[{"data":1,"prerenderedAt":1892},["ShallowReactive",2],{"blog-post-docs\u002Frz-gate":3,"sibling-dives-docs\u002Frz-gate":1730,"learn-track-docs\u002Frz-gate":1731,"learn-docs-groups":1732},{"id":4,"title":5,"authors":6,"body":7,"breadcrumb":6,"builders":6,"byline":6,"category":1711,"categoryName":1712,"challenge":6,"courseAuthor":6,"courseLead":6,"dek":6,"description":1713,"draft":1714,"extension":1715,"eyebrow":6,"featured":1714,"finish":6,"fork":6,"group":1716,"groupName":1717,"hero":6,"heroAlt":6,"heroCta":6,"heroImage":6,"homepageFeatured":1714,"kind":1718,"lessonCount":6,"meta":1719,"navigation":1425,"newsItems":6,"next":6,"ogImage":6,"order":1720,"outcomes":6,"path":1721,"publishDate":1722,"readingTime":6,"related":1723,"relatedProjects":6,"seo":1724,"stem":1727,"tags":1728,"track":6,"trackName":6,"__hash__":1729},"blog\u002Fblog\u002Flearn\u002Fdocs\u002Frz-gate.md","RZ gate",null,{"type":8,"value":9,"toc":1702},"minimark",[10,96,152,157,217,221,597,622,626,1287,1362,1366,1376,1380,1514,1644,1653,1657,1664,1668,1698],[11,12,13,14,61,62,90,91,95],"p",{},"The RZ gate rotates a qubit about the Z axis of the Bloch sphere by an angle ",[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 radians. The Circuit panel draws it as ",[92,93,94],"strong",{},"Rz(φ)"," with the angle shown as a multiple of π. 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measurement straight after RZ shows no change on ",[15,1291,1293,1310],{"className":1292},[18],[15,1294,1296],{"className":1295},[22],[24,1297,1298],{"xmlns":26},[28,1299,1300,1308],{},[31,1301,1302,1304,1306],{},[34,1303,114],{"mathvariant":113},[116,1305,118],{},[120,1307,123],{"stretchy":122},[38,1309,126],{"encoding":40},[15,1311,1313],{"className":1312,"ariaHidden":46},[45],[15,1314,1316,1319,1322],{"className":1315},[50],[15,1317],{"className":1318,"style":136},[54],[15,1320,140],{"className":1321},[59],[15,1323,123],{"className":1324},[144]," or ",[15,1327,1329,1346],{"className":1328},[18],[15,1330,1332],{"className":1331},[22],[24,1333,1334],{"xmlns":26},[28,1335,1336,1344],{},[31,1337,1338,1340,1342],{},[34,1339,114],{"mathvariant":113},[116,1341,795],{},[120,1343,123],{"stretchy":122},[38,1345,800],{"encoding":40},[15,1347,1349],{"className":1348,"ariaHidden":46},[45],[15,1350,1352,1355,1358],{"className":1351},[50],[15,1353],{"className":1354,"style":136},[54],[15,1356,813],{"className":1357},[59],[15,1359,123],{"className":1360},[144],", whatever the angle. The rotation shows once the qubit is in superposition.",[153,1363,1365],{"id":1364},"inverse","Inverse",[11,1367,1368,1369,1371,1372,1375],{},"The inverse of ",[184,1370,607],{}," is ",[184,1373,1374],{},"rz(-φ)",".",[153,1377,1379],{"id":1378},"usage","Usage",[1381,1382,1387],"pre",{"className":1383,"code":1384,"language":1385,"meta":1386,"style":1386},"language-python shiki shiki-themes one-dark-pro","from math import pi\nfrom qiskit import QuantumCircuit\n\nqc = QuantumCircuit(1, 1)\nqc.h(0)\nqc.rz(pi, 0)\nqc.h(0)\nqc.measure(0, 0)\n","python","",[184,1388,1389,1407,1420,1427,1453,1468,1483,1496],{"__ignoreMap":1386},[15,1390,1393,1397,1401,1404],{"class":1391,"line":1392},"line",1,[15,1394,1396],{"class":1395},"seHd6","from",[15,1398,1400],{"class":1399},"sn6KH"," math ",[15,1402,1403],{"class":1395},"import",[15,1405,1406],{"class":1399}," pi\n",[15,1408,1410,1412,1415,1417],{"class":1391,"line":1409},2,[15,1411,1396],{"class":1395},[15,1413,1414],{"class":1399}," qiskit ",[15,1416,1403],{"class":1395},[15,1418,1419],{"class":1399}," QuantumCircuit\n",[15,1421,1423],{"class":1391,"line":1422},3,[15,1424,1426],{"emptyLinePlaceholder":1425},true,"\n",[15,1428,1430,1433,1436,1440,1442,1445,1448,1450],{"class":1391,"line":1429},4,[15,1431,1432],{"class":1399},"qc ",[15,1434,254],{"class":1435},"sjrmR",[15,1437,1439],{"class":1438},"sVbv2"," QuantumCircuit",[15,1441,246],{"class":1399},[15,1443,795],{"class":1444},"sVC51",[15,1446,1447],{"class":1399},", ",[15,1449,795],{"class":1444},[15,1451,1452],{"class":1399},")\n",[15,1454,1456,1459,1462,1464,1466],{"class":1391,"line":1455},5,[15,1457,1458],{"class":1399},"qc.",[15,1460,1461],{"class":1438},"h",[15,1463,246],{"class":1399},[15,1465,118],{"class":1444},[15,1467,1452],{"class":1399},[15,1469,1471,1473,1476,1479,1481],{"class":1391,"line":1470},6,[15,1472,1458],{"class":1399},[15,1474,1475],{"class":1438},"rz",[15,1477,1478],{"class":1399},"(pi, ",[15,1480,118],{"class":1444},[15,1482,1452],{"class":1399},[15,1484,1486,1488,1490,1492,1494],{"class":1391,"line":1485},7,[15,1487,1458],{"class":1399},[15,1489,1461],{"class":1438},[15,1491,246],{"class":1399},[15,1493,118],{"class":1444},[15,1495,1452],{"class":1399},[15,1497,1499,1501,1504,1506,1508,1510,1512],{"class":1391,"line":1498},8,[15,1500,1458],{"class":1399},[15,1502,1503],{"class":1438},"measure",[15,1505,246],{"class":1399},[15,1507,118],{"class":1444},[15,1509,1447],{"class":1399},[15,1511,118],{"class":1444},[15,1513,1452],{"class":1399},[1381,1515,1519],{"className":1516,"code":1517,"language":1518,"meta":1386,"style":1386},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\n\nconst circuit = QuantumCircuit(1, 1);\ncircuit.h(0);\ncircuit.rz(Math.PI, 0);\ncircuit.h(0);\ncircuit.measure(0, 0);\n","js",[184,1520,1521,1544,1548,1573,1588,1612,1626],{"__ignoreMap":1386},[15,1522,1523,1525,1528,1532,1535,1537,1541],{"class":1391,"line":1392},[15,1524,1403],{"class":1395},[15,1526,1527],{"class":1399}," { ",[15,1529,1531],{"class":1530},"sVyAn","QuantumCircuit",[15,1533,1534],{"class":1399}," } ",[15,1536,1396],{"class":1395},[15,1538,1540],{"class":1539},"subq3"," 'qiskit'",[15,1542,1543],{"class":1399},";\n",[15,1545,1546],{"class":1391,"line":1409},[15,1547,1426],{"emptyLinePlaceholder":1425},[15,1549,1550,1553,1557,1560,1562,1564,1566,1568,1570],{"class":1391,"line":1422},[15,1551,1552],{"class":1395},"const",[15,1554,1556],{"class":1555},"sU0A5"," circuit",[15,1558,1559],{"class":1435}," =",[15,1561,1439],{"class":1438},[15,1563,246],{"class":1399},[15,1565,795],{"class":1444},[15,1567,1447],{"class":1399},[15,1569,795],{"class":1444},[15,1571,1572],{"class":1399},");\n",[15,1574,1575,1578,1580,1582,1584,1586],{"class":1391,"line":1429},[15,1576,1577],{"class":1555},"circuit",[15,1579,1375],{"class":1399},[15,1581,1461],{"class":1438},[15,1583,246],{"class":1399},[15,1585,118],{"class":1444},[15,1587,1572],{"class":1399},[15,1589,1590,1592,1594,1596,1598,1601,1603,1606,1608,1610],{"class":1391,"line":1455},[15,1591,1577],{"class":1555},[15,1593,1375],{"class":1399},[15,1595,1475],{"class":1438},[15,1597,246],{"class":1399},[15,1599,1600],{"class":1555},"Math",[15,1602,1375],{"class":1399},[15,1604,1605],{"class":1530},"PI",[15,1607,1447],{"class":1399},[15,1609,118],{"class":1444},[15,1611,1572],{"class":1399},[15,1613,1614,1616,1618,1620,1622,1624],{"class":1391,"line":1470},[15,1615,1577],{"class":1555},[15,1617,1375],{"class":1399},[15,1619,1461],{"class":1438},[15,1621,246],{"class":1399},[15,1623,118],{"class":1444},[15,1625,1572],{"class":1399},[15,1627,1628,1630,1632,1634,1636,1638,1640,1642],{"class":1391,"line":1485},[15,1629,1577],{"class":1555},[15,1631,1375],{"class":1399},[15,1633,1503],{"class":1438},[15,1635,246],{"class":1399},[15,1637,118],{"class":1444},[15,1639,1447],{"class":1399},[15,1641,118],{"class":1444},[15,1643,1572],{"class":1399},[11,1645,1646,1647,1649,1650,1652],{},"Every shot reads ",[184,1648,795],{},": ",[184,1651,615],{}," acts as a Z, and H Z H is an X.",[153,1654,1656],{"id":1655},"on-ionq-hardware","On IonQ hardware",[11,1658,1659,1660,1375],{},"RZ is the virtual Z itself. The hardware performs no physical operation for it; the compiler adds the angle to the phase of the pulses that follow, so RZ costs no gate and no time on the machine, whatever the angle. A circuit heavy in Z rotations can compile smaller than its written gate count suggests. See ",[147,1661,1663],{"href":1662},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",[153,1665,1667],{"id":1666},"related","Related",[1669,1670,1671,1676,1680,1686,1692],"ul",{},[1672,1673,1674],"li",{},[147,1675,603],{"href":602},[1672,1677,1678],{},[147,1679,620],{"href":619},[1672,1681,1682],{},[147,1683,1685],{"href":1684},"\u002Flearn\u002Fdocs\u002Frx-gate","RX gate",[1672,1687,1688],{},[147,1689,1691],{"href":1690},"\u002Flearn\u002Fdocs\u002Fry-gate","RY gate",[1672,1693,1694],{},[147,1695,1697],{"href":1696},"\u002Flearn\u002Fdocs\u002Fgates","Gate reference",[1699,1700,1701],"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 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