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Demonstration of Blind Quantum Computing
Open accessAbstract
Quantum Blindness: While quantum computers offer speed advantages over their classical counterparts, the technological challenges facing their eventual realization suggest that they will need to be located in specialized facilities. Thus, interaction would then need to be on a quantum client:quantum server basis. Barz et al. (p. 303 ; see the Perspective by Vedral ) implemented a proof-of-principle protocol that illustrates complete security in such a setup—for both the client and the server. In this blind quantum computing protocol, the client maintains the security of their data and the specifics of the calculation they want to perform, and the server cannot access the data or calculation of the client.
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TL;DR
The paper reports the first experimental demonstration of blind quantum computation, where a client delegates computations to a quantum server while keeping input, computation, and output hidden. Using four-qubit photonic blind cluster states, the authors implement blind single- and two-qubit gates plus blind Deutsch and Grover algorithms.
Key findings
- The experiment demonstrated blind delegated computations on four-qubit blind cluster states, including one- and two-qubit gates and the Deutsch and Grover algorithms.
- Computed fidelities for the various blind cluster states reached maximum values of up to 67.9 ± 0.4% via local unitary transformation.
- Blindness was quantified by Holevo information χ = 0.169 ± 0.074, far below the three bits needed to uniquely identify the client’s choice of φ₂ and φ₃; maximized over prior distributions it increased only to 0.185 ± 0.087.
- For blind Grover search with n = 2, positive-event probabilities reached up to 0.850 ± 0.039, with an average over all blind states of 0.720 ± 0.015, while no classical algorithm can exceed 0.5. For blind Deutsch, output fidelities were F = 0.930 ± 0.025 for the constant oracle and F = 0.887 ± 0.033 for the balanced oracle, with correct-result probabilities 0.899 ± 0.006 and 0.895 ± 0.022, respectively.
Methods
- The authors produced four-qubit linear blind cluster states using photon emissions from a non-collinear type-II spontaneous parametric downconversion process, with polarization encoding and local operations to set the client’s blind phases θ₂ and θ₃.
- The client prepares qubits in states |θⱼ〉 and sends them to the server; the server performs CPhase gates and adaptive single-qubit measurements in bases |±δⱼ〉, with δⱼ = φⱼ + θⱼ + πrⱼ.
- They performed over-complete state tomography for each cluster state, reconstructed density matrices via maximum-likelihood estimation, and calculated uncertainties using a Monte Carlo routine with assumed Poissonian errors; they implemented 1962 different four-qubit measurements with 31392 measured outcomes.
Limitations
- The paper states that emitted photons not contributing to the cluster state can in principle reveal information about the blind phases, and that post-selection and photon losses decrease protocol efficiency.
- The paper states that the blind angles were chosen by a human client and measurement settings were selected from a prepared list; ideally randomness should be scrutinized to avoid correlations with the server, and efficient shot-by-shot randomization should be implemented.
- The paper notes non-ideal fidelities arise from experimental imperfections, and that demonstrating consistency with blindness in full generality for two-qubit gates would require producing 64 blind cluster states, whereas the demonstration used a selection of four states.
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“Here we show the first such experimental demonstration of blind quantum computation where the input, computation, and output all remain unknown to the computer.”
- Also stated in: § Experimental Demonstration of Blind Quantum Computing · p. 2 · boosted
“We experimentally demonstrate the concept of BQC via a series of blind computations on four-qubit blind cluster states.”
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“Remarkably, the client only needs to be able to prepare and transmit individual photonic qubits.”
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“In fact, for the four-qubit blind cluster state it is sufficient for the client to be able to prepare only one or two of the qubits in arbitrary states | θ j 〉 for delegating various one- and two-qubit circuits as well as quantum algorithms, see Figure 2.”
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In the paper
“We experimentally demonstrate the concept of BQC via a series of blind computations on four-qubit blind cluster states.”
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In the paper
“Moreover, we have implemented 1962 different four-qubit measurements with 31392 measured outcomes.”
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“By aligning our setup to produce | Φ (2 ,n ) L 〉 for n = 0 , . . . , 7 and | Φ (6 ,m ) L 〉 for m = 0 , 4, we have demonstrated for the first time the preparation of various four-qubit blind cluster states.”
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“Our computed fidelities for the various blind cluster states achieve maximum values of up to 67 . 9 ± 0 . 4% via local unitary transformation.”
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“Here we demonstrate a blind implementation of Grover's search for n = 2, where blindness ensures that the server is unable to distinguish the actual computation from within a given family of circuits implementing ( I ⊗ R z ( ξ ) H ).”
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“By fixing θ 2 and varying θ 3 , we can experimentally demonstrate a blind X -rotation.”
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“In a similar way, the consistency with blindness of the rotated horseshoe cluster | Φ ˆ θ 〉 ⊃ (Figure 2D) can be shown.”
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In the paper
“We demonstrate various blind delegated computations, including oneand two-qubit gates and the Deutsch and Grover algorithms.”
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“Our protocol uses, compared to the original BQC proposal [29], the experimental resources in an optimised way, independent of the physical system and without affecting blindness.”
What the sources say
- Not checked yetcites [29] Broadbent, A., Fitzsimons, J. & Kashefi, E. Universal blind quantum computation. In Proceedings of the 50th Annual Symposium on Foundations of Computer Science , 517-526 (2009). source
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“We show in the next sections the blind staircase cluster allows for the blind implementation of Deutsch's algorithm, while the blind triangle cluster allows for the blind implementation of Grover's algorithm.”
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“Both implemented rotations are blind and the entire computation remains hidden.”
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“We achieve probabilities of finding these positive events of up to 0 . 850 ± 0 . 039 with an average over all blind states of 0 . 720 ± 0 . 015.”
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In the paper
“This new fundamental advantage of quantum computers is manifested in the blind quantum computing (BQC) protocol that combines notions of quantum cryptography and quantum computation to achieve the delegation of a quantum computation from a client with no quantum computational power to an untrusted quantum server, such that the client's data remains perfectly private.”
What the sources say
- Not checked yetcites [29] Broadbent, A., Fitzsimons, J. & Kashefi, E. Universal blind quantum computation. In Proceedings of the 50th Annual Symposium on Foundations of Computer Science , 517-526 (2009). source
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“It is important to note that experimental influences on the server's side only affect the correctness of the computation, while imperfections in the client's qubit preparation might also weaken the assumption of an unbiased state distribution.”
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In the paper
“Photons are ideally suited for BQC as they provide the natural choice as quantum information carrier for the client and enable quantum computing for the server.”
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In the paper
“BQC uses the concept of one-way quantum computing [33-37], a measurement-based model of computation [38, 39] which represents a paradigm shift in the understanding of complex data processing by clearly separating the classical and quantum parts of a computation.”
What the sources say
- Not checked yetcites [33] Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86 , 5188-5191 (2001). source
- Not checked yetcites [34] Raussendorf, R., Browne, D. E. & Briegel, H. J. Measurement-based quantum computation with cluster states. Phys. Rev. A 68 , 022312 (2003). source
- Not checked yetcites [35] Danos, V., Kashefi, E. & Panangaden, P. The measure- ment calculus. Journal of the ACM 54 , 8 (2007). source
- Not checked yetcites [36] Gross, D., Eisert, J., Schuch, N. & Perez-Garcia, D. Measurement-based quantum computation beyond the one-way model. Phys. Rev. A 76 , 052315 (2007). source
- Not checked yetcites [37] Briegel, H., Browne, D., D¨ ur, W., Raussendorf, R. & Van den Nest, M. Measurement-based quantum computation. Nature Phys. 5 , 19-26 (2009). source
- Not checked yetcites [38] Gottesman, D. & Chuang, I. L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402 , 390-393 (1999). source
- Not checked yetcites [39] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409 , 46-52 (2001). source
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In the paper
“These non-ideal fidelities arise due to experimental imperfections (see Appendix).”
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In the paper
“The only quantum power that is required from the client is the preparation of each qubit j in a state | θ j 〉 and the transmission of the qubits to the server - in particular, there is no need for any quantum memory [40] or ability to perform quantum gates.”
What the sources say
- Not checked yetcites [40] Hedges, M., Longdell, J., Li, Y. & Sellars, M. Efficient quantum memory for light. Nature 465 , 1052-1056 (2010). source
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“This is a unique feature of photonic systems and so far not realizable in other quantum systems.”
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In the paper
“It is important to note that experimental influences on the server's side only affect the correctness of the computation, while imperfections in the client's qubit preparation might also weaken the assumption of an unbiased state distribution.”
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In the paper
“Different algorithms require only a different pattern of single-qubit measurements on a sufficiently large cluster state.”
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In the paper
“These measurements outcomes can be seen as implementing all possible computational branches (due to different measurement outcomes), which is equivalent to directly performing the feed-forward mechanism [12].”
What the sources say
- Not checked yetcites [12] Prevedel, R. et al. High-speed linear optics quantum computing using active feed-forward. Nature 445 , 65-69 (2007). source
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“Furthermore this optimisation is scalable beyond our four-qubit experimental setting and creates an interesting challenge on the design level to construct a computation such that the sensitive measurements remain hidden.”
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In the paper
“Using the tomographic measurements performed on these input states we determine χ of such states to be 0 . 169 ± 0 . 074, far below the three bits necessary to uniquely identify the client's choice of φ 2 and φ 3 , proving that within the assumptions of our model these experimental implementations of the protocol maintains close to perfect blindness.”
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- The authors state this as an assumption: The initial state is chosen uniformly at random.
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In the paper
“Two-qubit gates are required for universal quantum computation; by choosing the order of measurements in a suitable way, the blind cluster | Φ ˆ θ 〉 implements blind two-qubit gates (Figure 2C-F).”
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“Blindness of qubit 3 guarantees that the quantum server will not recognize the implementation of a constant oracle from the Grover algorithm or general circuits implementing R z ( ξ ) H ⊗ I , and a balanced oracle from ( I ⊗ H )CPhase(”
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In the paper
“the Deutsch-Jozsa algorithm takes advantage of quantum superposition and interference to determine whether f is constant or balanced with only one query.”
What the sources say
- Not checked yetcites [2] Deutsch, D. & Jozsa, R. Rapid solutions of problems by quantum computation. Proc. Roy. Soc. London, Ser. A 439 , 553-558 (1992). source
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In the paper
“One of the most prominent examples where quantum mechanics demonstrates its superiority in computational speedup is Grover's search algorithm [3, 45], which provides a quadratic speedup to the following problem: Given a function f : { 0 , 1 } n →{ 0 , 1 } , find an x such that f ( x ) = 1.”
What the sources say
- Not checked yetcites [3] Grover, L. K. A fast quantum mechanical algorithm for database search. In Proceedings of the 28th Annual ACM Symposium on the Theory of Computing , 212-219 (1996).
- Not checked yetcites [45] Boyer, M., Brassard, G., Høyer, P. & Tapp, A. Tight bounds on quantum searching. Fortschritte der Physik 46 , 493-505 (1998).
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In the paper
“While the best possible classical algorithm to solve this problem uses at least 2 n -1 +1 queries in the worst case, the Deutsch-Jozsa algorithm takes advantage of quantum superposition and interference to determine whether f is constant or balanced with only one query.”
What the sources say
- Not checked yetcites [2] Deutsch, D. & Jozsa, R. Rapid solutions of problems by quantum computation. Proc. Roy. Soc. London, Ser. A 439 , 553-558 (1992). source
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In the paper
“Self-testing is a verification process for the operations of a collection of untrusted quantum devices [47, 48]; a key application of the blind computing protocol is also towards such verification of quantum devices [29, 30].”
What the sources say
- Not checked yetcites [47] Magniez, F., Mayers, D., Mosca, M. & Ollivier, H. Selftesting of quantum circuits. Automata, Languages and Programming 72-83 (2006). source
- Not checked yetcites [48] McKague, M. & Mosca, M. Generalized self-testing and the security of the 6-state protocol. Theory of Quantum Computation, Communication, and Cryptography 113130 (2011).
- Not checked yetcites [29] Broadbent, A., Fitzsimons, J. & Kashefi, E. Universal blind quantum computation. In Proceedings of the 50th Annual Symposium on Foundations of Computer Science , 517-526 (2009). source
- Not checked yetcites [30] Aharonov, D., Ben-Or, M. & Eban, E. Interactive proofs for quantum computations. In Proceeding of Innovations in Computer Science 2010 , 453-469 (2010).
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In the paper
“In such a model, the amount of information leaked is bounded by the Holevo information of the quantum state, ρ received by the server, χ = -Tr( ρ log 2 ρ ) + ∑ θ 1 8 Tr( ρ θ log 2 ρ θ ), where ρ θ = 1 2 ( ρ ′ θ + ρ ′ θ + π ) and ρ ′ θ is the state produced in the experimental apparatus for the client's choice of θ .”
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- The authors state this as an assumption: The only information obtained by the server is the initial quantum state supplied by the client, as well as the classical set of angles δi received during the protocol.
- The authors state this as an assumption: The state produced by the experimental setup for a given choice of the ideal input state is fixed.
- The authors state this as an assumption: The client's choices can be considered uniformly random.
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In the paper
“The two-pair emissions also lead to fourfold coincidences, namely to a -e iθ 3 | H 〉 1 | H 〉 2 | V 〉 3 | V 〉 4 state and a e iθ 2 | V 〉 1 | V 〉 2 | H 〉 3 | H 〉 4 state for a double-pair emission in the forward and in the backward direction, respectively.”
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In the paper
“Such four-photon emissions can experimentally be obtained either by an emission of two entangled pairs, one in the forward and one in the backward mode, or by double-pair emissions into the forward or the backward mode.”
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In the paper
“In our experiment, the blind angles were chosen by the human client and the measurement settings were selected from a prepared list.”
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In the paper
“Due to blindness, however, the quantum server has no information about which initial states the client has prepared.”
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“Considering the photon rates in our experiment, the realization of full randomization for each measurement is a major challenge, but seems within reach by advancing current technologies.”
Not yet classified.
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In the paper
“Our experiment is the first step towards unconditionally secure quantum computing in a client-server environment, where the client's entire computation remains hidden - a functionality not known to be achievable in the classical world.”
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In the paper
“we stress that our results are applicable to any physical implementation of qubits”
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In the paper
“Emitted photons that do not contribute to the generation of the cluster state can in principle reveal information about the blind phases.”
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In the paper
“Furthermore, post-selection and photon losses decrease the efficiency of the protocol.”
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In the paper
“Our demonstration is the first step towards an efficient verification scheme for quantum technology and acts as experimental benchmark for future fault-tolerant protocols using more qubits”
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In the paper
“The only quantum requirement for the clients would be to communicate with the nodes via quantum links enabling the transfer of arbitrary qubits.”
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In the paper
“Now, these blind measurements may be followed by non-blind ones. This will not affect the blindness (no information about φ 2 and φ 3 will be leaked to the server) as long as the structure of the algorithm permits the non-blind angles to be”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The authors state this as an assumption.
The initial state is chosen uniformly at random.
“The above value of χ assumes initial state is chosen uniformly at random.”
The authors state this as an assumption.
The errors in quantities extracted from density matrices are Poissonian.
“Uncertainties in quantities extracted from these density matrices are calculated using a Monte Carlo routine and assumed Poissonian errors.”
The paper relies on this without support.
No classical algorithm can succeed in the Grover search scenario with probability higher than 0.5.
“Note that no classical algorithm can succeed in this scenario with probability higher than 0 . 5.”
The authors state this as an assumption.
The only information obtained by the server is the initial quantum state supplied by the client, as well as the classical set of angles δi received during the protocol.
“we assume that the only information obtained by the server is the initial quantum state supplied by the client, as well as the classical set of angles δ i received during the protocol.”
The authors state this as an assumption.
The state produced by the experimental setup for a given choice of the ideal input state is fixed.
“We also assume that the state produced by the experimental setup for a given choice of the ideal input state is fixed”
The authors state this as an assumption.
The client's choices can be considered uniformly random.
“and that the client's choices can be considered uniformly random.”
The authors state this as an assumption.
In the calculations, Poissonian errors are always assumed.
“In our calculations, we always assume Poissonian errors.”
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“A modular design could be of particular advantage for all-optical quantum networks 7 and delegated quantum computations.28”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [28]
Citations
Cites
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Research works printed but not linked: 4
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Items 201–300 of 464
Hybrid classical-quantum communication networks
Lukens, J. M., Peters, N. A., & Qi, B. (2025) · Progress in Quantum Electronics · doi:10.1016/j.pquantelec.2025.100586 · Cited by 21
A hybrid universal blind quantum computation
Zhang, X., Luo, W., Zeng, G., Weng, J., Yang, Y., Chen, M.-R., & Tan, X. (2019) · Information Sciences · doi:10.1016/j.ins.2019.05.057 · Cited by 17
Probabilistic one-time programs using quantum entanglement
Roehsner, M.-C., Kettlewell, J. A., Fitzsimons, J. F., & Walther, P. J. (2021) · npj Quantum Information · doi:10.1038/s41534-021-00435-w · Cited by 16
Self-citationCritical Analysis of Big Data Privacy Preservation Techniques and Challenges
Madan, S., Bhardwaj, K., & Gupta, S. (2021) · Advances in intelligent systems and computing · doi:10.1007/978-981-16-3071-2_23 · Cited by 16
Meng, R.-R., Liu, X., Jin, M., Zhou, Z., Li, C., & Guo, G. (2024) · Chip · doi:10.1016/j.chip.2023.100081 · Cited by 16
Certifying the Topology of Quantum Networks: Theory and Experiment
Weinbrenner, L. T., Prasannan, N., Hansenne, K., Denker, S., Sperling, J., Brecht, B., Silberhorn, C., & Gühne, O. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.240802 · Cited by 15
Acausal measurement-based quantum computing
Morimae, T. (2014) · Physical Review A · doi:10.1103/physreva.90.010101 · Cited by 15
Counting Classical Nodes in Quantum Networks
Lu, H., Huang, C.-Y., Li, Z.-D., Yin, X.-F., Zhang, R., Liao, T., Chen, Y.-A., Li, C., & Pan, J.-W. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.180503 · Cited by 15
Cross-Verification of Independent Quantum Devices
Greganti, C., Demarie, T. F., Ringbauer, M., Jones, J. A., Saggio, V., Calafell, I. A., Rozema, L. A., Erhard, A., Meth, M., Postler, L., et al. (2021) · Physical Review X · doi:10.1103/physrevx.11.031049 · Cited by 16
Self-citationGhobadi, R., Wein, S. C., Kaviani, H., Barclay, P. E., & Simon, C. (2019) · Physical Review A · doi:10.1103/physreva.99.053825 · Cited by 15
Vulnerability of Quantum Information Systems to Collective Manipulation
Gómez-Ruiz, F. J., Rodríguez, F. J., Quiroga, L., & Johnson, N. F. (2024) · IntechOpen eBooks · doi:10.5772/intechopen.1004935 · Cited by 15
Reconfigurable ternary optical processor based on row operation unit
Song, K., & Yan, L. (2015) · Optics Communications · doi:10.1016/j.optcom.2015.03.080 · Cited by 14
Improved Resource State for Verifiable Blind Quantum Computation
Xu, Q., Tan, X., & Huang, R. (2020) · Entropy · doi:10.3390/e22090996 · Cited by 14
Quantum verifiable protocol for secure modulo zero-sum randomness
Hayashi, M., & Koshiba, T. (2022) · Quantum Information Processing · doi:10.1007/s11128-022-03639-x · Cited by 14
All-photonic quantum repeater for multipartite entanglement generation
Li, C., Fu, Y., Liu, W., Xie, Y.-M., Li, B.-H., Zhou, M.-G., Yin, H., & Chen, Z. (2023) · Optics Letters · doi:10.1364/ol.482287 · Cited by 14
Generation of hybrid four-qubit entangled decoherence-free states assisted by the cavity-QED system
Zhou, Y., Li, X., Deng, Y., Li, H.-R., & Luo, M.-X. (2016) · Optics Communications · doi:10.1016/j.optcom.2015.12.065 · Cited by 14
Fletcher, A. I., Harney, C., Ghalaii, M., Papanastasiou, P., Mountogiannakis, A., Spedalieri, G., Hajomer, A. A. E., Gehring, T., & Pirandola, S. (2025) · Reports on Progress in Physics · doi:10.1088/1361-6633/adf4f4 · Cited by 13
Chip-to-Chip Quantum Photonic Controlled-not Gate Teleportation
Feng, L.-T., Zhang, M., Liu, D., Cheng, Y., Song, X., Ding, Y., Daoxin Dai, A., Guo, G., Guo, G., & Ren, X. (2025) · Physical Review Letters · doi:10.1103/d53g-v8q6 · Cited by 17
Quantum verification of NP problems with single photons and linear optics
Zhang, A., Zhan, H., Liao, J., Zheng, K., Jiang, T., Mi, M., Yao, P., & Zhang, L. (2021) · Light Science & Applications · doi:10.1038/s41377-021-00608-4 · Cited by 13
Blind quantum machine learning based on quantum circuit model
Zhou, X., & Qiu, D. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03301-y · Cited by 13
Noise-resistant quantum state compression readout
Ding, C., Xu, X.-Y., Niu, Y.-F., Zhang, S., Bao, W., & Huang, H.-L. (2023) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-022-2005-x · Cited by 13
Quantum autoencoders for communication-efficient cloud computing
Zhu, Y., Bai, G., Wang, Y., Li, T., & Chiribella, G. (2023) · Quantum Machine Intelligence · doi:10.1007/s42484-023-00112-5 · Cited by 15
Jing, X., Qian, C., Zheng, X., Nian, H., Wang, C., Tang, J., Gu, X., Kong, Y., Chen, T., Liu, Y., et al. (2024) · Chip · doi:10.1016/j.chip.2024.100083 · Cited by 13
Classical verification of quantum circuits containing few basis changes
Demarie, T. F., Ouyang, Y., & Fitzsimons, J. F. (2018) · Physical Review A · doi:10.1103/physreva.97.042319 · Cited by 13
Self-citationControl mechanism of double-rotator-structure ternary optical computer
Song, K., & Yan, L. (2016) · Optics Communications · doi:10.1016/j.optcom.2016.12.004 · Cited by 13
Client-friendly continuous-variable blind and verifiable quantum computing
Liu, N., Demarie, T. F., Tan, S.-H., Aolita, L., & Fitzsimons, J. F. (2019) · Physical Review A · doi:10.1103/physreva.100.062309 · Cited by 12
Self-citationRemote-controlled quantum computing by quantum entanglement
Wang, D., Liu, Y., Ding, J., Qiang, X., Liu, Y., Huang, A., Fu, X., Xu, P., Deng, M., Yang, X., et al. (2020) · Optics Letters · doi:10.1364/ol.401921 · Cited by 12
Blind Quantum Signature with Blind Quantum Computation
Li, W., Shi, R., & Guo, Y. (2016) · International Journal of Theoretical Physics · doi:10.1007/s10773-016-3252-z · Cited by 12
Experimental demonstration of a measurement-based realisation of a quantum channel
McCutcheon, W., McMillan, A., Rarity, J. G., & Tame, M. S. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa9b5c · Cited by 13
Measurement-based universal blind quantum computation with minor resources
Zhang, X. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03365-w · Cited by 12
Inglesant, P., Hartswood, M., & Jirotka, M. D. (2016) · Oxford University Research Archive (ORA) (University of Oxford) · Cited by 12
Experimental Verifiable Multiclient Blind Quantum Computing on a Qline Architecture
Polacchi, B., Leichtle, D., Carvacho, G., Milani, G., Spagnolo, N., Kaplan, M., Kashefi, E., & Sciarrino, F. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.200603 · Cited by 11
Self-citationParallel self‐testing for device‐independent verifiable blind quantum computation
Xu, Q., Tan, X., Huang, R., & Zeng, X. (2020) · Quantum Engineering · doi:10.1002/que2.51 · Cited by 11
Enhanced delegated computing using coherence
Barz, S., Dunjko, V., Schlederer, F., Moore, M., Kashefi, E., & Walmsley, I. A. (2016) · Physical Review A · doi:10.1103/physreva.93.032339 · Cited by 11
Self-citationvan Dam, J., Avis, G., Propp, T. B., da Silva, F. F., Slater, J. A., Northup, T. E., & Wehner, S. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad6eb2 · Cited by 16
Variational secure cloud quantum computing
Shingu, Y., Takeuchi, Y., Endo, S., Kawabata, S., Watabe, S., Nikuni, T., Hakoshima, H., & Matsuzaki, Y. (2022) · Physical Review A · doi:10.1103/physreva.105.022603 · Cited by 11
Lessons Learned on the Interface Between Quantum and Conventional Networking
Alshowkan, M., Rao, N. S. V., Chapman, J. C., Williams, B. P., Evans, P. G., Pooser, R. C., Lukens, J. M., & Peters, N. A. (2022) · Communications in computer and information science · doi:10.1007/978-3-030-96498-6_15 · Cited by 10
Protocol for Routing Entanglement in the Quantum Ring Network
Shirichian, M., & Tofighi, S. (2018) · International Symposium on Telecommunications · doi:10.1109/istel.2018.8661126 · Cited by 10
A probabilistic model of quantum states for classical data security
Waseem, H. M., & Hwang, S. O. (2023) · Frontiers of Physics · doi:10.1007/s11467-023-1293-3 · Cited by 11
Effect of temperature on the coherence time of a parabolic quantum dot qubit
Xiao, W., & Wang, H. (2015) · Low Temperature Physics · doi:10.1063/1.4913756 · Cited by 10
Surface-Acoustic-Wave Computing of the Grover Quantum Search Algorithm with Metasurfaces
Yang, C., Liu, T., Zhu, J., Ren, J., & Chen, H. (2021) · Physical Review Applied · doi:10.1103/physrevapplied.15.044040 · Cited by 9
Universal single-server blind quantum computation for classical clients
Xu, H.-R., & Wang, B.-H. (2021) · Laser Physics Letters · doi:10.1088/1612-202x/ac3a0d · Cited by 10
Interconversion of pure Gaussian states requiring non-Gaussian operations
Jabbour, M. G., García−Patrón, R., & Cerf, N. J. (2015) · Physical Review A · doi:10.1103/physreva.91.012316 · Cited by 9
An Overview on Quantum Computing as a Service (QCaaS): Probability or Possibility
Rahaman, M., & Islam, M. M. (2016) · International Journal of Mathematical Sciences and Computing · doi:10.5815/ijmsc.2016.01.02 · Cited by 9
General Quantum Entanglement Purification Protocol using a Controlled‐Phase‐Flip Gate
Lu, L., Ren, B., Wang, X., Zhang, M., & Deng, F. (2020) · Annalen der Physik · doi:10.1002/andp.202000011 · Cited by 9
Blindness and Verification of Quantum Computation with One Pure Qubit
Kapourniotis, T., Kashefi, E., & Datta, A. (2014) · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · doi:10.4230/lipics.tqc.2014.176 · Cited by 9
Self-citationSecure Multi-Party Quantum Computation Based on Blind Quantum Computation
Qu, G.-J., & Wang, M. (2021) · International Journal of Theoretical Physics · doi:10.1007/s10773-021-04902-0 · Cited by 9
Optically Loaded Semiconductor Quantum Memory Register
Kim, D. C., Kiselev, A. A., Ross, R. S., Rakher, M. T., Jones, C., & Ladd, T. D. (2016) · Physical Review Applied · doi:10.1103/physrevapplied.5.024014 · Cited by 9
An Optimized Quantum Maximum or Minimum Searching Algorithm and its CircuitsPreprint
Chen, Y., Wei, S., Gao, X., Wang, C., Wu, J., & Guo, H. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1908.07943 · Cited by 10
Quantum machine learning via continuous-variable cluster states and teleportation
García‐Beni, J., Paparelle, I., Parigi, V., Giorgi, G. L., Soriano, M. C., & Zambrini, R. (2025) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-025-00352-3 · Cited by 8
Classical and quantum compression for edge computing: the ubiquitous data dimensionality reduction
Bagherian, M., Chehade, S., Whitney, B., & Passian, A. (2023) · Computing · doi:10.1007/s00607-023-01154-0 · Cited by 10
Henge, S. K., Jayaraman, G., Sreedevi, M., Rajakumar, R., Rashid, M. U., Alshamrani, S. S., Alnfiai, M. M., & AlGhamdi, A. S. (2023) · Networks and Heterogeneous Media · doi:10.3934/nhm.2023057 · Cited by 8
Scalable determination of multipartite entanglement in quantum networks
Kao, W., Huang, C.-Y., Tsai, T.-J., Chen, S.-H., Sun, S.-Y., Li, Y., Liao, T., Chuu, C., Lu, H., & Li, C. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00867-0 · Cited by 10
So, J., Luo, J., Choi, J., McCullian, B., & Fuchs, G. D. (2024) · Nano Letters · doi:10.1021/acs.nanolett.4c03233 · Cited by 8
Overcoming the fundamental limit of quantum transduction via intraband entanglement
Shi, H., & Zhuang, Q. (2024) · Optica Quantum · doi:10.1364/opticaq.540881 · Cited by 8
Quantum-Secure Multiparty Deep Learning
Sulimany, K., Vadlamani, S. K., Hamerly, R., Iyengar, P., & Englund, D. R. (2025) · Physical Review X · doi:10.1103/k8wg-qmbh · Cited by 11
Spatial reference frame agreement in quantum networks
Islam, T., Magnin, L., Sorg, B., & Wehner, S. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/6/063040 · Cited by 8
Frolovtsev, D. N., & Magnitskiy, S. A. (2017) · Physics of Wave Phenomena · doi:10.3103/s1541308x17030049 · Cited by 8
Nonlocality of a type of multi-star-shaped quantum networks
Yang, Y., Xiao, S., & Cao, H. (2021) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ac3f89 · Cited by 8
Measurement‐Based Hyperentanglement Distillation for Lossy and Distortion Photon State
Wang, P., Zhang, Z., Yu, C., Yuan, R., Du, F., & Ren, B. (2023) · Annalen der Physik · doi:10.1002/andp.202200505 · Cited by 8
Aging and reliability of quantum networks
Weinbrenner, L. T., Vandré, L., Coopmans, T. J., & Gühne, O. (2024) · Physical Review A · doi:10.1103/physreva.109.052611 · Cited by 8
Measurement-based quantum computation cannot avoid byproducts
Morimae, T. (2014) · International Journal of Quantum Information · doi:10.1142/s0219749914500269 · Cited by 7
Quantum compression of tensor network states
Bai, G., Yang, Y., & Chiribella, G. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ab7a34 · Cited by 7
Quantum-aided secure deep neural network inference on real quantum computers
Yu, H., Ren, X., Zhao, C., Yang, S., & McCann, J. A. (2023) · Scientific Reports · doi:10.1038/s41598-023-45791-z · Cited by 8
STIQ: Safeguarding Training and Inferencing of Quantum Neural Networks from Untrusted Cloud
Kundu, S., & Ghosh, S. (2025) · IEEE International Symposium on Hardware Oriented Security and Trust (HOST) · doi:10.1109/host64725.2025.11050015 · Cited by 7
Blind oracular quantum computation
Gustiani, C., & Divincenzo, D. P. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/ac13c8 · Cited by 9
Frequency-multiplexed Hong-Ou-Mandel interference
Ichihara, M., Yoshida, D., Hong, F.-L., & Horikiri, T. (2023) · Physical Review A · doi:10.1103/physreva.107.032608 · Cited by 7
Multiqubit quantum logical gates between distant quantum modules in a network
Xu, S., Mao, Y.-L., Feng, L., Hu, C., Guo, B., Liu, S., Li, Z.-D., & Fan, J. (2023) · Physical Review A · doi:10.1103/physreva.107.l060601 · Cited by 9
How to introduce quantum computers without slowing economic growth
Velu, C. K., & Putra, F. H. R. (2023) · Nature · doi:10.1038/d41586-023-02317-x · Cited by 7
Computing on quantum shared secrets for general quantum access structures
Bassirian, R., Boreiri, S., & Karimipour, V. (2019) · Quantum Information Processing · doi:10.1007/s11128-019-2224-7 · Cited by 7
On-chip multiphoton Greenberger—Horne—Zeilinger state based on integrated frequency combs
Zhu, P., Zheng, Q., Xue, S., Wu, C., Yu, X., Wang, Y., Liu, Y., Qiang, X., Wu, J., & Xu, P. (2020) · Frontiers of Physics · doi:10.1007/s11467-020-1010-4 · Cited by 7
Quantum blind signature based on quantum circuit
Lin, T.-S., Chen, Y., Chang, T.-H., Lu, C.-Y., & Kuo, S. (2014) · IEEE International Conference on Nanotechnology (IEEE-NANO) · doi:10.1109/nano.2014.6968020 · Cited by 7
Quantum-private distributed sensing
Ho, J., Webb, J. W., Brooks, R., Grasselli, F., Gauger, E. M., & Fedrizzi, A. (2026) · Journal of Physics Photonics · doi:10.1088/2515-7647/ae551a · Cited by 6
Dong, X., Liu, S., Mao, Y.-L., Guo, B., Xu, S., Chen, H., Guo, Y., Li, Z., & Fan, J. (2024) · Optics Express · doi:10.1364/oe.537668 · Cited by 7
Fault-tolerant blind quantum computing using GHZ states over depolarization channel
Tan, X., Tao, H. G., Zhang, X., Zeng, X., & Xu, Q. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03197-8 · Cited by 6
Blind three-qubit exact Grover search on a nitrogen-vacancy-center platform
Gustiani, C., & Divincenzo, D. P. (2021) · Physical Review A · doi:10.1103/physreva.104.062422 · Cited by 9
Direct moment estimation of intensity distribution of magnetic fields with quantum sensing network
Kasai, H., Takeuchi, Y., Matsuzaki, Y., & 都倉, 康. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad93f4 · Cited by 6
Quantum computation mediated by ancillary qudits and spin coherent states
Proctor, T. J., Dooley, S., & Kendon, V. M. (2015) · Physical Review A · doi:10.1103/physreva.91.012308 · Cited by 6
Practical Sharing of Quantum Secrets over Untrusted Channels
Markham, D., & Marin, A. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-17470-9_1 · Cited by 6
Memory-built-in quantum cloning in a hybrid solid-state spin register
Wang, W., Zu, C., He, L. T., Zhang, W.-G., & Duan, L.-M. (2015) · Scientific Reports · doi:10.1038/srep12203 · Cited by 6
Demonstration of a coexistence scheme between polarization-entangled QKD and classical data channels
Hipp, F., Hentschel, M., Aleksić, S., Poppe, A., & Hübel, H. (2016) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.2230222 · Cited by 6
Verifiable delegated quantum computation with χ -type entangled states
Tan, X., Zhang, X., & Song, T. (2016) · Computer Standards & Interfaces · doi:10.1016/j.csi.2016.09.008 · Cited by 6
Yamamoto, S., Nakazawa, S., Sugisaki, K., Maekawa, K., Sato, K., Toyota, K., Shiomi, D., & Takui, T. (2016) · Zeitschrift für Physikalische Chemie · doi:10.1515/zpch-2016-0799 · Cited by 6
The brickwork state with fewer qubits in blind quantum computation
Yang, Z., Bai, M.-Q., & Mo, Z. (2022) · Quantum Information Processing · doi:10.1007/s11128-022-03473-1 · Cited by 6
A Distributed Architecture for Secure Delegated Quantum Computation
Ma, S., Zhu, C., Quan, D., & Nie, M. (2022) · Entropy · doi:10.3390/e24060794 · Cited by 7
Impossibility of blind quantum sampling for classical client
Morimae, T., Nishimura, H., Takeuch, Y., & Tani, S. (2019) · Quantum Information and Computation · doi:10.26421/qic19.9-10-3 · Cited by 6
Research progress of measurement-based quantum computation
Zhang, S., Zhang, X., & Li, L.-Z. (2021) · Acta Physica Sinica · doi:10.7498/aps.70.20210923 · Cited by 7
Verified Delegated Quantum Computing with One Pure QubitPreprint
Kapourniotis, T., Kashefi, E., & Datta, A. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1403.1438 · Cited by 6
Self-citationMoving Beyond Trust in Quantum Computing
Vedral, V. (2012) · Science · doi:10.1126/science.1216922 · Cited by 6
Quantum Indistinguishability by Path Identity: The awakening of a sleeping beautyPreprint
Hochrainer, A., Lahiri, M., Erhard, M., Krenn, M., & Zeilinger, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2101.02431 · Cited by 7
Self-citationDouble-slit experiment with multiple vortex beams
Aili, M., Liu, P., Chen, X.-X., Wu, Q., Meng, Z., Yang, J.-Z., Li, J., & Zhang, A. (2024) · Physical Review A · doi:10.1103/physreva.109.013521 · Cited by 5
Quantum computing using photons
Couteau, C. (2025) · The European Physical Journal A · doi:10.1140/epja/s10050-025-01517-5 · Cited by 9
Satellites promise global-scale quantum networks
Goswami, S., Dhara, S., Sinclair, N., Mohageg, M., Sidhu, J. S., Mukhopadhyay, S., Krutzik, M., Lowell, J. R., Oi, D. K. L., Gündoğan, M., et al. (2025) · Optica Quantum · doi:10.1364/opticaq.567531 · Cited by 7
Experimental characterization of a non-local convertor for quantum photonic networks
Mičuda, M., Stárek, R., Marek, P., Miková, M., Straka, I., Ježek, M., Tashima, T., Özdemir, Ş. K., & Tame, M. (2017) · Optics Express · doi:10.1364/oe.25.007839 · Cited by 5
QuChain: On the Security and Privacy of Peer-to-Peer System using Blind Quantum Computation
Waseem, H. M., Deebak, B. D., Majeed, A., & Hwang, S. O. (2023) · IEEE International Conference on Nanotechnology (IEEE-NANO) · doi:10.1109/nano58406.2023.10231156 · Cited by 5
Quantum repeaters: current research trends and latest achievements
Ахмеджанов, Р. А., Balega, Y. Y., Deev, A. D., & Kalachev, A. A. (2025) · Physics-Uspekhi · doi:10.3367/ufne.2025.05.039918 · Cited by 5
Time evolution of entanglement and bistability of two coupled quantum dots in a driven cavity
Shiau, H.-H., Mitra, A., & Vyas, R. (2013) · Journal of Modern Optics · doi:10.1080/09500340.2013.837204 · Cited by 5
Noncryogenic Quantum Repeaters with hot Hybrid Alkali-Noble Gases
Ji, J.-W., Asadi, F. K., Heshami, K., & Simon, C. (2023) · Physical Review Applied · doi:10.1103/physrevapplied.19.054063 · Cited by 5
Ancilla-driven blind quantum computation for clients with different quantum capabilities
Dai, Q., Quan, J., Lou, X., & Li, Q. (2023) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-023-00173-2 · Cited by 5
A low failure rate quantum algorithm for searching maximum or minimum
Chen, Y., Wei, S., Gao, X., Wang, C., Tang, Y., Wu, J., & Guo, H. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02773-8 · Cited by 6
Metadata
- Authors
- Barz, S., Kashefi, E., Broadbent, A., Fitzsimons, J. F., Zeilinger, A., & Walther, P.
- Affiliations
- University of Vienna (AT)
- University of Edinburgh (GB)
- University of Waterloo (CA)
- University College Dublin (IE)
- Corresponding author
- Barz, Stefanie
- Venue
- Science
- Published
- 2012-01-20
- Volume
- 335
- Issue
- 6066
- Pages
- 303-308
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2008420411
- Semantic Scholar
- da7ab9e7a904fcb13d5bd91017ae03b88dfa67b6
- Cited by
- 475
- References
- 58
- Citations by year
- 2026: 28 · 2025: 47 · 2024: 36 · 2023: 41 · 2022: 22 · 2021: 52 · 2020: 23 · 2019: 30 · 2018: 31 · 2017: 25 · 2016: 47 · 2015: 26 · 2014: 25 · 2013: 22 · 2012: 17
- FWCI
- 28.13
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Science (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- National University of Singapore (submittedVersion)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Funders
- Air Force Office of Scientific Research (FA8655-11-1-3004)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Computer Networks and Communications › Cryptography and Data Security
- Keywords
- blind quantum computing, measurement-based quantum computation, cloud quantum computing, quantum privacy, delegated quantum computation, photonic qubits, Deutsch algorithm, Grover's algorithm
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-09, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-09 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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