Demonstration of Blind Quantum Computing

In the paper

“We demonstrate various blind delegated computations, including oneand two-qubit gates and the Deutsch and Grover algorithms.”

In the paper

“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

In the paper

“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.”

In the paper

“Both implemented rotations are blind and the entire computation remains hidden.”

In the paper

“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.”

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

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.”

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.”

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

In the paper

“These non-ideal fidelities arise due to experimental imperfections (see Appendix).”

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

In the paper

“This is a unique feature of photonic systems and so far not realizable in other quantum systems.”

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.”

In the paper

“Different algorithms require only a different pattern of single-qubit measurements on a sufficiently large cluster state.”

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

In the paper

“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.”

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.”

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).”

In the paper

“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(”

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

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).

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

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).

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 .”

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.”

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.”

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.”

In the paper

“Due to blindness, however, the quantum server has no information about which initial states the client has prepared.”

In the paper

“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.”

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.”

In the paper

“we stress that our results are applicable to any physical implementation of qubits”

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.”

In the paper

“Furthermore, post-selection and photon losses decrease the efficiency of the protocol.”

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”

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.”

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”