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\\rangle",[15,1755,1757],{"className":1756,"ariaHidden":52},[51],[15,1758,1760,1763,1801,1804],{"className":1759},[56],[15,1761],{"className":1762,"style":1499},[60],[15,1764,1766,1769],{"className":1765},[65],[15,1767,442],{"className":1768},[65,66],[15,1770,1772],{"className":1771},[746],[15,1773,1775],{"className":1774},[660],[15,1776,1778],{"className":1777},[665],[15,1779,1781],{"className":1780,"style":756},[669],[15,1782,1783,1786],{"style":759},[15,1784],{"className":1785,"style":763},[677],[15,1787,1789],{"className":1788},[767,768,769,770],[15,1790,1792,1795,1798],{"className":1791},[65,770],[15,1793,450],{"className":1794},[65,66,770],[15,1796,105],{"className":1797,"style":122},[65,66,770],[15,1799,786],{"className":1800},[65,770],[15,1802,365],{"className":1803},[65],[15,1805,184],{"className":1806},[205],[225,1808,1809,1847],{},[239,1810,1811],{},[15,1812,1814,1832],{"className":1813},[18],[15,1815,1817],{"className":1816},[22],[24,1818,1819],{"xmlns":26},[28,1820,1821,1829],{},[31,1822,1823,1825,1827],{},[34,1824,176],{"mathvariant":175},[178,1826,319],{},[38,1828,184],{"stretchy":183},[44,1830,1831],{"encoding":46},"\\vert 11 \\rangle",[15,1833,1835],{"className":1834,"ariaHidden":52},[51],[15,1836,1838,1841,1844],{"className":1837},[56],[15,1839],{"className":1840,"style":197},[60],[15,1842,378],{"className":1843},[65],[15,1845,184],{"className":1846},[205],[239,1848,1849],{},[15,1850,1852,1886],{"className":1851},[18],[15,1853,1855],{"className":1854},[22],[24,1856,1857],{"xmlns":26},[28,1858,1859,1883],{},[31,1860,1861,1877,1879,1881],{},[438,1862,1863,1865],{},[34,1864,442],{},[31,1866,1867,1869,1871,1873,1875],{},[38,1868,447],{},[34,1870,450],{},[34,1872,105],{},[34,1874,455],{"mathvariant":175},[178,1876,458],{},[34,1878,176],{"mathvariant":175},[178,1880,319],{},[38,1882,184],{"stretchy":183},[44,1884,1885],{"encoding":46},"e^{-i\\theta\u002F2}\\vert 11 \\rangle",[15,1887,1889],{"className":1888,"ariaHidden":52},[51],[15,1890,1892,1895,1936,1939],{"className":1891},[56],[15,1893],{"className":1894,"style":1499},[60],[15,1896,1898,1901],{"className":1897},[65],[15,1899,442],{"className":1900},[65,66],[15,1902,1904],{"className":1903},[746],[15,1905,1907],{"className":1906},[660],[15,1908,1910],{"className":1909},[665],[15,1911,1913],{"className":1912,"style":756},[669],[15,1914,1915,1918],{"style":759},[15,1916],{"className":1917,"style":763},[677],[15,1919,1921],{"className":1920},[767,768,769,770],[15,1922,1924,1927,1930,1933],{"className":1923},[65,770],[15,1925,447],{"className":1926},[65,770],[15,1928,450],{"className":1929},[65,66,770],[15,1931,105],{"className":1932,"style":122},[65,66,770],[15,1934,786],{"className":1935},[65,770],[15,1937,378],{"className":1938},[65],[15,1940,184],{"className":1941},[205],[11,1943,1944],{},"A measurement straight after RZZ shows no change on any basis state, whatever the angle. The phases show once the qubits are in superposition: this gate is the building block of Ising-model and QAOA circuits.",[214,1946,1948],{"id":1947},"inverse","Inverse",[11,1950,1951,1952,1955,1956,382],{},"The inverse of ",[245,1953,1954],{},"rzz(θ)"," is ",[245,1957,1958],{},"rzz(-θ)",[214,1960,1962],{"id":1961},"usage","Usage",[1964,1965,1970],"pre",{"className":1966,"code":1967,"language":1968,"meta":1969,"style":1969},"language-python shiki shiki-themes one-dark-pro","from math import pi\nfrom qiskit import QuantumCircuit\n\nqc = QuantumCircuit(2, 2)\nqc.h(0)\nqc.h(1)\nqc.rzz(pi, 0, 1)\nqc.h(0)\nqc.h(1)\nqc.measure([0, 1], [0, 1])\n","python","",[245,1971,1972,1990,2003,2010,2036,2051,2065,2084,2097,2110],{"__ignoreMap":1969},[15,1973,1976,1980,1984,1987],{"class":1974,"line":1975},"line",1,[15,1977,1979],{"class":1978},"seHd6","from",[15,1981,1983],{"class":1982},"sn6KH"," math ",[15,1985,1986],{"class":1978},"import",[15,1988,1989],{"class":1982}," pi\n",[15,1991,1993,1995,1998,2000],{"class":1974,"line":1992},2,[15,1994,1979],{"class":1978},[15,1996,1997],{"class":1982}," qiskit ",[15,1999,1986],{"class":1978},[15,2001,2002],{"class":1982}," QuantumCircuit\n",[15,2004,2006],{"class":1974,"line":2005},3,[15,2007,2009],{"emptyLinePlaceholder":2008},true,"\n",[15,2011,2013,2016,2019,2023,2025,2028,2031,2033],{"class":1974,"line":2012},4,[15,2014,2015],{"class":1982},"qc ",[15,2017,417],{"class":2018},"sjrmR",[15,2020,2022],{"class":2021},"sVbv2"," QuantumCircuit",[15,2024,409],{"class":1982},[15,2026,458],{"class":2027},"sVC51",[15,2029,2030],{"class":1982},", ",[15,2032,458],{"class":2027},[15,2034,2035],{"class":1982},")\n",[15,2037,2039,2042,2045,2047,2049],{"class":1974,"line":2038},5,[15,2040,2041],{"class":1982},"qc.",[15,2043,2044],{"class":2021},"h",[15,2046,409],{"class":1982},[15,2048,180],{"class":2027},[15,2050,2035],{"class":1982},[15,2052,2054,2056,2058,2060,2063],{"class":1974,"line":2053},6,[15,2055,2041],{"class":1982},[15,2057,2044],{"class":2021},[15,2059,409],{"class":1982},[15,2061,2062],{"class":2027},"1",[15,2064,2035],{"class":1982},[15,2066,2068,2070,2073,2076,2078,2080,2082],{"class":1974,"line":2067},7,[15,2069,2041],{"class":1982},[15,2071,2072],{"class":2021},"rzz",[15,2074,2075],{"class":1982},"(pi, ",[15,2077,180],{"class":2027},[15,2079,2030],{"class":1982},[15,2081,2062],{"class":2027},[15,2083,2035],{"class":1982},[15,2085,2087,2089,2091,2093,2095],{"class":1974,"line":2086},8,[15,2088,2041],{"class":1982},[15,2090,2044],{"class":2021},[15,2092,409],{"class":1982},[15,2094,180],{"class":2027},[15,2096,2035],{"class":1982},[15,2098,2100,2102,2104,2106,2108],{"class":1974,"line":2099},9,[15,2101,2041],{"class":1982},[15,2103,2044],{"class":2021},[15,2105,409],{"class":1982},[15,2107,2062],{"class":2027},[15,2109,2035],{"class":1982},[15,2111,2113,2115,2118,2121,2123,2125,2127,2130,2132,2134,2136],{"class":1974,"line":2112},10,[15,2114,2041],{"class":1982},[15,2116,2117],{"class":2021},"measure",[15,2119,2120],{"class":1982},"([",[15,2122,180],{"class":2027},[15,2124,2030],{"class":1982},[15,2126,2062],{"class":2027},[15,2128,2129],{"class":1982},"], [",[15,2131,180],{"class":2027},[15,2133,2030],{"class":1982},[15,2135,2062],{"class":2027},[15,2137,2138],{"class":1982},"])\n",[1964,2140,2144],{"className":2141,"code":2142,"language":2143,"meta":1969,"style":1969},"language-js shiki shiki-themes one-dark-pro","import { QuantumCircuit } from 'qiskit';\n\nconst circuit = QuantumCircuit(2, 2);\ncircuit.h(0);\ncircuit.h(1);\ncircuit.rzz(Math.PI, 0, 1);\ncircuit.h(0);\ncircuit.h(1);\ncircuit.measure([0, 1], [0, 1]);\n","js",[245,2145,2146,2169,2173,2198,2213,2227,2255,2269,2283],{"__ignoreMap":1969},[15,2147,2148,2150,2153,2157,2160,2162,2166],{"class":1974,"line":1975},[15,2149,1986],{"class":1978},[15,2151,2152],{"class":1982}," { ",[15,2154,2156],{"class":2155},"sVyAn","QuantumCircuit",[15,2158,2159],{"class":1982}," } ",[15,2161,1979],{"class":1978},[15,2163,2165],{"class":2164},"subq3"," 'qiskit'",[15,2167,2168],{"class":1982},";\n",[15,2170,2171],{"class":1974,"line":1992},[15,2172,2009],{"emptyLinePlaceholder":2008},[15,2174,2175,2178,2182,2185,2187,2189,2191,2193,2195],{"class":1974,"line":2005},[15,2176,2177],{"class":1978},"const",[15,2179,2181],{"class":2180},"sU0A5"," circuit",[15,2183,2184],{"class":2018}," =",[15,2186,2022],{"class":2021},[15,2188,409],{"class":1982},[15,2190,458],{"class":2027},[15,2192,2030],{"class":1982},[15,2194,458],{"class":2027},[15,2196,2197],{"class":1982},");\n",[15,2199,2200,2203,2205,2207,2209,2211],{"class":1974,"line":2012},[15,2201,2202],{"class":2180},"circuit",[15,2204,382],{"class":1982},[15,2206,2044],{"class":2021},[15,2208,409],{"class":1982},[15,2210,180],{"class":2027},[15,2212,2197],{"class":1982},[15,2214,2215,2217,2219,2221,2223,2225],{"class":1974,"line":2038},[15,2216,2202],{"class":2180},[15,2218,382],{"class":1982},[15,2220,2044],{"class":2021},[15,2222,409],{"class":1982},[15,2224,2062],{"class":2027},[15,2226,2197],{"class":1982},[15,2228,2229,2231,2233,2235,2237,2240,2242,2245,2247,2249,2251,2253],{"class":1974,"line":2053},[15,2230,2202],{"class":2180},[15,2232,382],{"class":1982},[15,2234,2072],{"class":2021},[15,2236,409],{"class":1982},[15,2238,2239],{"class":2180},"Math",[15,2241,382],{"class":1982},[15,2243,2244],{"class":2155},"PI",[15,2246,2030],{"class":1982},[15,2248,180],{"class":2027},[15,2250,2030],{"class":1982},[15,2252,2062],{"class":2027},[15,2254,2197],{"class":1982},[15,2256,2257,2259,2261,2263,2265,2267],{"class":1974,"line":2067},[15,2258,2202],{"class":2180},[15,2260,382],{"class":1982},[15,2262,2044],{"class":2021},[15,2264,409],{"class":1982},[15,2266,180],{"class":2027},[15,2268,2197],{"class":1982},[15,2270,2271,2273,2275,2277,2279,2281],{"class":1974,"line":2086},[15,2272,2202],{"class":2180},[15,2274,382],{"class":1982},[15,2276,2044],{"class":2021},[15,2278,409],{"class":1982},[15,2280,2062],{"class":2027},[15,2282,2197],{"class":1982},[15,2284,2285,2287,2289,2291,2293,2295,2297,2299,2301,2303,2305,2307],{"class":1974,"line":2099},[15,2286,2202],{"class":2180},[15,2288,382],{"class":1982},[15,2290,2117],{"class":2021},[15,2292,2120],{"class":1982},[15,2294,180],{"class":2027},[15,2296,2030],{"class":1982},[15,2298,2062],{"class":2027},[15,2300,2129],{"class":1982},[15,2302,180],{"class":2027},[15,2304,2030],{"class":1982},[15,2306,2062],{"class":2027},[15,2308,2309],{"class":1982},"]);\n",[11,2311,2312,2313,2315,2316,2319,2320,2357],{},"On a noiseless simulator every shot reads ",[245,2314,319],{},": between the H gates, ",[245,2317,2318],{},"rzz(π)"," flips the sign of both qubits' ",[15,2321,2323,2341],{"className":2322},[18],[15,2324,2326],{"className":2325},[22],[24,2327,2328],{"xmlns":26},[28,2329,2330,2338],{},[31,2331,2332,2334,2336],{},[34,2333,176],{"mathvariant":175},[178,2335,2062],{},[38,2337,184],{"stretchy":183},[44,2339,2340],{"encoding":46},"\\vert 1 \\rangle",[15,2342,2344],{"className":2343,"ariaHidden":52},[51],[15,2345,2347,2350,2354],{"className":2346},[56],[15,2348],{"className":2349,"style":197},[60],[15,2351,2353],{"className":2352},[65],"∣1",[15,2355,184],{"className":2356},[205]," components together.",[214,2359,2361],{"id":2360},"on-ionq-hardware","On IonQ hardware",[11,2363,2364,2365,2367,2368,2371,2372,2375,2376,382],{},"RZZ is the abstract form of Forte's native entangler: ",[245,2366,1954],{}," is exactly ",[245,2369,2370],{},"ZZ(θ\u002F2π)",", one native gate with no single-qubit pulses at all, and Forte is the hardware behind Qollab's QPU backends. On Aria it is one ",[245,2373,2374],{},"MS"," gate with single-qubit pulses around it. See ",[208,2377,2379],{"href":2378},"\u002Flearn\u002Fdocs\u002Fhow-your-circuit-is-compiled","How your circuit is compiled",[214,2381,2383],{"id":2382},"related","Related",[2385,2386,2387,2394,2400,2404,2409],"ul",{},[2388,2389,2390],"li",{},[208,2391,2393],{"href":2392},"\u002Flearn\u002Fdocs\u002Fzz-gate","ZZ gate",[2388,2395,2396],{},[208,2397,2399],{"href":2398},"\u002Flearn\u002Fdocs\u002Frxx-gate","RXX gate",[2388,2401,2402],{},[208,2403,1391],{"href":1390},[2388,2405,2406],{},[208,2407,2408],{"href":1385},"RZ gate",[2388,2410,2411],{},[208,2412,2414],{"href":2413},"\u002Flearn\u002Fdocs\u002Fgates","Gate reference",[2416,2417,2418],"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 .sU0A5{--shiki-default:#E5C07B}",{"title":1969,"searchDepth":1992,"depth":1992,"links":2420},[2421,2422,2423,2424,2425,2426,2427],{"id":216,"depth":1992,"text":217},{"id":270,"depth":1992,"text":271},{"id":1395,"depth":1992,"text":1396},{"id":1947,"depth":1992,"text":1948},{"id":1961,"depth":1992,"text":1962},{"id":2360,"depth":1992,"text":2361},{"id":2382,"depth":1992,"text":2383},"gates","Gates","The RZZ gate, a two-qubit rotation about Z⊗Z: matrix, effect on the basis states, the rzz() call in Python and JS, and its IonQ native-gate form.",false,"md","two-qubit","Two-qubit gates","doc",{},22,"\u002Fblog\u002Flearn\u002Fdocs\u002Frzz-gate","2026-09-16",[],{"title":2442,"description":2443},"RZZ gate · Qollab docs","Reference for the RZZ(θ) two-qubit rotation gate: matrix, action on the basis states, the Qiskit rzz() call in Python and JS, and its IonQ ZZ 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