104:
2371:
2361:
528:
449:
interact with nuclei in a higher energy state, causing the energy of the higher energy state to distribute itself between the two nuclei. Therefore, the energy gained by nuclei from the RF pulse is dissipated as increased vibration and rotation within the lattice, which can slightly increase the temperature of the sample. The name
448:
Nuclei are contained within a molecular structure, and are in constant vibrational and rotational motion, creating a complex magnetic field. The magnetic field caused by thermal motion of nuclei within the lattice is called the lattice field. The lattice field of a nucleus in a lower energy state can
549:) and then the excess energy is released in the form of a minuscule amount of heat to the surroundings as the spins return to their thermal equilibrium. The magnetization of the proton ensemble goes back to its equilibrium value with an exponential curve characterized by a time constant
453:
refers to the process in which the spins give the energy they obtained from the RF pulse back to the surrounding lattice, thereby restoring their equilibrium state. The same process occurs after the spin energy has been altered by a change of the surrounding static magnetic field (e.g.
869:
441:
476:
the transition from high to low energy states. However, at extremely high mobilities, the probability decreases as the vibrational and rotational frequencies no longer correspond to the energy gap between states.
272:
445:
It is thus the time it takes for the longitudinal magnetization to recover approximately 63% of its initial value after being flipped into the magnetic transverse plane by a 90° radiofrequency pulse.
472:
of the nucleus and the mobility of the lattice. As mobility increases, the vibrational and rotational frequencies increase, making it more likely for a component of the lattice field to be able to
494:
s (1500-2000 ms), and water-based tissues are in the 400-1200 ms range, while fat based tissues are in the shorter 100-150 ms range. The presence of strongly magnetic ions or particles (e.g.,
335:
749:
1560:
1361:
1522:
339:
691:
referred to as spin-lock (SL) pulse applied to the magnetization in the transverse plane. The magnetization is effectively spin-locked around an effective
2252:
2153:
1814:
1715:
581:
sequences, while in
Gradient Echo Sequences they can be obtained by using flip angles of larger than 50 while setting TE values to less than 15 ms.
133:
2040:
754:
967:
Relaxation Times and Basic Pulse
Sequences in MR Imaging. in: Magnetic Resonance in Medicine. A Critical Introduction. 12th edition. pp. 65-92
975:
630:, the transverse component of the magnetization vector, exponentially decays towards its equilibrium value of zero, under the influence of a
2364:
1550:
2400:
2395:
2322:
1898:
1000:
1312:
Witschey, WR; Pilla, JJ; Ferrari, G; Koomalsingh, K; Haris, M; Hinmon, R; Zsido, G; Gorman JH, 3rd; Gorman, RC; Reddy, R (Nov 2010).
2374:
2262:
1515:
1848:
924:
MRI has been used to image tissues such as cartilage, intervertebral discs, brain, and heart, as well as certain types of cancers.
545:
uses the resonance of the protons to generate images. Protons are excited by a radio frequency pulse at an appropriate frequency (
454:
pre-polarization by or insertion into high magnetic field) or if the nonequilibrium state has been achieved by other means (e.g.,
2190:
1067:
Li, X; Benjamin Ma, C; Link, TM; Castillo, DD; Blumenkrantz, G; Lozano, J; Carballido-Gamio, J; Ries, M; Majumdar, S (Jul 2007).
2185:
1913:
1893:
1692:
612:
contrast suitable for morphological assessment of the normal or pathological anatomy, e.g., for musculoskeletal applications.
2180:
70:
1375:
Li, LZ; Zhou, R; Xu, HN; Moon, L; Zhong, T; Kim, EJ; Qiao, H; Reddy, R; Leeper, D; Chance, B; Glickson, JD (Apr 21, 2009).
2213:
2035:
1938:
1599:
130:
component of the magnetization vector recovers exponentially towards its thermodynamic equilibrium, according to equation
896:
the signal expression above as a function of the duration of the spin-lock pulse while the amplitude of spin-lock pulse (
2218:
2086:
1677:
1508:
661:
1858:
1632:
2242:
1587:
1531:
455:
42:
vector (parallel to the constant magnetic field) exponentially relaxes from a higher energy, non-equilibrium state to
1687:
1167:"T1ρ magnetic resonance imaging and discography pressure as novel biomarkers for disc degeneration and low back pain"
2114:
1986:
1883:
1759:
1594:
639:
635:
542:
277:
92:
31:
1923:
1888:
1784:
1727:
43:
2008:
1622:
938:
2096:
2069:
2045:
1799:
1732:
1667:
1652:
1545:
1434:
Cai, K; Shore, A; Singh, A; Haris, M; Hiraki, T; Waghray, P; Reddy, D; Greenberg, JH; Reddy, R (Feb 2, 2012).
1165:
Borthakur, A; Maurer, PM; Fenty, M; Wang, C; Berger, R; Yoder, J; Balderston, RA; Elliott, DM (Dec 1, 2011).
1116:
Witschey, WR; Borthakur, A; Fenty, M; Kneeland, BJ; Lonner, JH; McArdle, EL; Sochor, M; Reddy, R (May 2010).
73:, which concerns the exponential relaxation of the transverse component of the nuclear magnetization vector (
2247:
1981:
1873:
1843:
1642:
1314:"Rotating frame spin lattice relaxation in a swine model of chronic, left ventricular myocardial infarction"
39:
103:
2317:
2081:
2074:
1821:
2237:
1789:
1754:
1436:"Blood oxygen level dependent angiography (BOLDangio) and its potential applications in cancer research"
1355:
712:, which is the time it takes for the magnetic resonance signal to reach 37% (1/e) of its initial value,
1863:
1263:
Cai, K; Haris, M; Singh, A; Kogan, F; Greenberg, JH; Hariharan, H; Detre, JA; Reddy, R (Jan 22, 2012).
970:. Offprint to download: TRTF - The Round Table Foundation / EMRF - European Magnetic Resonance Forum.
2027:
1776:
1627:
1388:
1069:"In vivo T(1rho) and T(2) mapping of articular cartilage in osteoarthritis of the knee using 3 T MRI"
2129:
2346:
2299:
1903:
1657:
1637:
1572:
1567:
473:
2062:
1710:
1647:
1377:"Quantitative magnetic resonance and optical imaging biomarkers of melanoma metastatic potential"
1022:
510:
469:
1908:
715:
705:
and any off-resonant component. The spin-locked magnetization will relax with a time constant
2326:
1971:
1878:
1835:
1766:
1682:
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17:
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2050:
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1794:
1231:
893:
495:
1016:
Borthakur, A; Mellon, E; Niyogi, S; Witschey, W; Kneeland, JB; Reddy, R (Nov 2006).
2270:
2195:
1214:
Borthakur, A; Sochor, M; Davatzikos, C; Trojanowski, JQ; Clark, CM (Jul 15, 2008).
595:
499:
1018:"Sodium and T1rho MRI for molecular and diagnostic imaging of articular cartilage"
1182:
2280:
2134:
1672:
944:
591:
468:(the average lifetime of nuclei in the higher energy state) is dependent on the
1381:
Proceedings of the
National Academy of Sciences of the United States of America
1118:"T1rho MRI quantification of arthroscopically confirmed cartilage degeneration"
1084:
605:
contrast is present between fluid and more solid anatomical structures, making
2341:
2275:
2139:
1500:
527:
2124:
1401:
864:{\displaystyle M_{xy}(t_{\rm {SL}})=M_{xy}(0)e^{-t_{\rm {SL}}/T_{1\rho }}\,}
578:
574:
1469:
1420:
1347:
1298:
1249:
1200:
1151:
1102:
1053:
2309:
2285:
2144:
2109:
436:{\displaystyle M_{z}(t)=M_{z,\mathrm {eq} }\left(1-2e^{-t/T_{1}}\right)}
2336:
1953:
1329:
1133:
2313:
1809:
1451:
1035:
1280:
910:
MRI relaxation maps reflect the biochemical composition of tissues.
46:
with its surroundings (the "lattice"). It is characterized by the
1582:
102:
38:
is the mechanism by which the longitudinal component of the total
2331:
1804:
1737:
1504:
993:
Spin
Dynamics: Basics of Nuclear Magnetic Resonance 2nd Edition
1948:
1933:
965:
267:{\displaystyle M_{z}(t)=M_{z,\mathrm {eq} }-\lefte^{-t/T_{1}}}
642:(MRI). It is characterized by the spin–lattice relaxation
77:
to the external magnetic field). Measuring the variation of
757:
718:
342:
280:
136:
2298:
2261:
2227:
2204:
2171:
2162:
2095:
2024:
1962:
1922:
1834:
1775:
1701:
1610:
1538:
598:and is used when undertaking brain scans. A strong
863:
743:
435:
329:
266:
569:weighted images can be obtained by setting short
123:characterizes the rate at which the longitudinal
698:field created by the vector sum of the applied
1516:
687:MRI by its use of a long-duration, low-power
621:Spin–lattice relaxation in the rotating frame
330:{\displaystyle M_{z}(0)=-M_{z,\mathrm {eq} }}
91:in different materials is the basis for some
8:
1360:: CS1 maint: numeric names: authors list (
113:relaxation or longitudinal relaxation curve
2168:
1772:
1523:
1509:
1501:
1459:
1410:
1400:
1337:
1288:
1265:"Magnetic resonance imaging of glutamate"
1239:
1190:
1141:
1092:
1043:
860:
849:
840:
830:
829:
821:
799:
779:
778:
762:
756:
723:
717:
420:
411:
404:
376:
369:
347:
341:
317:
310:
285:
279:
256:
247:
240:
216:
199:
192:
170:
163:
141:
135:
577:(TE) such as < 40 ms in conventional
526:
2041:Continuous-variable quantum information
956:
1353:
673:MRI is an alternative to conventional
487:values. For example, fluids have long
903:~0.1-few kHz) is fixed. Quantitative
7:
892:can be quantified (relaxometry) by
590:is significantly different between
1216:"T1rho MRI of Alzheimer's disease"
834:
831:
783:
780:
380:
377:
321:
318:
203:
200:
174:
171:
25:
878:is the duration of the RF field.
480:Different tissues have different
2370:
2369:
2360:
2359:
1232:10.1016/j.neuroimage.2008.03.030
62:There is a different parameter,
274:Or, for the specific case that
1318:Magnetic Resonance in Medicine
1122:Magnetic Resonance in Medicine
814:
808:
789:
771:
738:
732:
509:values and are widely used as
359:
353:
297:
291:
228:
222:
153:
147:
1:
2036:Adiabatic quantum computation
653:. It is named in contrast to
573:(TR) such as < 750 ms and
2087:Topological quantum computer
1488:MRI, From picture to proton.
1183:10.1097/BRS.0b013e31820287bf
1073:Osteoarthritis and Cartilage
662:spin-lattice relaxation time
48:spin–lattice relaxation time
2365:Quantum information science
1532:Quantum information science
991:Levitt, Malcolm H. (2016).
538:weighted image of the head.
50:, a time constant known as
2417:
2401:Nuclear magnetic resonance
2396:Magnetic resonance imaging
1760:quantum gate teleportation
1085:10.1016/j.joca.2007.01.011
640:magnetic resonance imaging
636:nuclear magnetic resonance
623:is the mechanism by which
543:Magnetic resonance imaging
93:magnetic resonance imaging
32:nuclear magnetic resonance
2355:
1889:Quantum Fourier transform
1785:Post-quantum cryptography
1728:Entanglement distillation
744:{\displaystyle M_{xy}(0)}
71:spin–spin relaxation time
44:thermodynamic equilibrium
2375:Quantum mechanics topics
2070:Quantum machine learning
2046:One-way quantum computer
1899:Quantum phase estimation
1800:Quantum key distribution
1733:Monogamy of entanglement
964:Rinck, Peter A. (2022).
1982:Randomized benchmarking
1844:Amplitude amplification
1402:10.1073/pnas.0901807106
751:. Hence the relation:
646:in the rotating frame,
451:spin–lattice relaxation
40:nuclear magnetic moment
36:spin–lattice relaxation
18:Spin-lattice relaxation
2082:Quantum Turing machine
2075:quantum neural network
1822:Quantum secret sharing
865:
745:
539:
502:) also strongly alter
437:
331:
268:
114:
2154:Entanglement-assisted
2115:quantum convolutional
1790:Quantum coin flipping
1755:Quantum teleportation
1716:entanglement-assisted
1546:DiVincenzo's criteria
866:
746:
616:In the rotating frame
530:
461:The relaxation time,
458:by optical pumping).
438:
332:
269:
106:
1965:processor benchmarks
1894:Quantum optimization
1777:Quantum cryptography
1588:physical vs. logical
1493:Hashemi Ray, et al.
1486:McRobbie D., et al.
939:Spin–spin relaxation
755:
716:
340:
278:
134:
1678:Quantum speed limit
1573:Quantum programming
1568:Quantum information
1393:2009PNAS..106.6608L
511:MRI contrast agents
27:Physical phenomenon
2327:Forest/Rigetti QCS
2063:quantum logic gate
1849:Bernstein–Vazirani
1836:Quantum algorithms
1711:Classical capacity
1595:Quantum processors
1578:Quantum simulation
1440:NMR in Biomedicine
1023:NMR in Biomedicine
861:
741:
540:
470:gyromagnetic ratio
433:
327:
264:
115:
2383:
2382:
2294:
2293:
2191:Linear optical QC
1972:Quantum supremacy
1926:complexity theory
1879:Quantum annealing
1830:
1829:
1767:Superdense coding
1556:Quantum computing
1446:(10): 1125–1132.
1330:10.1002/mrm.22543
1134:10.1002/mrm.22272
977:978-3-7460-9518-9
456:hyperpolarization
16:(Redirected from
2408:
2373:
2372:
2363:
2362:
2169:
2099:error correction
2028:computing models
1994:Relaxation times
1884:Quantum counting
1773:
1721:quantum capacity
1668:No-teleportation
1653:No-communication
1525:
1518:
1511:
1502:
1474:
1473:
1463:
1452:10.1002/nbm.2780
1431:
1425:
1424:
1414:
1404:
1372:
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1211:
1205:
1204:
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1113:
1107:
1106:
1096:
1064:
1058:
1057:
1047:
1036:10.1002/nbm.1102
1013:
1007:
1006:
988:
982:
981:
961:
934:Relaxation (NMR)
870:
868:
867:
862:
859:
858:
857:
856:
844:
839:
838:
837:
807:
806:
788:
787:
786:
770:
769:
750:
748:
747:
742:
731:
730:
558:Relaxation (NMR)
547:Larmor frequency
442:
440:
439:
434:
432:
428:
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21:
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2409:
2407:
2406:
2405:
2386:
2385:
2384:
2379:
2351:
2301:
2290:
2263:Superconducting
2257:
2223:
2214:Neutral atom QC
2206:Ultracold atoms
2200:
2165:implementations
2164:
2158:
2098:
2091:
2058:Quantum circuit
2026:
2020:
2014:
2004:
1964:
1958:
1925:
1918:
1874:Hidden subgroup
1826:
1815:other protocols
1771:
1748:quantum network
1743:Quantum channel
1703:
1697:
1643:No-broadcasting
1633:Gottesman–Knill
1606:
1534:
1529:
1495:MRI, The Basics
1483:
1481:Further reading
1478:
1477:
1433:
1432:
1428:
1387:(16): 6608–13.
1374:
1373:
1369:
1352:
1311:
1310:
1306:
1281:10.1038/nm.2615
1269:Nature Medicine
1262:
1261:
1257:
1226:(4): 1199–205.
1213:
1212:
1208:
1164:
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1115:
1114:
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719:
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689:radio frequency
686:
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672:
659:
652:
632:radio frequency
628:
618:
610:
603:
588:
571:repetition time
567:
554:
536:
525:
523:weighted images
522:
507:
492:
485:
466:
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365:
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252:
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212:
188:
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159:
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132:
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101:
99:Nuclear physics
89:
82:
67:
56:
28:
23:
22:
15:
12:
11:
5:
2414:
2412:
2404:
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2347:many others...
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2234:
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2225:
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2222:
2221:
2219:Trapped-ion QC
2216:
2210:
2208:
2202:
2201:
2199:
2198:
2193:
2188:
2183:
2177:
2175:
2173:Quantum optics
2166:
2160:
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2156:
2151:
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2142:
2137:
2132:
2127:
2122:
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2030:
2022:
2021:
2019:
2018:
2017:
2016:
2012:
2006:
2002:
1991:
1990:
1989:
1979:
1977:Quantum volume
1974:
1968:
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1919:
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1901:
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1854:Boson sampling
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1688:Solovay–Kitaev
1685:
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1505:
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1479:
1476:
1475:
1426:
1367:
1324:(5): 1453–60.
1304:
1255:
1206:
1177:(25): 2190–6.
1157:
1128:(5): 1376–82.
1108:
1059:
1030:(7): 781–821.
1008:
1002:978-0470511176
1001:
983:
976:
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684:
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650:
634:(RF) field in
626:
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299:
296:
293:
288:
284:
259:
255:
250:
246:
243:
239:
234:
230:
227:
224:
219:
215:
211:
205:
202:
198:
195:
191:
186:
182:
176:
173:
169:
166:
162:
158:
155:
152:
149:
144:
140:
126:
119:
109:
100:
97:
87:
80:
76:
65:
54:
34:observations,
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2413:
2402:
2399:
2397:
2394:
2393:
2391:
2376:
2368:
2366:
2358:
2357:
2354:
2348:
2345:
2343:
2340:
2338:
2335:
2333:
2330:
2328:
2324:
2321:
2319:
2315:
2311:
2308:
2307:
2305:
2303:
2297:
2287:
2284:
2282:
2279:
2277:
2274:
2272:
2269:
2268:
2266:
2264:
2260:
2254:
2251:
2249:
2246:
2244:
2243:Spin qubit QC
2241:
2239:
2236:
2235:
2233:
2230:
2226:
2220:
2217:
2215:
2212:
2211:
2209:
2207:
2203:
2197:
2194:
2192:
2189:
2187:
2184:
2182:
2179:
2178:
2176:
2174:
2170:
2167:
2161:
2155:
2152:
2148:
2147:
2143:
2141:
2138:
2136:
2133:
2131:
2128:
2126:
2123:
2121:
2118:
2116:
2113:
2111:
2108:
2107:
2105:
2104:
2102:
2100:
2094:
2088:
2085:
2083:
2080:
2076:
2073:
2072:
2071:
2068:
2064:
2061:
2060:
2059:
2056:
2052:
2051:cluster state
2049:
2048:
2047:
2044:
2042:
2039:
2037:
2034:
2033:
2031:
2029:
2023:
2015:
2011:
2007:
2005:
2001:
1997:
1996:
1995:
1992:
1988:
1985:
1984:
1983:
1980:
1978:
1975:
1973:
1970:
1969:
1967:
1961:
1955:
1952:
1950:
1947:
1945:
1942:
1940:
1937:
1935:
1932:
1931:
1929:
1927:
1921:
1915:
1912:
1910:
1907:
1905:
1902:
1900:
1897:
1895:
1892:
1890:
1887:
1885:
1882:
1880:
1877:
1875:
1872:
1870:
1867:
1865:
1862:
1860:
1859:Deutsch–Jozsa
1857:
1855:
1852:
1850:
1847:
1845:
1842:
1841:
1839:
1837:
1833:
1823:
1820:
1816:
1813:
1811:
1808:
1806:
1803:
1802:
1801:
1798:
1796:
1795:Quantum money
1793:
1791:
1788:
1786:
1783:
1782:
1780:
1778:
1774:
1768:
1765:
1761:
1758:
1757:
1756:
1753:
1749:
1746:
1745:
1744:
1741:
1739:
1736:
1734:
1731:
1729:
1726:
1722:
1719:
1717:
1714:
1713:
1712:
1709:
1708:
1706:
1704:communication
1700:
1694:
1691:
1689:
1686:
1684:
1681:
1679:
1676:
1674:
1671:
1669:
1666:
1664:
1661:
1659:
1656:
1654:
1651:
1649:
1646:
1644:
1641:
1639:
1636:
1634:
1631:
1629:
1626:
1624:
1621:
1619:
1616:
1615:
1613:
1609:
1601:
1598:
1597:
1596:
1593:
1589:
1586:
1585:
1584:
1581:
1579:
1576:
1574:
1571:
1569:
1566:
1562:
1559:
1558:
1557:
1554:
1552:
1549:
1547:
1544:
1543:
1541:
1537:
1533:
1526:
1521:
1519:
1514:
1512:
1507:
1506:
1503:
1496:
1492:
1489:
1485:
1484:
1480:
1471:
1467:
1462:
1457:
1453:
1449:
1445:
1441:
1437:
1430:
1427:
1422:
1418:
1413:
1408:
1403:
1398:
1394:
1390:
1386:
1382:
1378:
1371:
1368:
1363:
1357:
1349:
1345:
1340:
1335:
1331:
1327:
1323:
1319:
1315:
1308:
1305:
1300:
1296:
1291:
1286:
1282:
1278:
1274:
1270:
1266:
1259:
1256:
1251:
1247:
1242:
1237:
1233:
1229:
1225:
1221:
1217:
1210:
1207:
1202:
1198:
1193:
1188:
1184:
1180:
1176:
1172:
1168:
1161:
1158:
1153:
1149:
1144:
1139:
1135:
1131:
1127:
1123:
1119:
1112:
1109:
1104:
1100:
1095:
1090:
1086:
1082:
1079:(7): 789–97.
1078:
1074:
1070:
1063:
1060:
1055:
1051:
1046:
1041:
1037:
1033:
1029:
1025:
1024:
1019:
1012:
1009:
1004:
998:
994:
987:
984:
979:
973:
969:
968:
960:
957:
950:
946:
943:
940:
937:
935:
932:
931:
927:
925:
920:
913:
911:
906:
899:
895:
894:curve fitting
888:
881:
879:
874:
853:
850:
846:
841:
826:
822:
818:
811:
803:
800:
796:
792:
775:
766:
763:
759:
735:
727:
724:
720:
708:
701:
694:
690:
683:
676:
669:
665:
663:
656:
649:
645:
644:time constant
641:
637:
633:
629:
622:
615:
613:
611:
604:
597:
593:
589:
582:
580:
576:
572:
568:
561:
559:
555:
548:
544:
537:
529:
519:
516:
514:
512:
508:
501:
497:
496:ferromagnetic
493:
486:
478:
475:
471:
467:
459:
457:
452:
446:
443:
429:
421:
417:
412:
408:
405:
401:
397:
394:
391:
387:
373:
370:
366:
362:
356:
348:
344:
314:
311:
307:
303:
300:
294:
286:
282:
257:
253:
248:
244:
241:
237:
232:
225:
217:
213:
209:
196:
193:
189:
184:
180:
167:
164:
160:
156:
150:
142:
138:
129:
122:
112:
105:
98:
96:
94:
90:
83:
75:perpendicular
74:
72:
68:
60:
58:
57:
49:
45:
41:
37:
33:
19:
2271:Charge qubit
2196:KLM protocol
2145:
2009:
1999:
1998:
1693:Purification
1623:Eastin–Knill
1494:
1487:
1443:
1439:
1429:
1384:
1380:
1370:
1356:cite journal
1321:
1317:
1307:
1275:(2): 302–6.
1272:
1268:
1258:
1223:
1219:
1209:
1174:
1170:
1160:
1125:
1121:
1111:
1076:
1072:
1062:
1027:
1021:
1011:
992:
986:
966:
959:
918:
917:
904:
897:
886:
885:
872:
706:
699:
692:
681:
674:
667:
666:
654:
647:
643:
624:
620:
619:
606:
599:
596:white matter
584:
583:
563:
562:
550:
541:
532:
517:
503:
500:paramagnetic
488:
481:
479:
462:
460:
450:
447:
444:
124:
117:
116:
107:
95:techniques.
85:
78:
63:
61:
52:
51:
47:
35:
29:
2302:programming
2281:Phase qubit
2186:Circuit QED
1658:No-deleting
1600:cloud-based
945:Ernst angle
882:Measurement
592:grey matter
2390:Categories
2342:libquantum
2276:Flux qubit
2181:Cavity QED
2130:Bacon–Shor
2120:stabilizer
1648:No-cloning
1220:NeuroImage
951:References
638:(NMR) and
2248:NV center
1683:Threshold
1663:No-hiding
1628:Gleason's
1497:2ED. 2004
995:. Wiley.
854:ρ
823:−
579:spin echo
575:echo time
474:stimulate
406:−
395:−
304:−
242:−
210:−
181:−
2310:OpenQASM
2286:Transmon
2163:Physical
1963:Quantum
1864:Grover's
1638:Holevo's
1611:Theorems
1561:timeline
1551:NISQ era
1470:22302557
1421:19366661
1348:20677236
1299:22270722
1250:18479942
1201:21358489
1152:20432308
1103:17307365
1054:17075961
928:See also
871:, where
2300:Quantum
2238:Kane QC
2097:Quantum
2025:Quantum
1954:PostBQP
1924:Quantum
1909:Simon's
1702:Quantum
1539:General
1461:3390450
1412:2672511
1389:Bibcode
1339:2965811
1290:3274604
1241:2473861
1192:4002043
1143:2933515
1094:2040334
1045:2896046
914:Imaging
30:During
2318:IBM QX
2314:Qiskit
2253:NMR QC
2231:-based
2135:Steane
2106:Codes
1904:Shor's
1810:SARG04
1618:Bell's
1468:
1458:
1419:
1409:
1346:
1336:
1297:
1287:
1248:
1238:
1199:
1189:
1150:
1140:
1101:
1091:
1052:
1042:
999:
974:
660:, the
69:, the
2140:Toric
1583:Qubit
1171:Spine
556:(see
2332:Cirq
2323:Quil
2229:Spin
2125:Shor
1805:BB84
1738:LOCC
1490:2003
1466:PMID
1417:PMID
1362:link
1344:PMID
1295:PMID
1246:PMID
1197:PMID
1148:PMID
1099:PMID
1050:PMID
997:ISBN
972:ISBN
941:time
680:and
594:and
84:and
2146:gnu
2110:CSS
1987:XEB
1949:QMA
1944:QIP
1939:EQP
1934:BQP
1914:VQE
1869:HHL
1673:PBR
1456:PMC
1448:doi
1407:PMC
1397:doi
1385:106
1334:PMC
1326:doi
1285:PMC
1277:doi
1236:PMC
1228:doi
1187:PMC
1179:doi
1138:PMC
1130:doi
1089:PMC
1081:doi
1040:PMC
1032:doi
560:).
498:or
2392::
2337:Q#
1464:.
1454:.
1444:25
1442:.
1438:.
1415:.
1405:.
1395:.
1383:.
1379:.
1358:}}
1354:{{
1342:.
1332:.
1322:64
1320:.
1316:.
1293:.
1283:.
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1271:.
1267:.
1244:.
1234:.
1224:41
1222:.
1218:.
1195:.
1185:.
1175:36
1173:.
1169:.
1146:.
1136:.
1126:63
1124:.
1120:.
1097:.
1087:.
1077:15
1075:.
1071:.
1048:.
1038:.
1028:19
1026:.
1020:.
922:1ρ
908:1ρ
898:γB
890:1ρ
876:SL
710:1ρ
671:1ρ
664:.
651:1ρ
627:xy
531:A
513:.
59:.
2325:–
2316:–
2312:–
2013:2
2010:T
2003:1
2000:T
1524:e
1517:t
1510:v
1472:.
1450::
1423:.
1399::
1391::
1364:)
1350:.
1328::
1301:.
1279::
1252:.
1230::
1203:.
1181::
1154:.
1132::
1105:.
1083::
1056:.
1034::
1005:.
980:.
919:T
905:T
901:1
887:T
873:t
851:1
847:T
842:/
835:L
832:S
827:t
819:e
815:)
812:0
809:(
804:y
801:x
797:M
793:=
790:)
784:L
781:S
776:t
772:(
767:y
764:x
760:M
739:)
736:0
733:(
728:y
725:x
721:M
707:T
703:1
700:B
696:1
693:B
685:2
682:T
678:1
675:T
668:T
658:1
655:T
648:T
625:M
609:1
607:T
602:1
600:T
587:1
585:T
566:1
564:T
553:1
551:T
535:1
533:T
521:1
518:T
506:1
504:T
491:1
489:T
484:1
482:T
465:1
463:T
430:)
422:1
418:T
413:/
409:t
402:e
398:2
392:1
388:(
381:q
378:e
374:,
371:z
367:M
363:=
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357:t
354:(
349:z
345:M
322:q
319:e
315:,
312:z
308:M
301:=
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295:0
292:(
287:z
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258:1
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245:t
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226:0
223:(
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204:q
201:e
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