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observables.
Moreover,theconnectionsestablishedbetweenmodelsofmeasurement-based
quantumcomputation,permitanaturaltranslationofeachone-dimensionalone-
way quantum computer into a sequence of state transfers. Therefore, by these
close connections, the measurement-based quantum computer is unified: a one-
way quantum computer is nothing but a quantum computer based on state
transfers, in which a large part of the measurements (those independent on
the program we want to perform) are grouped in a stage of initialization. Note
that this initialization can be performed using an Ising transformation, which
is unitary. The initialization produces the cluster state, on which the rest of
themeasurements(composedofone-qubitmeasurementsonly)areperformedin
order to complete the computation.
Final remark. This paper deals with unifying models of quantum computation
via measurementsonly, and withminimizing universal families of observables. It
has been submitted to a conference on April 1st, 2004.The authors have recently
noticed a report posted on arXiv.org, by P. Aliferis and D. W. Leung [10], deal-
ing with unifying models of quantum computation via measurements only. The
relations among both approaches are certainly worth investigating further.
9
References
1. A.Y.Kitaev,A.H.ShenandM.N.Vyalyi.Classical andQuantum Computation,
American Mathematical Society, 2002.
2. D.W. Leung. Two-qubit projective measurements are universal for quantum com-
putation, arXiv.org report quant-ph/0111077, 2001.
3. D. W. Leung. Quantum computation by measurements, arXiv.org report
quant-ph/0310189, 2003.
4. M. A. Nielsen. Universal quantum computation using only projective mea-
surement, quantum memory, and preparation of the 0 state, arXiv.org report
quant-ph/0108020, 2001.
5. M.A.NielsenandI.L.Chuang.QuantumComputationandQuantumInformation,
Cambridge University Press, 2000.
6. S.PerdrixState Transfer instead of Teleportation inMeasurement-based Quantum
Computation , arXiv.org report quant-ph/0402204, 2004.
7. R. Raussendorf and H. J. Briegel. Quantum computing via measurements only
Phys.Rev.Lett. 86 5188, 2000.
8. R. Raussendorf, D. E. Browne and H. J. Briegel. Measurement-based quantum
computation with cluster states, arXiv,quant-ph/0301052, 2003.
9. F.Verstraete,J.I.Cirac.ValenceBondSolidsforQuantumComputation,arXiv.org
report quant-ph/0311130, 2003.
10. P. Aliferis, D. W. Leung. Computation by measurements: a unifying picture,
arXiv.org report quant-ph/0404082, 2004.
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Measurement-only verifiable blind quantum computing with quantum input
verification
Tomoyuki Morimae1,∗
1ASRLD Unit, Gunma University, 1-5-1 Tenjin-cho Kiryu-shi Gunma-ken, 376-0052, Japan
Verifiableblindquantumcomputingisasecuredelegatedquantumcomputingwhereaclientwith
a limited quantum technology delegates her quantum computing to a server who has a universal
quantumcomputer. Theclient’s privacyisprotected (blindness)andthecorrectness ofthecompu-
tationisverifiablebytheclientinspiteofherlimitedquantumtechnology(verifiability). Thereare
mainlytwotypesofprotocolsforverifiableblindquantumcomputing: theprotocolwheretheclient
has only to generate single-qubit states, and the protocol where the client needs only the ability
6102 of single-qubit measurements. The latter is called the measurement-only verifiable blind quantum
computing. If the input of the client’s quantum computing is a quantum state whose classical ef-
ficient description is not known to the client, there was no way for the measurement-only client to
verifythecorrectnessoftheinput. Hereweintroduceanewprotocolofmeasurement-onlyverifiable
nuJ blind quantumcomputing where thecorrectness of the quantuminput is also verifiable.
I. INTRODUCTION ifiability: although the blindness guarantees that Bob
12
cannot learn Alice’s quantum computing, he can still
deviate from the correct procedure, mess up her quan-
Blind quantum computing is a secure delegated quan-
]hp-tnauq[ tum computing, and give Alice a completely wrong re-
tum computingwhere aclient(Alice) whodoes nothave
sult. Since Alice cannotperformquantumcomputing by
enoughquantumtechnologydelegatesherquantumcom-
herself, she cannot check the correctness of the result by
puting to a server (Bob) who has a universal quan-
herself unless the problem is, say, in NP, and therefore
tum computer without leaking any information about
shecanacceptawrongresult. Tosolvetheproblem,veri-
her quantum computing. By using measurement-based
fiableblindquantumcomputingprotocolwasintroduced
quantum computing [1, 2], Broadbent, Fitzsimons, and
inRef.[16],andsometheoreticalimprovementswerealso
Kashefi first showed that blind quantum computing is
obtained [17–19]. Experimental demonstrations of the
indeed possible for a client who can do only the single
1v76460.6061:viXra qubitstategeneration[3]. Sincethebreakthrough,many verification were also done [20, 21]. The basic idea of
theseprotocolsissocalledthetraptechnique: Alicehides
theoreticalimprovementshavebeenobtained[4–12],and
sometrapqubitsintheregister,andanychangeofatrap
even a proof-of-principle experiment was achieved with
signals Bob’s malicious behavior. By checking traps, Al-
photonic qubits [13]. These blind quantum computing
ice can detect any Bob’s malicious behavior with high
protocols guarantee two properties: first, if Bob is hon-
probability. Ifthecomputationisencodedbyaquantum
est, Alice can obtain the correct result of her quantum
error detection code, the probability that Alice is fooled
computing (correctness). Second, whatever Bob does,
by Bob can be exponentially small, since in that case in
he cannot gain any information about Alice’s quantum
orderto changethe logicalstate, Bobhastotouchmany
computing (blindness) [14].
qubits,anditconsequentlyincreasestheprobabilitythat