4053:
2085:
4043:
2741:(rate at which the qubit relaxes into modes other than the resonator mode) the strong coupling regime is reached. Due to the high fields and low losses of the coplanar resonators together with the large dipole moments and long decoherence times of the qubits, the strong coupling regime can easily be reached in the field of circuit QED. Combination of the Jaynes–Cummings model and the coupled cavities leads to the
1592:
1868:
1376:
2080:{\displaystyle {\mathcal {H}}_{\text{JC}}=\underbrace {\hbar \omega _{r}\left(a^{\dagger }a+{\frac {1}{2}}\right)} _{\text{cavity term}}+\underbrace {{\frac {1}{2}}\hbar \omega _{a}\sigma _{z}} _{\text{atomic term}}+\underbrace {\hbar g\left(\sigma _{+}a+a^{\dagger }\sigma _{-}\right)} _{\text{interaction term}}}
2484:
1587:{\displaystyle \lambda /2:\quad \nu _{n}={\frac {c}{\sqrt {\varepsilon _{\text{eff}}}}}{\frac {n}{2\ell }}\quad (n=1,2,3,\ldots )\qquad \lambda /4:\quad \nu _{n}={\frac {c}{\sqrt {\varepsilon _{\text{eff}}}}}{\frac {2n+1}{4\ell }}\quad (n=0,1,2,\ldots )}
1169:
106:
1011:
of the peripheric microwave equipment to avoid partial reflection of the signal. The electric field is basically confined between the center conductor and the ground planes resulting in a very small mode volume
905:
coherently couples to a quantum object (atom). In contrast to cavity QED, the photon is stored in a one-dimensional on-chip resonator and the quantum object is no natural atom but an artificial one. These
2387:
2679:
2604:
1792:
is tuned. Due to the nonlinearity of the
Josephson junctions the Cooper-pair box shows an atom like energy spectrum. Other more recent examples for qubits used in circuit QED are so called
1621:
2298:
2558:
1250:
2376:
2350:
2324:
2254:
1751:
1699:
2516:
2141:
2223:
2196:
2114:
1790:
1223:
3164:
2639:
1313:
1285:
2739:
1009:
1863:. The three terms of the Jaynes–Cummings model can be ascribed to a cavity term, which is mimicked by a harmonic oscillator, an atomic term and an interaction term.
1192:
3242:
1337:
1091:
1064:
1037:
1725:
3204:
2719:
2699:
2161:
1842:
1822:
1673:
1361:
372:
3934:
873:
3835:
3496:
1098:
2794:
Alexandre Blais; et al. (2004). "Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computing".
1367:
at its ends. Quarter-wavelength resonators are short pieces of a coplanar line, which are shorted to ground on one end and capacitively coupled to a
3397:
580:
124:
36:
3722:
2742:
353:
536:
4077:
4046:
3232:
2606:) depending on the atomic state. This provides the possibility to read out the atomic (qubit) state by measuring the transition frequency.
459:
4004:
3580:
2889:
Luigi
Frunzio; et al. (2005). "Fabrication and Characterization of Superconducting Circuit QED Devices for Quantum Computation".
2479:{\displaystyle \mid n,\pm \rangle ={\frac {1}{\sqrt {2}}}\left(\mid g\rangle \mid n\rangle \pm \mid e\rangle \mid n-1\rangle \right)}
952:
4056:
3944:
3197:
3005:
119:
3530:
3872:
208:
315:
295:
3595:
3575:
2754:
2164:
866:
163:
3374:
2850:
285:
3862:
3024:; et al. (2004). "Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics".
898:
555:
3895:
3717:
3620:
3281:
595:
333:
233:
348:
3900:
3768:
3359:
3190:
531:
526:
497:
129:
3680:
3540:
3314:
1804:
in a superconducting loop intersected by
Josephson junctions). All of these devices feature very large dipole moments
310:
300:
3924:
3269:
3213:
2644:
915:
565:
3369:
2563:
482:
3796:
3668:
3565:
3441:
3276:
2944:
1253:
859:
511:
1860:
430:
3605:
3570:
3466:
3409:
1754:
516:
477:
405:
328:
188:
3690:
3304:
3778:
3751:
3727:
3481:
3414:
3349:
3334:
2775:
1599:
988:
600:
3227:
2263:
3929:
3663:
3555:
3525:
3324:
3155:
3035:
1195:
769:
487:
445:
395:
343:
109:
2870:
3999:
3763:
3756:
3503:
774:
492:
400:
320:
290:
253:
3153:(1963). "Comparison of Quantum and Semiclassical Radiation Theories with Application to the Beam Maser".
914:
devices which exhibit an atom-like energy spectrum. The field of circuit QED is a prominent example for
3919:
3471:
3436:
2379:
243:
228:
3545:
2525:
155:
1228:
3709:
3458:
3309:
3112:
3049:
2962:
2908:
2815:
956:
925:
In the late 2010s decade, experiments involving cQED in 3 dimensions have demonstrated deterministic
804:
560:
472:
198:
3811:
2355:
2329:
2303:
2232:
1730:
1678:
4028:
3981:
3585:
3339:
3319:
3254:
3249:
3091:
Jens Koch; et al. (2007). "Charge insensitive qubit design derived from the Cooper pair box".
2942:
M. Göppl; et al. (2008). "Coplanar waveguide resonators for circuit quantum electrodynamics".
2491:
659:
467:
385:
213:
193:
145:
2119:
3744:
3392:
3329:
3128:
3102:
3073:
3039:
2978:
2952:
2924:
2898:
2831:
2805:
2519:
2201:
2174:
2092:
1848:
1768:
1201:
945:
926:
911:
380:
305:
238:
150:
3590:
2612:
1290:
1262:
959:
planes. This planar structure is put on a dielectric substrate by a photolithographic process.
4008:
3653:
3560:
3517:
3448:
3364:
3344:
3299:
3259:
3237:
3093:
3065:
3001:
2796:
2163:
are photon creation and annihilation operators, respectively. The atomic term is given by the
960:
942:
814:
789:
729:
724:
624:
590:
570:
168:
27:
2724:
994:
3675:
3625:
3402:
3168:
3120:
3057:
3026:
2970:
2916:
2823:
1762:
1648:
1177:
919:
819:
809:
799:
699:
679:
664:
634:
502:
390:
1322:
1069:
1042:
1015:
3801:
3739:
3429:
3424:
2641:(for electric dipolar coupling). If the coupling is much larger than the cavity loss rate
2257:
1636:
907:
844:
714:
694:
440:
280:
1704:
3116:
3053:
2966:
2912:
2819:
3910:
3887:
3854:
3658:
3535:
3150:
2704:
2684:
2226:
2146:
1827:
1807:
1658:
1346:
902:
894:
779:
739:
719:
689:
669:
619:
585:
435:
425:
218:
2721:, the longer the photon remains inside the resonator) as well as the decoherence rate
4071:
3732:
3550:
3476:
893:) provides a means of studying the fundamental interaction between light and matter (
839:
834:
764:
734:
704:
575:
521:
248:
223:
3132:
3077:
2982:
2928:
2835:
1319:
resonators are made by breaking the center conductor at two spots with the distance
3952:
3877:
3146:
1844:
1801:
1640:
1624:
829:
824:
759:
744:
709:
203:
1164:{\displaystyle E_{0}={\sqrt {\frac {\hbar \omega _{r}}{2\varepsilon _{0}V_{m}}}}}
3962:
3816:
3354:
3021:
1644:
794:
749:
684:
639:
3124:
2872:
Teleported operations between logical qubits in circuit quantum electrodynamics
2827:
2518:. If the detuning is significantly larger than the combined cavity and atomic
4023:
3957:
3821:
3182:
1797:
1316:
784:
754:
674:
649:
644:
629:
2920:
955:. Coplanar waveguides consist of a signal carrying centerline flanked by two
101:{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }
3806:
1368:
1340:
964:
948:
275:
3172:
3069:
1796:
qubits (more charge noise insensitive compared to the Cooper-pair box) and
971:(Nb). Dielectrics typically used as substrates are either surface oxidized
3991:
3967:
3826:
3791:
3107:
3044:
2903:
2810:
2168:
1859:
The full quantum description of matter-light interaction is given by the
1793:
1364:
976:
654:
3061:
4018:
3635:
1758:
991:
is given by the geometric properties, which are chosen to match the 50
972:
968:
2974:
3995:
3491:
1651:
to a gated superconducting island. The state of the Cooper-pair box (
1635:
The first realized artificial atom in circuit QED was the so-called
1066:(compared to three-dimensional cavities). Mathematically, the field
3264:
2957:
2300:) the interaction lifts the degeneracy of the photon number state
1652:
930:
951:
resonators, which are two-dimensional microwave analogues of the
4013:
3486:
3419:
1343:
coupled to the input and output and represents a resonator with
3186:
1259:
One can distinguish between two different types of resonators:
3630:
3615:
2378:
and pairs of dressed states are formed. These new states are
2852:
Multiqubit experiments in 3D circuit quantum electrodynamics
1875:
1339:. The resulting piece of center conductor is in this way
1039:
which gives rise to very high electric fields per photon
2260:) for the atomic states. For the case of zero detuning (
1655:) is given by the number of Cooper pairs on the island (
2727:
2707:
2687:
2647:
2615:
2566:
2528:
2494:
2390:
2358:
2332:
2306:
2266:
2235:
2204:
2177:
2149:
2122:
2095:
1871:
1830:
1810:
1771:
1733:
1707:
1681:
1661:
1602:
1379:
1371:
on the other. The resonance frequencies are given by
1349:
1325:
1293:
1265:
1231:
1204:
1180:
1101:
1072:
1045:
1018:
997:
39:
16:
Means of studying the interaction of light and matter
2998:
Coplanar
Waveguide Circuits, Components, and Systems
3980:
3943:
3909:
3886:
3853:
3844:
3777:
3706:
3644:
3604:
3516:
3457:
3383:
3292:
3220:
2733:
2713:
2693:
2673:
2633:
2598:
2552:
2510:
2478:
2370:
2344:
2318:
2292:
2248:
2217:
2190:
2155:
2135:
2108:
2079:
1836:
1816:
1784:
1745:
1719:
1693:
1667:
1615:
1586:
1355:
1331:
1307:
1279:
1244:
1217:
1186:
1163:
1085:
1058:
1031:
1003:
100:
1851:counterparts for the light field in circuit QED.
2674:{\displaystyle \kappa ={\frac {\omega _{r}}{Q}}}
2599:{\displaystyle \Delta =\omega _{a}-\omega _{r}}
2891:IEEE Transactions on Applied Superconductivity
1847:), which qualifies them as extremely suitable
941:The resonant devices used for circuit QED are
3198:
2116:is the resonance frequency of the cavity and
867:
8:
2468:
2453:
2441:
2432:
2403:
2365:
2339:
2313:
1800:(whose state is given by the direction of a
1740:
1688:
95:
69:
3850:
3454:
3205:
3191:
3183:
874:
860:
18:
3106:
3043:
2956:
2902:
2809:
2726:
2706:
2686:
2660:
2654:
2646:
2614:
2590:
2577:
2565:
2542:
2536:
2527:
2501:
2493:
2409:
2389:
2357:
2331:
2305:
2284:
2271:
2265:
2240:
2234:
2209:
2203:
2182:
2176:
2148:
2127:
2121:
2100:
2094:
2071:
2054:
2044:
2028:
2010:
2000:
1988:
1978:
1961:
1958:
1948:
1927:
1915:
1900:
1890:
1880:
1874:
1873:
1870:
1829:
1809:
1776:
1770:
1732:
1706:
1680:
1660:
1616:{\displaystyle \varepsilon _{\text{eff}}}
1607:
1601:
1524:
1515:
1505:
1496:
1480:
1427:
1418:
1408:
1399:
1383:
1378:
1348:
1324:
1297:
1292:
1269:
1264:
1236:
1230:
1209:
1203:
1179:
1151:
1141:
1126:
1115:
1106:
1100:
1077:
1071:
1050:
1044:
1023:
1017:
996:
87:
76:
75:
61:
46:
38:
2522:the cavity states are merely shifted by
3723:Continuous-variable quantum information
2766:
2293:{\displaystyle \omega _{r}=\omega _{a}}
2013:
1971:
1893:
1181:
1119:
901:, a single photon within a single mode
43:
26:
1765:(flux bias) the transition frequency
918:and a promising candidate for future
7:
2256:are raising and lowering operators (
2849:Blumoff, Jacob Z. (December 2017).
2198:being the transition frequency and
2567:
2547:
1675:Cooper pairs for the ground state
998:
406:Sum-over-histories (path integral)
92:
66:
22:Part of a series of articles about
14:
2553:{\displaystyle \pm g^{2}/\Delta }
1643:. In this device, a reservoir of
929:and other operations on multiple
4052:
4051:
4042:
4041:
1245:{\displaystyle \varepsilon _{0}}
2777:Circuit Quantum Electrodynamics
2774:Schuster, David I. (May 2007).
2755:Superconducting radio frequency
2488:and are energetically split by
1623:being the effective dielectric
1550:
1491:
1476:
1442:
1394:
887:Circuit quantum electrodynamics
2878:(PhD thesis). Yale University.
2858:(PhD thesis). Yale University.
2783:(PhD thesis). Yale University.
2426:
2391:
2371:{\displaystyle \mid e\rangle }
2359:
2345:{\displaystyle \mid g\rangle }
2333:
2319:{\displaystyle \mid n\rangle }
2307:
2249:{\displaystyle \sigma _{\pm }}
1824:(up to 10 times that of large
1746:{\displaystyle \mid e\rangle }
1734:
1694:{\displaystyle \mid g\rangle }
1682:
1581:
1551:
1473:
1443:
1225:is the angular frequency, and
916:quantum information processing
899:cavity quantum electrodynamics
556:Relativistic quantum mechanics
88:
81:
62:
1:
3718:Adiabatic quantum computation
3000:. John Wiley & Sons Inc.
2743:Jaynes–Cummings–Hubbard model
2511:{\displaystyle 2g{\sqrt {n}}}
596:Quantum statistical mechanics
3769:Topological quantum computer
2136:{\displaystyle a^{\dagger }}
4078:Quantum information science
4047:Quantum information science
3214:Quantum information science
2869:Chou, Kevin S. (May 2018).
2218:{\displaystyle \sigma _{z}}
2191:{\displaystyle \omega _{a}}
2109:{\displaystyle \omega _{r}}
1785:{\displaystyle \omega _{a}}
1218:{\displaystyle \omega _{r}}
566:Quantum information science
4094:
3442:quantum gate teleportation
3125:10.1103/PhysRevA.76.042319
2996:Simons, Rainee N. (2001).
2828:10.1103/PhysRevA.69.062320
2634:{\displaystyle g=E\cdot d}
2382:of cavity and atom states
1308:{\displaystyle \lambda /4}
1280:{\displaystyle \lambda /2}
1254:permittivity of free space
963:materials used are mostly
953:Fabry–Pérot interferometer
4037:
3571:Quantum Fourier transform
3467:Post-quantum cryptography
3410:Entanglement distillation
2609:The coupling is given by
4057:Quantum mechanics topics
3752:Quantum machine learning
3728:One-way quantum computer
3581:Quantum phase estimation
3482:Quantum key distribution
3415:Monogamy of entanglement
2921:10.1109/TASC.2005.850084
1631:Artificial atoms, Qubits
601:Quantum machine learning
354:Wheeler's delayed-choice
3664:Randomized benchmarking
3526:Amplitude amplification
3156:Proceedings of the IEEE
3036:Nature Publishing Group
2951:(11): 113904–113904–8.
2734:{\displaystyle \gamma }
1196:reduced Planck constant
1004:{\displaystyle \Omega }
311:Leggett–Garg inequality
3764:Quantum Turing machine
3757:quantum neural network
3504:Quantum secret sharing
3173:10.1109/proc.1963.1664
2735:
2715:
2695:
2675:
2635:
2600:
2554:
2512:
2480:
2372:
2346:
2326:and the atomic states
2320:
2294:
2250:
2219:
2192:
2157:
2137:
2110:
2081:
1838:
1818:
1786:
1753:). By controlling the
1747:
1727:for the excited state
1721:
1695:
1669:
1617:
1588:
1357:
1333:
1309:
1281:
1246:
1219:
1188:
1187:{\displaystyle \hbar }
1165:
1087:
1060:
1033:
1005:
897:). As in the field of
102:
3836:Entanglement-assisted
3797:quantum convolutional
3472:Quantum coin flipping
3437:Quantum teleportation
3398:entanglement-assisted
3228:DiVincenzo's criteria
2736:
2716:
2696:
2676:
2636:
2601:
2555:
2513:
2481:
2373:
2347:
2321:
2295:
2251:
2220:
2193:
2158:
2138:
2111:
2082:
1861:Jaynes–Cummings model
1839:
1819:
1787:
1748:
1722:
1696:
1670:
1618:
1589:
1358:
1334:
1332:{\displaystyle \ell }
1310:
1282:
1247:
1220:
1189:
1166:
1088:
1086:{\displaystyle E_{0}}
1061:
1059:{\displaystyle E_{0}}
1034:
1032:{\displaystyle V_{m}}
1006:
296:Elitzur–Vaidman
286:Davisson–Germer
103:
3647:processor benchmarks
3576:Quantum optimization
3459:Quantum cryptography
3270:physical vs. logical
2725:
2705:
2685:
2645:
2613:
2564:
2526:
2492:
2388:
2356:
2330:
2304:
2264:
2233:
2202:
2175:
2147:
2120:
2093:
2089:In this formulation
1869:
1828:
1808:
1769:
1731:
1705:
1679:
1659:
1639:, also known as the
1600:
1377:
1347:
1323:
1291:
1263:
1229:
1202:
1178:
1099:
1070:
1043:
1016:
995:
561:Quantum field theory
473:Consistent histories
110:Schrödinger equation
37:
3360:Quantum speed limit
3255:Quantum programming
3250:Quantum information
3117:2007PhRvA..76d2319K
3062:10.1038/nature02851
3054:2004Natur.431..162W
2967:2008JAP...104k3904G
2913:2005ITAS...15..860F
2820:2004PhRvA..69f2320B
2560:(with the detuning
1720:{\displaystyle N+1}
1649:Josephson junctions
920:quantum computation
349:Stern–Gerlach
146:Classical mechanics
4009:Forest/Rigetti QCS
3745:quantum logic gate
3531:Bernstein–Vazirani
3518:Quantum algorithms
3393:Classical capacity
3277:Quantum processors
3260:Quantum simulation
2731:
2711:
2691:
2671:
2631:
2596:
2550:
2508:
2476:
2368:
2342:
2316:
2290:
2246:
2215:
2188:
2153:
2133:
2106:
2077:
2076:
2069:
2005:
1998:
1953:
1946:
1834:
1814:
1782:
1743:
1717:
1691:
1665:
1613:
1584:
1353:
1329:
1305:
1277:
1242:
1215:
1184:
1161:
1083:
1056:
1029:
1001:
946:coplanar waveguide
927:gate teleportation
537:Von Neumann–Wigner
517:Objective-collapse
316:Mach–Zehnder
306:Leggett inequality
301:Franck–Hertz
151:Old quantum theory
98:
4065:
4064:
3976:
3975:
3873:Linear optical QC
3654:Quantum supremacy
3608:complexity theory
3561:Quantum annealing
3512:
3511:
3449:Superdense coding
3238:Quantum computing
2975:10.1063/1.3010859
2714:{\displaystyle Q}
2694:{\displaystyle Q}
2669:
2506:
2419:
2418:
2156:{\displaystyle a}
2074:
2011:
2009:
2003:
1969:
1959:
1957:
1951:
1935:
1891:
1889:
1883:
1837:{\displaystyle n}
1817:{\displaystyle d}
1668:{\displaystyle N}
1610:
1548:
1522:
1521:
1518:
1440:
1425:
1424:
1421:
1356:{\displaystyle E}
1315:resonators. Half-
1159:
1158:
884:
883:
591:Scattering theory
571:Quantum computing
344:Schrödinger's cat
276:Bell's inequality
84:
59:
28:Quantum mechanics
4085:
4055:
4054:
4045:
4044:
3851:
3781:error correction
3710:computing models
3676:Relaxation times
3566:Quantum counting
3455:
3403:quantum capacity
3350:No-teleportation
3335:No-communication
3207:
3200:
3193:
3184:
3177:
3176:
3143:
3137:
3136:
3110:
3108:cond-mat/0703002
3088:
3082:
3081:
3047:
3045:cond-mat/0407325
3018:
3012:
3011:
2993:
2987:
2986:
2960:
2939:
2933:
2932:
2906:
2904:cond-mat/0411708
2886:
2880:
2879:
2877:
2866:
2860:
2859:
2857:
2846:
2840:
2839:
2813:
2811:cond-mat/0402216
2791:
2785:
2784:
2782:
2771:
2740:
2738:
2737:
2732:
2720:
2718:
2717:
2712:
2700:
2698:
2697:
2692:
2681:(quality factor
2680:
2678:
2677:
2672:
2670:
2665:
2664:
2655:
2640:
2638:
2637:
2632:
2605:
2603:
2602:
2597:
2595:
2594:
2582:
2581:
2559:
2557:
2556:
2551:
2546:
2541:
2540:
2517:
2515:
2514:
2509:
2507:
2502:
2485:
2483:
2482:
2477:
2475:
2471:
2420:
2414:
2410:
2377:
2375:
2374:
2369:
2351:
2349:
2348:
2343:
2325:
2323:
2322:
2317:
2299:
2297:
2296:
2291:
2289:
2288:
2276:
2275:
2258:ladder operators
2255:
2253:
2252:
2247:
2245:
2244:
2229:. The operators
2224:
2222:
2221:
2216:
2214:
2213:
2197:
2195:
2194:
2189:
2187:
2186:
2162:
2160:
2159:
2154:
2142:
2140:
2139:
2134:
2132:
2131:
2115:
2113:
2112:
2107:
2105:
2104:
2086:
2084:
2083:
2078:
2075:
2073:interaction term
2072:
2070:
2065:
2064:
2060:
2059:
2058:
2049:
2048:
2033:
2032:
2004:
2001:
1999:
1994:
1993:
1992:
1983:
1982:
1970:
1962:
1952:
1949:
1947:
1942:
1941:
1937:
1936:
1928:
1920:
1919:
1905:
1904:
1885:
1884:
1881:
1879:
1878:
1843:
1841:
1840:
1835:
1823:
1821:
1820:
1815:
1791:
1789:
1788:
1783:
1781:
1780:
1763:Josephson energy
1752:
1750:
1749:
1744:
1726:
1724:
1723:
1718:
1700:
1698:
1697:
1692:
1674:
1672:
1671:
1666:
1622:
1620:
1619:
1614:
1612:
1611:
1608:
1593:
1591:
1590:
1585:
1549:
1547:
1539:
1525:
1523:
1520:
1519:
1516:
1510:
1506:
1501:
1500:
1484:
1441:
1439:
1428:
1426:
1423:
1422:
1419:
1413:
1409:
1404:
1403:
1387:
1362:
1360:
1359:
1354:
1338:
1336:
1335:
1330:
1314:
1312:
1311:
1306:
1301:
1286:
1284:
1283:
1278:
1273:
1251:
1249:
1248:
1243:
1241:
1240:
1224:
1222:
1221:
1216:
1214:
1213:
1193:
1191:
1190:
1185:
1170:
1168:
1167:
1162:
1160:
1157:
1156:
1155:
1146:
1145:
1132:
1131:
1130:
1117:
1116:
1111:
1110:
1093:can be found as
1092:
1090:
1089:
1084:
1082:
1081:
1065:
1063:
1062:
1057:
1055:
1054:
1038:
1036:
1035:
1030:
1028:
1027:
1010:
1008:
1007:
1002:
908:artificial atoms
876:
869:
862:
503:Superdeterminism
156:Bra–ket notation
107:
105:
104:
99:
91:
86:
85:
77:
65:
60:
58:
47:
19:
4093:
4092:
4088:
4087:
4086:
4084:
4083:
4082:
4068:
4067:
4066:
4061:
4033:
3983:
3972:
3945:Superconducting
3939:
3905:
3896:Neutral atom QC
3888:Ultracold atoms
3882:
3847:implementations
3846:
3840:
3780:
3773:
3740:Quantum circuit
3708:
3702:
3696:
3686:
3646:
3640:
3607:
3600:
3556:Hidden subgroup
3508:
3497:other protocols
3453:
3430:quantum network
3425:Quantum channel
3385:
3379:
3325:No-broadcasting
3315:Gottesman–Knill
3288:
3216:
3211:
3181:
3180:
3145:
3144:
3140:
3090:
3089:
3085:
3020:
3019:
3015:
3008:
2995:
2994:
2990:
2941:
2940:
2936:
2888:
2887:
2883:
2875:
2868:
2867:
2863:
2855:
2848:
2847:
2843:
2793:
2792:
2788:
2780:
2773:
2772:
2768:
2763:
2751:
2723:
2722:
2703:
2702:
2683:
2682:
2656:
2643:
2642:
2611:
2610:
2586:
2573:
2562:
2561:
2532:
2524:
2523:
2490:
2489:
2425:
2421:
2386:
2385:
2354:
2353:
2328:
2327:
2302:
2301:
2280:
2267:
2262:
2261:
2236:
2231:
2230:
2205:
2200:
2199:
2178:
2173:
2172:
2145:
2144:
2123:
2118:
2117:
2096:
2091:
2090:
2050:
2040:
2024:
2023:
2019:
2012:
1984:
1974:
1960:
1911:
1910:
1906:
1896:
1892:
1872:
1867:
1866:
1857:
1826:
1825:
1806:
1805:
1772:
1767:
1766:
1729:
1728:
1703:
1702:
1677:
1676:
1657:
1656:
1647:is coupled via
1637:Cooper-pair box
1633:
1627:of the device.
1603:
1598:
1597:
1540:
1526:
1511:
1492:
1432:
1414:
1395:
1375:
1374:
1345:
1344:
1321:
1320:
1289:
1288:
1261:
1260:
1232:
1227:
1226:
1205:
1200:
1199:
1176:
1175:
1147:
1137:
1133:
1122:
1118:
1102:
1097:
1096:
1073:
1068:
1067:
1046:
1041:
1040:
1019:
1014:
1013:
993:
992:
986:
982:
961:Superconducting
943:superconducting
939:
880:
851:
850:
849:
614:
606:
605:
551:
550:Advanced topics
543:
542:
541:
493:Hidden-variable
483:de Broglie–Bohm
462:
460:Interpretations
452:
451:
450:
420:
412:
411:
410:
368:
360:
359:
358:
325:
281:CHSH inequality
270:
262:
261:
260:
189:Complementarity
183:
175:
174:
173:
141:
112:
51:
35:
34:
17:
12:
11:
5:
4091:
4089:
4081:
4080:
4070:
4069:
4063:
4062:
4060:
4059:
4049:
4038:
4035:
4034:
4032:
4031:
4029:many others...
4026:
4021:
4016:
4011:
4002:
3988:
3986:
3978:
3977:
3974:
3973:
3971:
3970:
3965:
3960:
3955:
3949:
3947:
3941:
3940:
3938:
3937:
3932:
3927:
3922:
3916:
3914:
3907:
3906:
3904:
3903:
3901:Trapped-ion QC
3898:
3892:
3890:
3884:
3883:
3881:
3880:
3875:
3870:
3865:
3859:
3857:
3855:Quantum optics
3848:
3842:
3841:
3839:
3838:
3833:
3832:
3831:
3824:
3819:
3814:
3809:
3804:
3799:
3794:
3785:
3783:
3775:
3774:
3772:
3771:
3766:
3761:
3760:
3759:
3749:
3748:
3747:
3737:
3736:
3735:
3725:
3720:
3714:
3712:
3704:
3703:
3701:
3700:
3699:
3698:
3694:
3688:
3684:
3673:
3672:
3671:
3661:
3659:Quantum volume
3656:
3650:
3648:
3642:
3641:
3639:
3638:
3633:
3628:
3623:
3618:
3612:
3610:
3602:
3601:
3599:
3598:
3593:
3588:
3583:
3578:
3573:
3568:
3563:
3558:
3553:
3548:
3543:
3538:
3536:Boson sampling
3533:
3528:
3522:
3520:
3514:
3513:
3510:
3509:
3507:
3506:
3501:
3500:
3499:
3494:
3489:
3479:
3474:
3469:
3463:
3461:
3452:
3451:
3446:
3445:
3444:
3434:
3433:
3432:
3422:
3417:
3412:
3407:
3406:
3405:
3400:
3389:
3387:
3381:
3380:
3378:
3377:
3372:
3370:Solovay–Kitaev
3367:
3362:
3357:
3352:
3347:
3342:
3337:
3332:
3327:
3322:
3317:
3312:
3307:
3302:
3296:
3294:
3290:
3289:
3287:
3286:
3285:
3284:
3274:
3273:
3272:
3262:
3257:
3252:
3247:
3246:
3245:
3235:
3230:
3224:
3222:
3218:
3217:
3212:
3210:
3209:
3202:
3195:
3187:
3179:
3178:
3151:F. W. Cummings
3138:
3083:
3013:
3006:
2988:
2945:J. Appl. Phys.
2934:
2897:(2): 860–863.
2881:
2861:
2841:
2786:
2765:
2764:
2762:
2759:
2758:
2757:
2750:
2747:
2730:
2710:
2690:
2668:
2663:
2659:
2653:
2650:
2630:
2627:
2624:
2621:
2618:
2593:
2589:
2585:
2580:
2576:
2572:
2569:
2549:
2545:
2539:
2535:
2531:
2505:
2500:
2497:
2474:
2470:
2467:
2464:
2461:
2458:
2455:
2452:
2449:
2446:
2443:
2440:
2437:
2434:
2431:
2428:
2424:
2417:
2413:
2408:
2405:
2402:
2399:
2396:
2393:
2380:superpositions
2367:
2364:
2361:
2341:
2338:
2335:
2315:
2312:
2309:
2287:
2283:
2279:
2274:
2270:
2243:
2239:
2212:
2208:
2185:
2181:
2152:
2130:
2126:
2103:
2099:
2068:
2063:
2057:
2053:
2047:
2043:
2039:
2036:
2031:
2027:
2022:
2018:
2015:
2008:
1997:
1991:
1987:
1981:
1977:
1973:
1968:
1965:
1956:
1945:
1940:
1934:
1931:
1926:
1923:
1918:
1914:
1909:
1903:
1899:
1895:
1888:
1877:
1856:
1853:
1833:
1813:
1779:
1775:
1755:Coulomb energy
1742:
1739:
1736:
1716:
1713:
1710:
1690:
1687:
1684:
1664:
1632:
1629:
1606:
1583:
1580:
1577:
1574:
1571:
1568:
1565:
1562:
1559:
1556:
1553:
1546:
1543:
1538:
1535:
1532:
1529:
1514:
1509:
1504:
1499:
1495:
1490:
1487:
1483:
1479:
1475:
1472:
1469:
1466:
1463:
1460:
1457:
1454:
1451:
1448:
1445:
1438:
1435:
1431:
1417:
1412:
1407:
1402:
1398:
1393:
1390:
1386:
1382:
1352:
1328:
1304:
1300:
1296:
1276:
1272:
1268:
1239:
1235:
1212:
1208:
1183:
1154:
1150:
1144:
1140:
1136:
1129:
1125:
1121:
1114:
1109:
1105:
1080:
1076:
1053:
1049:
1026:
1022:
1000:
989:line impedance
984:
980:
938:
935:
895:quantum optics
882:
881:
879:
878:
871:
864:
856:
853:
852:
848:
847:
842:
837:
832:
827:
822:
817:
812:
807:
802:
797:
792:
787:
782:
777:
772:
767:
762:
757:
752:
747:
742:
737:
732:
727:
722:
717:
712:
707:
702:
697:
692:
687:
682:
677:
672:
667:
662:
657:
652:
647:
642:
637:
632:
627:
622:
616:
615:
612:
611:
608:
607:
604:
603:
598:
593:
588:
586:Density matrix
583:
578:
573:
568:
563:
558:
552:
549:
548:
545:
544:
540:
539:
534:
529:
524:
519:
514:
509:
508:
507:
506:
505:
490:
485:
480:
475:
470:
464:
463:
458:
457:
454:
453:
449:
448:
443:
438:
433:
428:
422:
421:
418:
417:
414:
413:
409:
408:
403:
398:
393:
388:
383:
377:
376:
375:
369:
366:
365:
362:
361:
357:
356:
351:
346:
340:
339:
338:
337:
336:
334:Delayed-choice
329:Quantum eraser
324:
323:
318:
313:
308:
303:
298:
293:
288:
283:
278:
272:
271:
268:
267:
264:
263:
259:
258:
257:
256:
246:
241:
236:
231:
226:
221:
219:Quantum number
216:
211:
206:
201:
196:
191:
185:
184:
181:
180:
177:
176:
172:
171:
166:
160:
159:
158:
153:
148:
142:
139:
138:
135:
134:
133:
132:
127:
122:
114:
113:
108:
97:
94:
90:
83:
80:
74:
71:
68:
64:
57:
54:
50:
45:
42:
31:
30:
24:
23:
15:
13:
10:
9:
6:
4:
3:
2:
4090:
4079:
4076:
4075:
4073:
4058:
4050:
4048:
4040:
4039:
4036:
4030:
4027:
4025:
4022:
4020:
4017:
4015:
4012:
4010:
4006:
4003:
4001:
3997:
3993:
3990:
3989:
3987:
3985:
3979:
3969:
3966:
3964:
3961:
3959:
3956:
3954:
3951:
3950:
3948:
3946:
3942:
3936:
3933:
3931:
3928:
3926:
3925:Spin qubit QC
3923:
3921:
3918:
3917:
3915:
3912:
3908:
3902:
3899:
3897:
3894:
3893:
3891:
3889:
3885:
3879:
3876:
3874:
3871:
3869:
3866:
3864:
3861:
3860:
3858:
3856:
3852:
3849:
3843:
3837:
3834:
3830:
3829:
3825:
3823:
3820:
3818:
3815:
3813:
3810:
3808:
3805:
3803:
3800:
3798:
3795:
3793:
3790:
3789:
3787:
3786:
3784:
3782:
3776:
3770:
3767:
3765:
3762:
3758:
3755:
3754:
3753:
3750:
3746:
3743:
3742:
3741:
3738:
3734:
3733:cluster state
3731:
3730:
3729:
3726:
3724:
3721:
3719:
3716:
3715:
3713:
3711:
3705:
3697:
3693:
3689:
3687:
3683:
3679:
3678:
3677:
3674:
3670:
3667:
3666:
3665:
3662:
3660:
3657:
3655:
3652:
3651:
3649:
3643:
3637:
3634:
3632:
3629:
3627:
3624:
3622:
3619:
3617:
3614:
3613:
3611:
3609:
3603:
3597:
3594:
3592:
3589:
3587:
3584:
3582:
3579:
3577:
3574:
3572:
3569:
3567:
3564:
3562:
3559:
3557:
3554:
3552:
3549:
3547:
3544:
3542:
3541:Deutsch–Jozsa
3539:
3537:
3534:
3532:
3529:
3527:
3524:
3523:
3521:
3519:
3515:
3505:
3502:
3498:
3495:
3493:
3490:
3488:
3485:
3484:
3483:
3480:
3478:
3477:Quantum money
3475:
3473:
3470:
3468:
3465:
3464:
3462:
3460:
3456:
3450:
3447:
3443:
3440:
3439:
3438:
3435:
3431:
3428:
3427:
3426:
3423:
3421:
3418:
3416:
3413:
3411:
3408:
3404:
3401:
3399:
3396:
3395:
3394:
3391:
3390:
3388:
3386:communication
3382:
3376:
3373:
3371:
3368:
3366:
3363:
3361:
3358:
3356:
3353:
3351:
3348:
3346:
3343:
3341:
3338:
3336:
3333:
3331:
3328:
3326:
3323:
3321:
3318:
3316:
3313:
3311:
3308:
3306:
3303:
3301:
3298:
3297:
3295:
3291:
3283:
3280:
3279:
3278:
3275:
3271:
3268:
3267:
3266:
3263:
3261:
3258:
3256:
3253:
3251:
3248:
3244:
3241:
3240:
3239:
3236:
3234:
3231:
3229:
3226:
3225:
3223:
3219:
3215:
3208:
3203:
3201:
3196:
3194:
3189:
3188:
3185:
3174:
3170:
3166:
3162:
3158:
3157:
3152:
3148:
3142:
3139:
3134:
3130:
3126:
3122:
3118:
3114:
3109:
3104:
3101:(4): 042319.
3100:
3096:
3095:
3087:
3084:
3079:
3075:
3071:
3067:
3063:
3059:
3055:
3051:
3046:
3041:
3037:
3033:
3029:
3028:
3023:
3017:
3014:
3009:
3007:0-471-16121-7
3003:
2999:
2992:
2989:
2984:
2980:
2976:
2972:
2968:
2964:
2959:
2954:
2950:
2947:
2946:
2938:
2935:
2930:
2926:
2922:
2918:
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2905:
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2892:
2885:
2882:
2874:
2873:
2865:
2862:
2854:
2853:
2845:
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2837:
2833:
2829:
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2821:
2817:
2812:
2807:
2804:(6): 062320.
2803:
2799:
2798:
2790:
2787:
2779:
2778:
2770:
2767:
2760:
2756:
2753:
2752:
2748:
2746:
2744:
2728:
2708:
2701:; the higher
2688:
2666:
2661:
2657:
2651:
2648:
2628:
2625:
2622:
2619:
2616:
2607:
2591:
2587:
2583:
2578:
2574:
2570:
2543:
2537:
2533:
2529:
2521:
2503:
2498:
2495:
2486:
2472:
2465:
2462:
2459:
2456:
2450:
2447:
2444:
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2406:
2400:
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2394:
2383:
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2336:
2310:
2285:
2281:
2277:
2272:
2268:
2259:
2241:
2237:
2228:
2210:
2206:
2183:
2179:
2170:
2166:
2150:
2128:
2124:
2101:
2097:
2087:
2066:
2061:
2055:
2051:
2045:
2041:
2037:
2034:
2029:
2025:
2020:
2016:
2006:
1995:
1989:
1985:
1979:
1975:
1966:
1963:
1954:
1943:
1938:
1932:
1929:
1924:
1921:
1916:
1912:
1907:
1901:
1897:
1886:
1864:
1862:
1854:
1852:
1850:
1846:
1845:Rydberg atoms
1831:
1811:
1803:
1799:
1795:
1777:
1773:
1764:
1760:
1756:
1737:
1714:
1711:
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1497:
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1138:
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1127:
1123:
1112:
1107:
1103:
1094:
1078:
1074:
1051:
1047:
1024:
1020:
990:
978:
974:
970:
966:
962:
958:
954:
950:
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936:
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932:
928:
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917:
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909:
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900:
896:
892:
888:
877:
872:
870:
865:
863:
858:
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855:
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846:
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836:
833:
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826:
823:
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816:
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806:
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798:
796:
793:
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788:
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776:
773:
771:
768:
766:
763:
761:
758:
756:
753:
751:
748:
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728:
726:
723:
721:
718:
716:
713:
711:
708:
706:
703:
701:
698:
696:
693:
691:
688:
686:
683:
681:
678:
676:
673:
671:
668:
666:
663:
661:
658:
656:
653:
651:
648:
646:
643:
641:
638:
636:
633:
631:
628:
626:
623:
621:
618:
617:
610:
609:
602:
599:
597:
594:
592:
589:
587:
584:
582:
579:
577:
576:Quantum chaos
574:
572:
569:
567:
564:
562:
559:
557:
554:
553:
547:
546:
538:
535:
533:
532:Transactional
530:
528:
525:
523:
522:Quantum logic
520:
518:
515:
513:
510:
504:
501:
500:
499:
496:
495:
494:
491:
489:
486:
484:
481:
479:
476:
474:
471:
469:
466:
465:
461:
456:
455:
447:
444:
442:
439:
437:
434:
432:
429:
427:
424:
423:
416:
415:
407:
404:
402:
399:
397:
394:
392:
389:
387:
384:
382:
379:
378:
374:
371:
370:
364:
363:
355:
352:
350:
347:
345:
342:
341:
335:
332:
331:
330:
327:
326:
322:
319:
317:
314:
312:
309:
307:
304:
302:
299:
297:
294:
292:
289:
287:
284:
282:
279:
277:
274:
273:
266:
265:
255:
252:
251:
250:
249:Wave function
247:
245:
242:
240:
237:
235:
232:
230:
229:Superposition
227:
225:
222:
220:
217:
215:
212:
210:
207:
205:
202:
200:
197:
195:
192:
190:
187:
186:
179:
178:
170:
167:
165:
162:
161:
157:
154:
152:
149:
147:
144:
143:
137:
136:
131:
128:
126:
123:
121:
118:
117:
116:
115:
111:
78:
72:
55:
52:
48:
40:
33:
32:
29:
25:
21:
20:
3953:Charge qubit
3878:KLM protocol
3867:
3827:
3691:
3681:
3375:Purification
3305:Eastin–Knill
3160:
3154:
3147:E. T. Jaynes
3141:
3098:
3094:Phys. Rev. A
3092:
3086:
3031:
3025:
3016:
2997:
2991:
2948:
2943:
2937:
2894:
2890:
2884:
2871:
2864:
2851:
2844:
2801:
2797:Phys. Rev. A
2795:
2789:
2776:
2769:
2608:
2487:
2384:
2227:Pauli matrix
2171:system with
2088:
1865:
1858:
1802:supercurrent
1759:bias voltage
1645:Cooper pairs
1641:charge qubit
1634:
1625:permittivity
1595:
1373:
1341:capacitively
1258:
1173:
1095:
940:
924:
910:usually are
890:
886:
885:
431:Klein–Gordon
367:Formulations
204:Energy level
199:Entanglement
182:Fundamentals
169:Interference
120:Introduction
3984:programming
3963:Phase qubit
3868:Circuit QED
3340:No-deleting
3282:cloud-based
3038:: 162–167.
3022:A. Wallraff
2165:Hamiltonian
2002:atomic term
1950:cavity term
1798:flux qubits
891:circuit QED
820:von Neumann
805:Schrödinger
581:EPR paradox
512:Many-worlds
446:Schrödinger
401:Schrödinger
396:Phase-space
386:Interaction
291:Double-slit
269:Experiments
244:Uncertainty
214:Nonlocality
209:Measurement
194:Decoherence
164:Hamiltonian
4024:libquantum
3958:Flux qubit
3863:Cavity QED
3812:Bacon–Shor
3802:stabilizer
3330:No-cloning
3167:: 89–109.
2761:References
1761:) and the
1317:wavelength
912:mesoscopic
815:Sommerfeld
730:Heisenberg
725:Gutzwiller
665:de Broglie
613:Scientists
527:Relational
478:Copenhagen
381:Heisenberg
239:Tunnelling
140:Background
3930:NV center
3365:Threshold
3345:No-hiding
3310:Gleason's
2958:0807.4094
2729:γ
2658:ω
2649:κ
2626:⋅
2588:ω
2584:−
2575:ω
2568:Δ
2548:Δ
2530:±
2520:linewidth
2469:⟩
2463:−
2457:∣
2454:⟩
2448:∣
2445:±
2442:⟩
2436:∣
2433:⟩
2427:∣
2404:⟩
2401:±
2392:∣
2366:⟩
2360:∣
2340:⟩
2334:∣
2314:⟩
2308:∣
2282:ω
2269:ω
2242:±
2238:σ
2207:σ
2180:ω
2129:†
2098:ω
2067:⏟
2056:−
2052:σ
2046:†
2026:σ
2014:ℏ
1996:⏟
1986:σ
1976:ω
1972:ℏ
1944:⏟
1917:†
1898:ω
1894:ℏ
1774:ω
1741:⟩
1735:∣
1689:⟩
1683:∣
1605:ε
1579:…
1545:ℓ
1513:ε
1494:ν
1478:λ
1471:…
1437:ℓ
1416:ε
1397:ν
1381:λ
1369:feed line
1365:antinodes
1327:ℓ
1295:λ
1267:λ
1234:ε
1207:ω
1182:ℏ
1139:ε
1124:ω
1120:ℏ
999:Ω
965:aluminium
949:microwave
937:Resonator
845:Zeilinger
690:Ehrenfest
419:Equations
96:⟩
93:Ψ
82:^
70:⟩
67:Ψ
44:ℏ
4072:Category
3992:OpenQASM
3968:Transmon
3845:Physical
3645:Quantum
3546:Grover's
3320:Holevo's
3293:Theorems
3243:timeline
3233:NISQ era
3133:53983107
3078:55812008
3070:15356625
3034:(7005).
2983:56398614
2929:12789596
2836:20427333
2749:See also
2169:spin-1/2
1849:coupling
1794:transmon
977:sapphire
975:(Si) or
967:(Al) or
957:grounded
770:Millikan
695:Einstein
680:Davisson
635:Blackett
620:Aharonov
488:Ensemble
468:Bayesian
373:Overview
254:Collapse
234:Symmetry
125:Glossary
3982:Quantum
3920:Kane QC
3779:Quantum
3707:Quantum
3636:PostBQP
3606:Quantum
3591:Simon's
3384:Quantum
3221:General
3113:Bibcode
3050:Bibcode
2963:Bibcode
2909:Bibcode
2816:Bibcode
1363:-field
1252:is the
1194:is the
987:). The
973:silicon
969:niobium
810:Simmons
800:Rydberg
765:Moseley
745:Kramers
735:Hilbert
720:Glauber
715:Feynman
700:Everett
670:Compton
441:Rydberg
130:History
4000:IBM QX
3996:Qiskit
3935:NMR QC
3913:-based
3817:Steane
3788:Codes
3586:Shor's
3492:SARG04
3300:Bell's
3131:
3076:
3068:
3027:Nature
3004:
2981:
2927:
2834:
1855:Theory
1174:where
931:qubits
903:cavity
840:Zeeman
835:Wigner
785:Planck
755:Landau
740:Jordan
391:Matrix
321:Popper
3822:Toric
3265:Qubit
3129:S2CID
3103:arXiv
3074:S2CID
3040:arXiv
2979:S2CID
2953:arXiv
2925:S2CID
2899:arXiv
2876:(PDF)
2856:(PDF)
2832:S2CID
2806:arXiv
2781:(PDF)
2167:of a
1653:qubit
1596:with
795:Raman
780:Pauli
775:Onnes
710:Fermi
685:Debye
675:Dirac
640:Bloch
630:Bethe
498:Local
436:Pauli
426:Dirac
224:State
4014:Cirq
4005:Quil
3911:Spin
3807:Shor
3487:BB84
3420:LOCC
3165:IEEE
3149:and
3066:PMID
3002:ISBN
2352:and
2225:the
2143:and
1701:and
1287:and
830:Wien
825:Weyl
790:Rabi
760:Laue
750:Lamb
705:Fock
660:Bose
655:Born
650:Bohr
645:Bohm
625:Bell
3828:gnu
3792:CSS
3669:XEB
3631:QMA
3626:QIP
3621:EQP
3616:BQP
3596:VQE
3551:HHL
3355:PBR
3169:doi
3121:doi
3058:doi
3032:431
2971:doi
2949:104
2917:doi
2824:doi
1609:eff
1517:eff
1420:eff
979:(Al
4074::
4019:Q#
3163:.
3161:51
3159:.
3127:.
3119:.
3111:.
3099:76
3097:.
3072:.
3064:.
3056:.
3048:.
3030:.
2977:.
2969:.
2961:.
2923:.
2915:.
2907:.
2895:15
2893:.
2830:.
2822:.
2814:.
2802:69
2800:.
2745:.
1882:JC
1256:.
1198:,
1171:,
933:.
922:.
4007:–
3998:–
3994:–
3695:2
3692:T
3685:1
3682:T
3206:e
3199:t
3192:v
3175:.
3171::
3135:.
3123::
3115::
3105::
3080:.
3060::
3052::
3042::
3010:.
2985:.
2973::
2965::
2955::
2931:.
2919::
2911::
2901::
2838:.
2826::
2818::
2808::
2709:Q
2689:Q
2667:Q
2662:r
2652:=
2629:d
2623:E
2620:=
2617:g
2592:r
2579:a
2571:=
2544:/
2538:2
2534:g
2504:n
2499:g
2496:2
2473:)
2466:1
2460:n
2451:e
2439:n
2430:g
2423:(
2416:2
2412:1
2407:=
2398:,
2395:n
2363:e
2337:g
2311:n
2286:a
2278:=
2273:r
2211:z
2184:a
2151:a
2125:a
2102:r
2062:)
2042:a
2038:+
2035:a
2030:+
2021:(
2017:g
2007:+
1990:z
1980:a
1967:2
1964:1
1955:+
1939:)
1933:2
1930:1
1925:+
1922:a
1913:a
1908:(
1902:r
1887:=
1876:H
1832:n
1812:d
1778:a
1757:(
1738:e
1715:1
1712:+
1709:N
1686:g
1663:N
1582:)
1576:,
1573:2
1570:,
1567:1
1564:,
1561:0
1558:=
1555:n
1552:(
1542:4
1537:1
1534:+
1531:n
1528:2
1508:c
1503:=
1498:n
1489::
1486:4
1482:/
1474:)
1468:,
1465:3
1462:,
1459:2
1456:,
1453:1
1450:=
1447:n
1444:(
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1430:n
1411:c
1406:=
1401:n
1392::
1389:2
1385:/
1351:E
1303:4
1299:/
1275:2
1271:/
1238:0
1211:r
1153:m
1149:V
1143:0
1135:2
1128:r
1113:=
1108:0
1104:E
1079:0
1075:E
1052:0
1048:E
1025:m
1021:V
985:3
983:O
981:2
889:(
875:e
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861:v
89:|
79:H
73:=
63:|
56:t
53:d
49:d
41:i
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