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for which a computationally unbounded prover can convince a polynomial-time verifier to accept when the input is in the language (with high probability) and cannot convince the verifier to accept when the input is not in the language (again, with high probability). In other words, the prover and
52:
verifier may interact for polynomially many rounds, and if the input is in the language the verifier should accept with probability greater than 2/3, and if the input is not in the language, the verifier should be reject with probability greater than 2/3. In IP, the verifier is like a
94:, the set of problems solvable by a deterministic Turing machine in polynomial space. Both results were subsumed by the 2009 result that QIP is contained in PSPACE, which also proves that QIP = IP = PSPACE, since PSPACE is easily shown to be in QIP using the result
71:, who along with Kitaev proved in a later paper that QIP = QIP(3), which shows that 3 messages are sufficient to simulate a polynomial-round quantum interactive protocol. Since QIP(3) is already QIP, this leaves 4 possibly different classes: QIP(0), which is
56:
machine. In QIP, the communication between the prover and verifier is quantum, and the verifier can perform quantum computation. In this case the verifier is like a
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161:(2000), "Parallelization, amplification, and exponential time simulation of quantum interactive proof systems",
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FOCS '09: Proceedings of the 2009 50th Annual IEEE Symposium on
Foundations of Computer Science
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STOC '00: Proceedings of the thirty-second annual ACM symposium on Theory of computing
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verifier and one computationally unbounded prover. Informally, IP is the set of
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67:, we get the complexity class QIP(k). QIP and QIP(k) were introduced by
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118:(2003), "PSPACE has constant-round quantum interactive proof systems",
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STOC '10: Proceedings of the 42nd ACM symposium on Theory of computing
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By restricting the number of messages used in the protocol to at most
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189:(2009), "Two-Message Quantum Interactive Proofs Are in PSPACE",
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in exponential time. QIP(2) was then shown to be contained in
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126:(3), Essex, UK: Elsevier Science Publishers Ltd.: 575–588,
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Kitaev and
Watrous also showed that QIP is contained in
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193:, IEEE Computer Society, pp. 534–543,
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86:, the class of problems solvable by a
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26:Quantum Interactive Polynomial time
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1525:Probabilistically checkable proof
185:Jain, Rahul; Upadhyay, Sarvagya;
1560:Probabilistic complexity classes
1125:
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18:computational complexity theory
1:
791:Adiabatic quantum computation
133:10.1016/S0304-3975(01)00375-9
842:Topological quantum computer
88:deterministic Turing machine
1120:Quantum information science
287:Quantum information science
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1541:List of complexity classes
515:quantum gate teleportation
32:analogue of the classical
1565:Quantum complexity theory
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644:Quantum Fourier transform
540:Post-quantum cryptography
483:Entanglement distillation
221:, ACM, pp. 573–582,
165:, ACM, pp. 608–617,
1530:Interactive proof system
1130:Quantum mechanics topics
825:Quantum machine learning
801:One-way quantum computer
654:Quantum phase estimation
555:Quantum key distribution
488:Monogamy of entanglement
217:(2010), "QIP = PSPACE",
41:interactive proof system
737:Randomized benchmarking
599:Amplitude amplification
1484:Arithmetical hierarchy
837:Quantum Turing machine
830:quantum neural network
577:Quantum secret sharing
1479:Grzegorczyk hierarchy
1474:Exponential hierarchy
1406:Considered infeasible
909:Entanglement-assisted
870:quantum convolutional
545:Quantum coin flipping
510:Quantum teleportation
471:entanglement-assisted
301:DiVincenzo's criteria
1469:Polynomial hierarchy
1299:Suspected infeasible
720:processor benchmarks
649:Quantum optimization
532:Quantum cryptography
343:physical vs. logical
1498:Families of classes
1179:Considered feasible
433:Quantum speed limit
328:Quantum programming
323:Quantum information
120:Theor. Comput. Sci.
75:, QIP(1), which is
1172:Complexity classes
1082:Forest/Rigetti QCS
818:quantum logic gate
604:Bernstein–Vazirani
591:Quantum algorithms
466:Classical capacity
350:Quantum processors
333:Quantum simulation
79:, QIP(2) and QIP.
24:(which stands for
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1462:Class hierarchies
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946:Linear optical QC
727:Quantum supremacy
681:complexity theory
634:Quantum annealing
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522:Superdense coding
311:Quantum computing
228:978-1-4503-0050-6
200:978-0-7695-3850-1
172:978-1-58113-184-0
30:quantum computing
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854:error correction
783:computing models
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639:Quantum counting
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476:quantum capacity
423:No-teleportation
408:No-communication
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969:Neutral atom QC
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69:John Watrous
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20:, the class
15:
1378:#P-complete
1316:NP-complete
1231:NL-complete
1057:programming
1036:Phase qubit
941:Circuit QED
413:No-deleting
355:cloud-based
96:IP = PSPACE
1554:Categories
1433:ELEMENTARY
1258:P-complete
1097:libquantum
1031:Flux qubit
936:Cavity QED
885:Bacon–Shor
875:stabilizer
403:No-cloning
102:References
1428:2-EXPTIME
1003:NV center
438:Threshold
418:No-hiding
383:Gleason's
142:0304-3975
60:machine.
49:languages
28:) is the
1423:EXPSPACE
1418:NEXPTIME
1186:DLOGTIME
1065:OpenQASM
1041:Transmon
918:Physical
718:Quantum
619:Grover's
393:Holevo's
366:Theorems
316:timeline
306:NISQ era
1413:EXPTIME
1321:NP-hard
1055:Quantum
993:Kane QC
852:Quantum
780:Quantum
709:PostBQP
679:Quantum
664:Simon's
457:Quantum
294:General
43:with a
1520:NSPACE
1515:DSPACE
1390:PSPACE
1073:IBM QX
1069:Qiskit
1008:NMR QC
986:-based
890:Steane
861:Codes
659:Shor's
565:SARG04
373:Bell's
225:
197:
169:
140:
92:PSPACE
1510:NTIME
1505:DTIME
1326:co-NP
895:Toric
338:Qubit
1338:TFNP
1087:Cirq
1078:Quil
984:Spin
880:Shor
560:BB84
493:LOCC
223:ISBN
195:ISBN
167:ISBN
138:ISSN
1453:ALL
1353:QMA
1343:FNP
1285:APX
1280:BQP
1275:BPP
1265:ZPP
1196:ACC
901:gnu
865:CSS
742:XEB
704:QMA
699:QIP
694:EQP
689:BQP
669:VQE
624:HHL
428:PBR
251:QIP
128:doi
124:292
84:EXP
77:QMA
73:BQP
58:BQP
54:BPP
22:QIP
16:In
1556::
1448:RE
1438:PR
1385:IP
1373:#P
1368:PP
1363:⊕P
1358:PH
1348:AM
1311:NP
1306:UP
1290:FP
1270:RP
1248:CC
1243:SC
1238:NC
1226:NL
1221:FL
1216:RL
1211:SL
1201:TC
1191:AC
1092:Q#
249::
149:^
136:,
122:,
98:.
37:IP
1443:R
1253:P
1206:L
1164:e
1157:t
1150:v
1080:–
1071:–
1067:–
768:2
765:T
758:1
755:T
279:e
272:t
265:v
130::
65:k
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