Topologically-Protected Quantum Cloud Computing
Authors: Tomoyuki Morimae1 and Keisuke Fujii2
1Department of Physics, Imperial College, London, UK
2Graduate School of Engineering Science, Osaka University, Japan
A first generation quantum computer, which must be an integration of extremely high technologies, will be used in a ``cloud computing" style since only limited number of groups, such as governments and huge industries, will be able to possess it. Clients who do not have enough money and technologies to possess their own quantum computers will access a quantum ``server" from their terminals and remotely run their quantum algorithm on the server. One of the most essential requirements in such a cloud quantum computing is the security of the client's privacy: a client should be able to delegate her quantum computation to a server in such a way that the server cannot learn anything about client's privacy.
Blind quantum computation provides a solution to such a privacy issue. Blind quantum computation is a novel secure quantum computing protocol which enables Alice, who does not have enough quantum technologies, to delegate her quantum computation to Bob, who has a fully-fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. A protocol of blind quantum computation for almost classical Alice was first invented by Broadbent, Fitzsimons, and Kashefi  using the measurement-based quantum computation  (Fig.1). In their protocol, Alice has only to possess a device which emits randomly-rotated single qubit states. Recently, the Broadbent-Fitzsimons-Kashefi (BFK) protocol was experimentally demonstrated in an optical system . This proof-of-principle experiment of blind quantum computation has raised new challenges regarding the scalability of blind quantum computation in noisy conditions.
Fig. 1 The first blind protocol for almost classical Alice by Broadbent, Fitzsimons, and Kashefi.(Image courtesy of Liu Jia)
In Ref. , we have shown that fault-tolerant blind quantum computation is possible. We adopt the topological quantum computing scheme by Raussendorf, Harrington, and Goyal  to the BFK protocol. The topological quantum computing scheme is one of the most promising fault-tolerant methods in today's quantum computing architecture. In this scheme, a certain three-dimensional system of entangled qubits is first prepared, and then defects are created by measuring out some qubits of the three-dimensional system. These defects behave as anyons, and therefore braiding of defects can implement quantum gates .
Fig.2 Illustration of our protocol. Alice knows her topological quantum computation, whereas Bob cannot.
In our protocol, Alice can run her topologically-protected quantum computation on Bob's quantum computer in such a way that Alice's privacy is kept secret to Bob (Fig. 2). More precisely, our protocol runs as follows (Fig.3). Like the BFK protocol, Alice first sends randomly-rotated qubits to Bob (Fig.3 (a)). By entangling these qubits, Bob next creates a certain three-dimensional system, which is a modification of the Raussendorf-Harrington-Goyal one (Fig.3 (b)). Then, Alice and Bob perform measurement-based quantum computing with exchanging classical messages (Fig.3 (c) and (d)). If Bob is honest, Alice can perform the correct topologically-protected quantum computation (Fig. 3 (e)). On the other hand, whatever evil Bob does, he cannot learn anything about Alice's input, output, and algorithm (Fig.3 (e)).
Fig. 3 Explanation of our topological blind protocol.
We have also calculated the error threshold of our topological blind scheme. The error threshold is 0.43%, which is comparable to that (0.75%) of the normal (non-blind) topological quantum computation . As the error per gate of the order 0.1% has already been achieved in some experimental systems, such as trapped ions, our result suggests that secure cloud quantum computation is within reach.
 ``Universal blind quantum computation", Anne Broadbent, Joe Fitzsimons, and Elham Kashefi, in Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, 517-527 (IEEE Computer Society, Los Alamitos, USA, 2009). Abstract.
 ``A one-way quantum computer", Robert Raussendorf and Hans J. Briegel, Physical Review Letters, 86, 5188 (2001). Abstract.
 ``Experimental demonstration of blind quantum computing", Stefanie Barz, Elham Kashefi, Anne Broadbent, Joe Fitzsimons, Anton Zeilinger, and Philip Walther, Science, 335, 303-308 (2012). Abstract.
 ``Blind topological measurement-based quantum computationh, Tomoyuki Morimae and Keisuke Fujii, Nature Communications 3, 1036 (2012). Abstract.
 ``Topological fault-tolerance in cluster state quantum computation", Robert Raussendorf, Jim Harrington, and Kovid Goyal, New Journal of Physics, 9, 199 (2007). Abstract.