370],{"className":1371},[198,730],[15,1373,1375],{"className":1374},[560],[15,1376,1378,1423],{"className":1377},[167,699],[15,1379,1381,1420],{"className":1380},[171],[15,1382,1384,1398,1406],{"className":1383,"style":743},[175],[15,1385,1386,1389],{"style":746},[15,1387],{"className":1388,"style":713},[183],[15,1390,1392],{"className":1391},[188,189,190,191],[15,1393,1395],{"className":1394},[59,191],[15,1396,124],{"className":1397},[59,191],[15,1399,1400,1403],{"style":761},[15,1401],{"className":1402,"style":713},[183],[15,1404],{"className":1405,"style":769},[768],[15,1407,1408,1411],{"style":772},[15,1409],{"className":1410,"style":713},[183],[15,1412,1414],{"className":1413},[188,189,190,191],[15,1415,1417],{"className":1416},[59,191],[15,1418,36],{"className":1419,"style":61},[59,60,191],[15,1421,789],{"className":1422},[788],[15,1424,1426],{"className":1425},[171],[15,1427,1429],{"className":1428,"style":796},[175],[15,1430],{},[15,1432],{"className":1433},[209,730],[15,1435,1437],{"className":1436},[59],"∣1",[15,1439,406],{"className":1440},[209],[445,1442,1443,1481],{},[459,1444,1445],{},[15,1446,1448,1466],{"className":1447},[18],[15,1449,1451],{"className":1450},[22],[24,1452,1453],{"xmlns":26},[28,1454,1455,1463],{},[31,1456,1457,1459,1461],{},[34,1458,401],{"mathvariant":133},[122,1460,1241],{},[118,1462,406],{"stretchy":127},[38,1464,1465],{"encoding":40},"\\vert 1 \\rangle",[15,1467,1469],{"className":1468,"ariaHidden":46},[45],[15,1470,1472,1475,1478],{"className":1471},[50],[15,1473],{"className":1474,"style":322},[54],[15,1476,1437],{"className":1477},[59],[15,1479,406],{"className":1480},[209],[459,1482,1483],{},[15,1484,1486,1537],{"className":1485},[18],[15,1487,1489],{"className":1488},[22],[24,1490,1491],{"xmlns":26},[28,1492,1493,1534],{},[31,1494,1495,1497,1499,1501,1503,1509,1511,1513,1515,1518,1520,1522,1528,1530,1532],{},[118,1496,574],{},[34,1498,577],{},[34,1500,116],{},[118,1502,120],{},[560,1504,1505,1507],{},[34,1506,36],{},[122,1508,124],{},[34,1510,401],{"mathvariant":133},[122,1512,230],{},[118,1514,406],{"stretchy":127},[118,1516,1517],{},"+",[34,1519,556],{},[118,1521,120],{},[560,1523,1524,1526],{},[34,1525,36],{},[122,1527,124],{},[34,1529,401],{"mathvariant":133},[122,1531,1241],{},[118,1533,406],{"stretchy":127},[38,1535,1536],{"encoding":40},"-i\\sin\\frac{\\theta}{2}\\vert 0 \\rangle + \\cos\\frac{\\theta}{2}\\vert 1 \\rangle",[15,1538,1540,1644],{"className":1539,"ariaHidden":46},[45],[15,1541,1543,1546,1549,1552,1555,1558,1561,1629,1632,1635,1638,1641],{"className":1542},[50],[15,1544],{"className":1545,"style":1256},[54],[15,1547,574],{"className":1548},[59],[15,1550,577],{"className":1551},[59,60],[15,1553],{"className":1554,"style":723},[249],[15,1556,116],{"className":1557},[156],[15,1559],{"className":1560,"style":723},[249],[15,1562,1564,1567,1626],{"className":1563},[59],[15,1565],{"className":1566},[198,730],[15,1568,1570],{"className":1569},[560],[15,1571,1573,1618],{"className":1572},[167,699],[15,1574,1576,1615],{"className":1575},[171],[15,1577,1579,1593,1601],{"className":1578,"style":743},[175],[15,1580,1581,1584],{"style":746},[15,1582],{"className":1583,"style":713},[183],[15,1585,1587],{"className":1586},[188,189,190,191],[15,1588,1590],{"className":1589},[59,191],[15,1591,124],{"className":1592},[59,191],[15,1594,1595,1598],{"style":761},[15,1596],{"className":1597,"style":713},[183],[15,1599],{"className":1600,"style":769},[768],[15,1602,1603,1606],{"style":772},[15,1604],{"className":1605,"style":713},[183],[15,1607,1609],{"className":1608},[188,189,190,191],[15,1610,1612],{"className":1611},[59,191],[15,1613,36],{"className":1614,"style":61},[59,60,191],[15,1616,789],{"className":1617},[788],[15,1619,1621],{"className":1620},[171],[15,1622,1624],{"className":1623,"style":796},[175],[15,1625],{},[15,1627],{"className":1628},[209,730],[15,1630,422],{"className":1631},[59],[15,1633,406],{"className":1634},[209],[15,1636],{"className":1637,"style":1340},[249],[15,1639,1517],{"className":1640},[1344],[15,1642],{"className":1643,"style":1340},[249],[15,1645,1647,1650,1653,1656,1724,1727],{"className":1646},[50],[15,1648],{"className":1649,"style":1256},[54],[15,1651,556],{"className":1652},[156],[15,1654],{"className":1655,"style":723},[249],[15,1657,1659,1662,1721],{"className":1658},[59],[15,1660],{"className":1661},[198,730],[15,1663,1665],{"className":1664},[560],[15,1666,1668,1713],{"className":1667},[167,699],[15,1669,1671,1710],{"className":1670},[171],[15,1672,1674,1688,1696],{"className":1673,"style":743},[175],[15,1675,1676,1679],{"style":746},[15,1677],{"className":1678,"style":713},[183],[15,1680,1682],{"className":1681},[188,189,190,191],[15,1683,1685],{"className":1684},[59,191],[15,1686,124],{"className":1687},[59,191],[15,1689,1690,1693],{"style":761},[15,1691],{"className":1692,"style":713},[183],[15,1694],{"className":1695,"style":769},[768],[15,1697,1698,1701],{"style":772},[15,1699],{"className":1700,"style":713},[183],[15,1702,1704],{"className":1703},[188,189,190,191],[15,1705,1707],{"className":1706},[59,191],[15,1708,36],{"className":1709,"style":61},[59,60,191],[15,1711,789],{"className":1712},[788],[15,1714,1716],{"className":1715},[171],[15,1717,1719],{"className":1718,"style":796},[175],[15,1720],{},[15,1722],{"className":1723},[209,730],[15,1725,1437],{"className":1726},[59],[15,1728,406],{"className":1729},[209],[11,1731,1732,1733,1736,1737,1772,1773,1857,1858,1908,1909,1966,1967,383],{},"Measured straight after ",[465,1734,1735],{},"rx(θ)",", a qubit that started in ",[15,1738,1740,1757],{"className":1739},[18],[15,1741,1743],{"className":1742},[22],[24,1744,1745],{"xmlns":26},[28,1746,1747,1755],{},[31,1748,1749,1751,1753],{},[34,1750,401],{"mathvariant":133},[122,1752,230],{},[118,1754,406],{"stretchy":127},[38,1756,409],{"encoding":40},[15,1758,1760],{"className":1759,"ariaHidden":46},[45],[15,1761,1763,1766,1769],{"className":1762},[50],[15,1764],{"className":1765,"style":322},[54],[15,1767,422],{"className":1768},[59],[15,1770,406],{"className":1771},[209]," reads 1 with probability ",[15,1774,1776,1807],{"className":1775},[18],[15,1777,1779],{"className":1778},[22],[24,1780,1781],{"xmlns":26},[28,1782,1783,1805],{},[31,1784,1785,1795,1797,1799,1801,1803],{},[110,1786,1787,1793],{},[31,1788,1789,1791],{},[34,1790,116],{},[118,1792,120],{},[122,1794,124],{},[118,1796,128],{"stretchy":127},[34,1798,36],{},[34,1800,134],{"mathvariant":133},[122,1802,124],{},[118,1804,139],{"stretchy":127},[38,1806,142],{"encoding":40},[15,1808,1810],{"className":1809,"ariaHidden":46},[45],[15,1811,1813,1816,1845,1848,1851,1854],{"className":1812},[50],[15,1814],{"className":1815,"style":152},[54],[15,1817,1819,1822],{"className":1818},[156],[15,1820,116],{"className":1821},[156],[15,1823,1825],{"className":1824},[163],[15,1826,1828],{"className":1827},[167],[15,1829,1831],{"className":1830},[171],[15,1832,1834],{"className":1833,"style":176},[175],[15,1835,1836,1839],{"style":179},[15,1837],{"className":1838,"style":184},[183],[15,1840,1842],{"className":1841},[188,189,190,191],[15,1843,124],{"className":1844},[59,191],[15,1846,128],{"className":1847},[198],[15,1849,36],{"className":1850,"style":61},[59,60],[15,1852,205],{"className":1853},[59],[15,1855,139],{"className":1856},[209],": 0 at ",[15,1859,1861,1878],{"className":1860},[18],[15,1862,1864],{"className":1863},[22],[24,1865,1866],{"xmlns":26},[28,1867,1868,1876],{},[31,1869,1870,1872,1874],{},[34,1871,36],{},[118,1873,227],{},[122,1875,230],{},[38,1877,233],{"encoding":40},[15,1879,1881,1899],{"className":1880,"ariaHidden":46},[45],[15,1882,1884,1887,1890,1893,1896],{"className":1883},[50],[15,1885],{"className":1886,"style":55},[54],[15,1888,36],{"className":1889,"style":61},[59,60],[15,1891],{"className":1892,"style":250},[249],[15,1894,227],{"className":1895},[254],[15,1897],{"className":1898,"style":250},[249],[15,1900,1902,1905],{"className":1901},[50],[15,1903],{"className":1904,"style":264},[54],[15,1906,230],{"className":1907},[59],", one half at ",[15,1910,1912,1933],{"className":1911},[18],[15,1913,1915],{"className":1914},[22],[24,1916,1917],{"xmlns":26},[28,1918,1919,1931],{},[31,1920,1921,1923,1925,1927,1929],{},[34,1922,36],{},[118,1924,227],{},[34,1926,287],{},[34,1928,134],{"mathvariant":133},[122,1930,124],{},[38,1932,294],{"encoding":40},[15,1934,1936,1954],{"className":1935,"ariaHidden":46},[45],[15,1937,1939,1942,1945,1948,1951],{"className":1938},[50],[15,1940],{"className":1941,"style":55},[54],[15,1943,36],{"className":1944,"style":61},[59,60],[15,1946],{"className":1947,"style":250},[249],[15,1949,227],{"className":1950},[254],[15,1952],{"className":1953,"style":250},[249],[15,1955,1957,1960,1963],{"className":1956},[50],[15,1958],{"className":1959,"style":322},[54],[15,1961,287],{"className":1962,"style":326},[59,60],[15,1964,205],{"className":1965},[59],", certainty at ",[15,1968,1970,1987],{"className":1969},[18],[15,1971,1973],{"className":1972},[22],[24,1974,1975],{"xmlns":26},[28,1976,1977,1985],{},[31,1978,1979,1981,1983],{},[34,1980,36],{},[118,1982,227],{},[34,1984,287],{},[38,1986,351],{"encoding":40},[15,1988,1990,2008],{"className":1989,"ariaHidden":46},[45],[15,1991,1993,1996,1999,2002,2005],{"className":1992},[50],[15,1994],{"className":1995,"style":55},[54],[15,1997,36],{"className":1998,"style":61},[59,60],[15,2000],{"className":2001,"style":250},[249],[15,2003,227],{"className":2004},[254],[15,2006],{"className":2007,"style":250},[249],[15,2009,2011,2014],{"className":2010},[50],[15,2012],{"className":2013,"style":379},[54],[15,2015,287],{"className":2016,"style":326},[59,60],[434,2018,2020],{"id":2019},"inverse","Inverse",[11,2022,2023,2024,2026,2027,383],{},"The inverse of ",[465,2025,1735],{}," is ",[465,2028,2029],{},"rx(-θ)",[434,2031,2033],{"id":2032},"usage","Usage",[2035,2036,2041],"pre",{"className":2037,"code":2038,"language":2039,"meta":2040,"style":2040},"language-python shiki shiki-themes one-dark-pro","from math import pi\nfrom qiskit import QuantumCircuit\n\nqc = QuantumCircuit(1, 1)\nqc.rx(pi \u002F 3, 0)\nqc.measure(0, 0)\n","python","",[465,2042,2043,2061,2074,2081,2107,2130],{"__ignoreMap":2040},[15,2044,2047,2051,2055,2058],{"class":2045,"line":2046},"line",1,[15,2048,2050],{"class":2049},"seHd6","from",[15,2052,2054],{"class":2053},"sn6KH"," math ",[15,2056,2057],{"class":2049},"import",[15,2059,2060],{"class":2053}," pi\n",[15,2062,2064,2066,2069,2071],{"class":2045,"line":2063},2,[15,2065,2050],{"class":2049},[15,2067,2068],{"class":2053}," qiskit ",[15,2070,2057],{"class":2049},[15,2072,2073],{"class":2053}," QuantumCircuit\n",[15,2075,2077],{"class":2045,"line":2076},3,[15,2078,2080],{"emptyLinePlaceholder":2079},true,"\n",[15,2082,2084,2087,2090,2094,2096,2099,2102,2104],{"class":2045,"line":2083},4,[15,2085,2086],{"class":2053},"qc ",[15,2088,227],{"class":2089},"sjrmR",[15,2091,2093],{"class":2092},"sVbv2"," QuantumCircuit",[15,2095,128],{"class":2053},[15,2097,1241],{"class":2098},"sVC51",[15,2100,2101],{"class":2053},", ",[15,2103,1241],{"class":2098},[15,2105,2106],{"class":2053},")\n",[15,2108,2110,2113,2116,2119,2121,2124,2126,2128],{"class":2045,"line":2109},5,[15,2111,2112],{"class":2053},"qc.",[15,2114,2115],{"class":2092},"rx",[15,2117,2118],{"class":2053},"(pi ",[15,2120,134],{"class":2089},[15,2122,2123],{"class":2098}," 3",[15,2125,2101],{"class":2053},[15,2127,230],{"class":2098},[15,2129,2106],{"class":2053},[15,2131,2133,2135,2138,2140,2142,2144,2146],{"class":2045,"line":2132},6,[15,2134,2112],{"class":2053},[15,2136,2137],{"class":2092},"measure",[15,2139,128],{"class":2053},[15,2141,230],{"class":2098},[15,2143,2101],{"class":2053},[15,2145,230],{"class":2098},[15,2147,2106],{"class":2053},[2035,2149,2153],{"className":2150,"code":2151,"language":2152,"meta":2040,"style":2040},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\n\nconst circuit = QuantumCircuit(1, 1);\ncircuit.rx(Math.PI \u002F 3, 0);\ncircuit.measure(0, 0);\n","js",[465,2154,2155,2178,2182,2207,2237],{"__ignoreMap":2040},[15,2156,2157,2159,2162,2166,2169,2171,2175],{"class":2045,"line":2046},[15,2158,2057],{"class":2049},[15,2160,2161],{"class":2053}," { ",[15,2163,2165],{"class":2164},"sVyAn","QuantumCircuit",[15,2167,2168],{"class":2053}," } ",[15,2170,2050],{"class":2049},[15,2172,2174],{"class":2173},"subq3"," 'qiskit'",[15,2176,2177],{"class":2053},";\n",[15,2179,2180],{"class":2045,"line":2063},[15,2181,2080],{"emptyLinePlaceholder":2079},[15,2183,2184,2187,2191,2194,2196,2198,2200,2202,2204],{"class":2045,"line":2076},[15,2185,2186],{"class":2049},"const",[15,2188,2190],{"class":2189},"sU0A5"," circuit",[15,2192,2193],{"class":2089}," =",[15,2195,2093],{"class":2092},[15,2197,128],{"class":2053},[15,2199,1241],{"class":2098},[15,2201,2101],{"class":2053},[15,2203,1241],{"class":2098},[15,2205,2206],{"class":2053},");\n",[15,2208,2209,2212,2214,2216,2218,2221,2223,2226,2229,2231,2233,2235],{"class":2045,"line":2083},[15,2210,2211],{"class":2189},"circuit",[15,2213,383],{"class":2053},[15,2215,2115],{"class":2092},[15,2217,128],{"class":2053},[15,2219,2220],{"class":2189},"Math",[15,2222,383],{"class":2053},[15,2224,2225],{"class":2164},"PI",[15,2227,2228],{"class":2089}," \u002F",[15,2230,2123],{"class":2098},[15,2232,2101],{"class":2053},[15,2234,230],{"class":2098},[15,2236,2206],{"class":2053},[15,2238,2239,2241,2243,2245,2247,2249,2251,2253],{"class":2045,"line":2109},[15,2240,2211],{"class":2189},[15,2242,383],{"class":2053},[15,2244,2137],{"class":2092},[15,2246,128],{"class":2053},[15,2248,230],{"class":2098},[15,2250,2101],{"class":2053},[15,2252,230],{"class":2098},[15,2254,2206],{"class":2053},[11,2256,2257,2258,2260,2261,383],{},"Over many shots about a quarter of them read ",[465,2259,1241],{},": ",[15,2262,2264,2302],{"className":2263},[18],[15,2265,2267],{"className":2266},[22],[24,2268,2269],{"xmlns":26},[28,2270,2271,2299],{},[31,2272,2273,2283,2285,2287,2289,2292,2294,2296],{},[110,2274,2275,2281],{},[31,2276,2277,2279],{},[34,2278,116],{},[118,2280,120],{},[122,2282,124],{},[118,2284,128],{"stretchy":127},[34,2286,287],{},[34,2288,134],{"mathvariant":133},[122,2290,2291],{},"6",[118,2293,139],{"stretchy":127},[118,2295,227],{},[122,2297,2298],{},"0.25",[38,2300,2301],{"encoding":40},"\\sin^2(\\pi\u002F6) = 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