2098:
130:
exploit these spin-spin interactions to perform 2-qubit gates such as CNOTs that are necessary for universal quantum computation. In addition to the spin-spin interactions native to the molecule an external magnetic field can be applied (in NMR laboratories) and these impose single qubit gates. By exploiting the fact that different spins will experience different local fields we have control over the individual spins.
2088:
31:
138:. The other significant issue with regards to working close to thermal equilibrium is the mixedness of the state. This required the introduction of ensemble quantum processing, whose principal limitation is that as we introduce more logical qubits into our system we require larger samples in order to attain discernable signals during measurement.
647:
frequencies only, and therefore affects only that spin; and "hard" or nonselective pulses whose frequency range is broad enough to contain both resonant frequencies and therefore these pulses couple to both spins. For detailed examples of the effects of pulses on such a spin system, the reader is referred to
Section 2 of work by Cory et al.
886:
Cory, David G.; Fahmy, Amr F.; Havel, Timothy F. (1996). "Nuclear
Magnetic Resonance Spectroscopy: An Experimentally Accessible Paradigm for Quantum Computing". Phys-Comp 96, Proceedings of the Fourth Workshop on Physics and Computation, edited by T.Toffoli, M.Biafore, and J.Leao (New England Complex
646:
Control of a spin system can be realized by means of selective RF pulses applied perpendicular to the quantization axis. In the case of a two spin system as described above, we can distinguish two types of pulses: "soft" or spin-selective pulses, whose frequency range encompasses one of the resonant
146:
Solid state NMR (SSNMR), unlike LSNMR uses a solid state sample, for example a nitrogen vacancy diamond lattice rather than a liquid sample. This has many advantages such as lack of molecular diffusion decoherence, lower temperatures can be achieved to the point of suppressing phonon decoherence and
133:
The picture described above is far from realistic since we are treating a single molecule. NMR is performed on an ensemble of molecules, usually with as many as 10^15 molecules. This introduces complications to the model, one of which is introduction of decoherence. In particular we have the problem
386:
the temperature. That the initial state in NMR quantum computing is in thermal equilibrium is one of the main differences compared to other quantum computing techniques, where they are initialized in a pure state. Nevertheless, suitable mixed states are capable of reflecting quantum dynamics which
129:
systems. Depending on which nuclei we are considering they will have different energy levels and different interaction with its neighbours and so we can treat them as distinguishable qubits. In this system we tend to consider the inter-atomic bonds as the source of interactions between qubits and
147:
a greater variety of control operations that allow us to overcome one of the major problems of LSNMR that is initialisation. Moreover, as in a crystal structure we can localize precisely the qubits, we can measure each qubit individually, instead of having an ensemble measurement as in LSNMR.
134:
of an open quantum system interacting with a macroscopic number of particles near thermal equilibrium (~mK to ~300 K). This has led the development of decoherence suppression techniques that have spread to other disciplines such as
288:
641:
401:
Consider applying a magnetic field along the z axis, fixing this as the principal quantization axis, on a liquid sample. The
Hamiltonian for a single spin would be given by the Zeeman or chemical shift term:
100:
Initially the approach was to use the spin properties of atoms of particular molecules in a liquid sample as qubits - this is known as liquid state NMR (LSNMR). This approach has since been superseded by
455:
337:
1029:
Vandersypen LM, Steffen M, Breyta G, Yannoni CS, Sherwood MH, Chuang IL (2001). "Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance".
175:
in 1997. Some early success was obtained in performing quantum algorithms in NMR systems due to the relative maturity of NMR technology. For instance, in 2001 researchers at
183:
in a 7-qubit NMR quantum computer. However, even from the early days, it was recognized that NMR quantum computers would never be very useful due to the poor scaling of the
505:
1287:
485:
195:, thought to be required for quantum computation. Hence NMR quantum computing experiments are likely to have been only classical simulations of a quantum computer.
1249:
384:
360:
113:
The ideal picture of liquid state NMR (LSNMR) quantum information processing (QIP) is based on a molecule in which some of its atom's nuclei behave as spin-
1880:
1541:
217:
1442:
1767:
86:
532:
2122:
2091:
1277:
2127:
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1625:
1178:
Cory D.; et al. (1998). "Nuclear magnetic resonance spectroscopy: An experimentally accessible paradigm for quantum computing".
2101:
1989:
1242:
1575:
1917:
85:. The quantum states are probed through the nuclear magnetic resonances, allowing the system to be implemented as a variation of
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204:
1945:
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1585:
1359:
1969:
1314:
1258:
1414:
1117:
Menicucci NC, Caves CM (2002). "Local realistic model for the dynamics of bulk-ensemble NMR information processing".
1841:
1713:
1610:
1486:
1321:
395:
42:
191:
and others, shows that all experiments in liquid state bulk ensemble NMR quantum computing to date do not possess
1650:
1615:
1511:
1454:
1735:
1349:
1823:
1796:
1772:
1526:
1459:
1394:
1379:
1272:
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303:
163:. Manipulation of nuclear spins for quantum computing using liquid state NMR was introduced independently by
1974:
1708:
1600:
1570:
1369:
2044:
1808:
1801:
1548:
977:
394:(RF) pulses applied perpendicular to a strong, static magnetic field, created by a very large magnet. See
164:
1964:
1516:
1481:
656:
184:
1590:
1754:
1503:
1354:
1197:
1136:
1048:
911:
822:
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706:
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102:
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1187:
1160:
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1072:
1038:
1011:
846:
812:
782:
363:
1635:
968:
Gershenfeld, Neil A.; Chuang, Isaac L. (1997-01-17). "Bulk Spin-Resonance
Quantum Computation".
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nuclei, the system
Hamiltonian will have two chemical shift terms and a dipole coupling term:
507:
is the resonance frequency of the spin, which is proportional to the applied magnetic field.
490:
1720:
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1447:
1205:
1144:
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90:
74:
463:
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391:
1201:
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1052:
915:
826:
762:
710:
1955:
1932:
1899:
1703:
1580:
369:
345:
208:
78:
50:
1209:
718:
2116:
1777:
1595:
1521:
942:
899:
53:
17:
1164:
786:
1997:
1922:
1076:
1015:
850:
172:
1217:
1148:
1103:
770:
676:
30:
991:
691:
2007:
1861:
1399:
283:{\displaystyle \rho ={\frac {e^{-\beta H}}{\operatorname {Tr} (e^{-\beta H})}},}
2068:
2002:
1866:
1227:
746:
156:
999:
933:
834:
1851:
1156:
1068:
924:
778:
1007:
951:
842:
2036:
2012:
1871:
1836:
1192:
1131:
1043:
817:
636:{\displaystyle H=\omega _{1}I_{z1}+\omega _{2}I_{z2}+2J_{12}I_{z1}I_{z2}}
487:
is the operator for the z component of the nuclear angular momentum, and
135:
34:
2063:
1680:
38:
155:
The use of nuclear spins for quantum computing was first discussed by
2040:
1536:
203:
The ensemble is initialized to be the thermal equilibrium state (see
97:
of systems, in this case molecules, rather than a single pure state.
57:
1060:
510:
Considering the molecules in the liquid sample to contain two spin-
1309:
387:
lead to
Gershenfeld and Chuang to term them "pseudo-pure states".
82:
46:
803:(1995). "A Two-bit gates are universal for quantum computation".
2058:
1531:
1464:
60:
1231:
898:
Cory, David G.; Fahmy, Amr F.; Havel, Timothy F. (1997-03-04).
73:) is one of the several proposed approaches for constructing a
1675:
1660:
176:
1090:
Warren WS (1997). "The usefulness of NMR quantum computing".
297:
is the hamiltonian matrix of an individual molecule and
207:). In mathematical parlance, this state is given by the
677:"Nuclear Magnetic Resonance Quantum Computing (NMRQC)"
749:(1993). "A Potentially Realizable Quantum Computer".
535:
493:
466:
411:
372:
348:
306:
220:
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1988:
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1898:
1889:
1822:
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1689:
1649:
1561:
1502:
1428:
1337:
1265:
187:in such systems. More recent work, particularly by
27:
Proposed spin-based quantum computer implementation
635:
499:
479:
449:
378:
354:
331:
282:
390:Operations are performed on the ensemble through
900:"Ensemble quantum computing by NMR spectroscopy"
904:Proceedings of the National Academy of Sciences
105:NMR (SSNMR) as a means of quantum computation.
1243:
8:
89:. NMR differs from other implementations of
67:Nuclear magnetic resonance quantum computing
1895:
1499:
1250:
1236:
1228:
690:Neil Gershenfeld; Isaac L. Chuang (1998).
179:reported the successful implementation of
1191:
1130:
1042:
981:
941:
923:
816:
624:
611:
601:
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492:
471:
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371:
347:
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305:
259:
233:
227:
219:
450:{\displaystyle H=\mu B_{z}=I_{z}\omega }
332:{\displaystyle \beta ={\frac {1}{k\,T}}}
29:
1768:Continuous-variable quantum information
733:"Diamond Sparkles in Quantum Computing"
668:
87:nuclear magnetic resonance spectroscopy
81:states of nuclei within molecules as
45:implementation of quantum computing.
7:
963:
961:
887:Systems Institute. pp. 87–91.
692:"Quantum computing with molecules"
25:
719:10.1038/scientificamerican0698-66
2097:
2096:
2087:
2086:
867:(1995). "Quantum computation".
271:
252:
1:
1763:Adiabatic quantum computation
1210:10.1016/S0167-2789(98)00046-3
1149:10.1103/PhysRevLett.88.167901
1104:10.1126/science.277.5332.1688
771:10.1126/science.261.5128.1569
205:quantum statistical mechanics
1814:Topological quantum computer
992:10.1126/science.275.5298.350
2123:Quantum information science
2092:Quantum information science
1259:Quantum information science
199:Mathematical representation
2144:
2128:Nuclear magnetic resonance
1487:quantum gate teleportation
396:nuclear magnetic resonance
2082:
1616:Quantum Fourier transform
1512:Post-quantum cryptography
1455:Entanglement distillation
2102:Quantum mechanics topics
1797:Quantum machine learning
1773:One-way quantum computer
1626:Quantum phase estimation
1527:Quantum key distribution
1460:Monogamy of entanglement
835:10.1103/PhysRevA.51.1015
1709:Randomized benchmarking
1571:Amplitude amplification
1119:Physical Review Letters
500:{\displaystyle \omega }
1809:Quantum Turing machine
1802:quantum neural network
1549:Quantum secret sharing
925:10.1073/pnas.94.5.1634
637:
501:
481:
451:
380:
356:
333:
284:
167:, Fahmy and Havel and
63:
1881:Entanglement-assisted
1842:quantum convolutional
1517:Quantum coin flipping
1482:Quantum teleportation
1443:entanglement-assisted
1273:DiVincenzo's criteria
657:Kane quantum computer
638:
502:
482:
480:{\displaystyle I_{z}}
452:
381:
357:
334:
285:
185:signal-to-noise ratio
33:
18:NMR quantum computing
1692:processor benchmarks
1621:Quantum optimization
1504:Quantum cryptography
1315:physical vs. logical
533:
491:
464:
409:
370:
346:
304:
218:
193:quantum entanglement
1405:Quantum speed limit
1300:Quantum programming
1295:Quantum information
1202:1998PhyD..120...82C
1141:2002PhRvL..88p7901M
1098:(5332): 1688–1689.
1053:2001Natur.414..883V
916:1997PNAS...94.1634C
827:1995PhRvA..51.1015D
763:1993Sci...261.1569L
757:(5128): 1569–1571.
711:1998SciAm.278f..66G
699:Scientific American
93:in that it uses an
49:are implemented by
2054:Forest/Rigetti QCS
1790:quantum logic gate
1576:Bernstein–Vazirani
1563:Quantum algorithms
1438:Classical capacity
1322:Quantum processors
1305:Quantum simulation
633:
497:
477:
447:
376:
364:Boltzmann constant
352:
329:
280:
64:
2110:
2109:
2021:
2020:
1918:Linear optical QC
1699:Quantum supremacy
1653:complexity theory
1606:Quantum annealing
1557:
1556:
1494:Superdense coding
1283:Quantum computing
1037:(6866): 883–887.
976:(5298): 350–356.
379:{\displaystyle T}
355:{\displaystyle k}
327:
275:
91:quantum computers
16:(Redirected from
2135:
2100:
2099:
2090:
2089:
1896:
1826:error correction
1755:computing models
1721:Relaxation times
1611:Quantum counting
1500:
1448:quantum capacity
1395:No-teleportation
1380:No-communication
1252:
1245:
1238:
1229:
1222:
1221:
1195:
1193:quant-ph/9709001
1175:
1169:
1168:
1134:
1132:quant-ph/0111152
1114:
1108:
1107:
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1081:
1080:
1046:
1044:quant-ph/0112176
1026:
1020:
1019:
985:
965:
956:
955:
945:
927:
910:(5): 1634–1639.
895:
889:
888:
883:
877:
876:
865:David DiVincenzo
861:
855:
854:
820:
818:cond-mat/9407022
811:(2): 1015–1022.
801:David DiVincenzo
797:
791:
790:
743:
737:
736:
729:
723:
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244:
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228:
181:Shor's algorithm
161:David DiVincenzo
128:
126:
125:
122:
119:
109:Liquid state NMR
77:, that uses the
75:quantum computer
21:
2143:
2142:
2138:
2137:
2136:
2134:
2133:
2132:
2113:
2112:
2111:
2106:
2078:
2028:
2017:
1990:Superconducting
1984:
1950:
1941:Neutral atom QC
1933:Ultracold atoms
1927:
1892:implementations
1891:
1885:
1825:
1818:
1785:Quantum circuit
1753:
1747:
1741:
1731:
1691:
1685:
1652:
1645:
1601:Hidden subgroup
1553:
1542:other protocols
1498:
1475:quantum network
1470:Quantum channel
1430:
1424:
1370:No-broadcasting
1360:Gottesman–Knill
1333:
1261:
1256:
1226:
1225:
1186:(1–2): 82–101.
1177:
1176:
1172:
1116:
1115:
1111:
1089:
1088:
1084:
1061:10.1038/414883a
1028:
1027:
1023:
967:
966:
959:
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892:
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863:
862:
858:
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489:
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467:
462:
461:
434:
421:
407:
406:
392:radio frequency
368:
367:
344:
343:
318:
302:
301:
255:
245:
229:
216:
215:
201:
153:
144:
142:Solid state NMR
123:
120:
117:
116:
114:
111:
28:
23:
22:
15:
12:
11:
5:
2141:
2139:
2131:
2130:
2125:
2115:
2114:
2108:
2107:
2105:
2104:
2094:
2083:
2080:
2079:
2077:
2076:
2074:many others...
2071:
2066:
2061:
2056:
2047:
2033:
2031:
2023:
2022:
2019:
2018:
2016:
2015:
2010:
2005:
2000:
1994:
1992:
1986:
1985:
1983:
1982:
1977:
1972:
1967:
1961:
1959:
1952:
1951:
1949:
1948:
1946:Trapped-ion QC
1943:
1937:
1935:
1929:
1928:
1926:
1925:
1920:
1915:
1910:
1904:
1902:
1900:Quantum optics
1893:
1887:
1886:
1884:
1883:
1878:
1877:
1876:
1869:
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1854:
1849:
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1816:
1811:
1806:
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1804:
1794:
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1770:
1765:
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1749:
1748:
1746:
1745:
1744:
1743:
1739:
1733:
1729:
1718:
1717:
1716:
1706:
1704:Quantum volume
1701:
1695:
1693:
1687:
1686:
1684:
1683:
1678:
1673:
1668:
1663:
1657:
1655:
1647:
1646:
1644:
1643:
1638:
1633:
1628:
1623:
1618:
1613:
1608:
1603:
1598:
1593:
1588:
1583:
1581:Boson sampling
1578:
1573:
1567:
1565:
1559:
1558:
1555:
1554:
1552:
1551:
1546:
1545:
1544:
1539:
1534:
1524:
1519:
1514:
1508:
1506:
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1491:
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1489:
1479:
1478:
1477:
1467:
1462:
1457:
1452:
1451:
1450:
1445:
1434:
1432:
1426:
1425:
1423:
1422:
1417:
1415:Solovay–Kitaev
1412:
1407:
1402:
1397:
1392:
1387:
1382:
1377:
1372:
1367:
1362:
1357:
1352:
1347:
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1339:
1335:
1334:
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1331:
1330:
1329:
1319:
1318:
1317:
1307:
1302:
1297:
1292:
1291:
1290:
1280:
1275:
1269:
1267:
1263:
1262:
1257:
1255:
1254:
1247:
1240:
1232:
1224:
1223:
1170:
1125:(16): 167901.
1109:
1082:
1021:
983:10.1.1.28.8877
957:
890:
878:
856:
792:
738:
724:
682:
667:
666:
664:
661:
660:
659:
652:
649:
644:
643:
630:
627:
623:
617:
614:
610:
604:
600:
596:
593:
588:
585:
581:
575:
571:
567:
562:
559:
555:
549:
545:
541:
538:
496:
474:
470:
458:
457:
446:
441:
437:
433:
428:
424:
420:
417:
414:
375:
351:
340:
339:
325:
321:
317:
312:
309:
291:
290:
279:
273:
268:
265:
262:
258:
254:
251:
248:
242:
239:
236:
232:
226:
223:
209:density matrix
200:
197:
152:
149:
143:
140:
110:
107:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2140:
2129:
2126:
2124:
2121:
2120:
2118:
2103:
2095:
2093:
2085:
2084:
2081:
2075:
2072:
2070:
2067:
2065:
2062:
2060:
2057:
2055:
2051:
2048:
2046:
2042:
2038:
2035:
2034:
2032:
2030:
2024:
2014:
2011:
2009:
2006:
2004:
2001:
1999:
1996:
1995:
1993:
1991:
1987:
1981:
1978:
1976:
1973:
1971:
1970:Spin qubit QC
1968:
1966:
1963:
1962:
1960:
1957:
1953:
1947:
1944:
1942:
1939:
1938:
1936:
1934:
1930:
1924:
1921:
1919:
1916:
1914:
1911:
1909:
1906:
1905:
1903:
1901:
1897:
1894:
1888:
1882:
1879:
1875:
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1870:
1868:
1865:
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1840:
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1832:
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1821:
1815:
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1807:
1803:
1800:
1799:
1798:
1795:
1791:
1788:
1787:
1786:
1783:
1779:
1778:cluster state
1776:
1775:
1774:
1771:
1769:
1766:
1764:
1761:
1760:
1758:
1756:
1750:
1742:
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1586:Deutsch–Jozsa
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1522:Quantum money
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76:
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68:
62:
59:
56:of the black
55:
52:
48:
44:
40:
36:
32:
19:
1998:Charge qubit
1979:
1923:KLM protocol
1872:
1736:
1726:
1420:Purification
1350:Eastin–Knill
1183:
1179:
1173:
1122:
1118:
1112:
1095:
1091:
1085:
1034:
1030:
1024:
973:
969:
907:
903:
893:
881:
872:
868:
859:
808:
805:Phys. Rev. A
804:
795:
754:
750:
741:
727:
705:(6): 66–71.
702:
698:
685:
671:
645:
509:
459:
400:
389:
341:
294:
292:
202:
154:
145:
136:trapped ions
132:
112:
99:
70:
66:
65:
2029:programming
2008:Phase qubit
1913:Circuit QED
1385:No-deleting
1327:cloud-based
169:Gershenfeld
103:solid state
2117:Categories
2069:libquantum
2003:Flux qubit
1908:Cavity QED
1857:Bacon–Shor
1847:stabilizer
1375:No-cloning
747:Seth Lloyd
663:References
157:Seth Lloyd
1975:NV center
1410:Threshold
1390:No-hiding
1355:Gleason's
1180:Physica D
1000:0036-8075
978:CiteSeerX
934:0027-8424
570:ω
544:ω
495:ω
445:ω
419:μ
308:β
264:β
261:−
250:
238:β
235:−
222:ρ
2037:OpenQASM
2013:Transmon
1890:Physical
1690:Quantum
1591:Grover's
1365:Holevo's
1338:Theorems
1288:timeline
1278:NISQ era
1165:14583916
1157:11955265
1069:11780055
787:38100483
779:17798117
651:See also
95:ensemble
41:used in
35:Molecule
2027:Quantum
1965:Kane QC
1824:Quantum
1752:Quantum
1681:PostBQP
1651:Quantum
1636:Simon's
1429:Quantum
1266:General
1198:Bibcode
1137:Bibcode
1092:Science
1077:4400832
1049:Bibcode
1016:2262147
1008:8994025
970:Science
952:9050830
912:Bibcode
875:(5234).
869:Science
851:2317415
843:9911679
823:Bibcode
759:Bibcode
751:Science
707:Bibcode
524:
512:
362:is the
159:and by
151:History
127:
115:
39:alanine
2045:IBM QX
2041:Qiskit
1980:NMR QC
1958:-based
1862:Steane
1833:Codes
1631:Shor's
1537:SARG04
1345:Bell's
1218:219400
1216:
1163:
1155:
1075:
1067:
1031:Nature
1014:
1006:
998:
980:
950:
940:
932:
849:
841:
785:
777:
460:where
342:where
293:where
173:Chuang
83:qubits
58:carbon
54:states
47:Qubits
1867:Toric
1310:Qubit
1214:S2CID
1188:arXiv
1161:S2CID
1127:arXiv
1073:S2CID
1039:arXiv
1012:S2CID
943:19968
847:S2CID
813:arXiv
783:S2CID
695:(PDF)
189:Caves
71:NMRQC
61:atoms
2059:Cirq
2050:Quil
1956:Spin
1852:Shor
1532:BB84
1465:LOCC
1153:PMID
1065:PMID
1004:PMID
996:ISSN
948:PMID
930:ISSN
839:PMID
775:PMID
366:and
171:and
165:Cory
79:spin
51:spin
1873:gnu
1837:CSS
1714:XEB
1676:QMA
1671:QIP
1666:EQP
1661:BQP
1641:VQE
1596:HHL
1400:PBR
1206:doi
1184:120
1145:doi
1100:doi
1096:277
1057:doi
1035:414
988:doi
974:275
938:PMC
920:doi
873:270
831:doi
767:doi
755:261
715:doi
703:278
177:IBM
43:NMR
37:of
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2064:Q#
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