The tensor-network representation, which is a popular tool in condensed matter physics, enables efficient descriptions of quantum many-body states in an exponentially-large Hilbert space. If a resource many-body state of the measurement-based quantum computation is represented in the tensor-network form, we can obtain a clear view of what is going on in the measurement-based quantum computation [1,2]. This new framework of the measurement-based quantum computation has enabled the systematic exploration of new resource states beyond the cluster state [1].

In this talk, I will first briefly review the basics of the tensor-network representation and the measurement-based quantum computation on the tensor-network states including our recent results [2,3,4,5].

Next, I will give one recent application of such a general measurement-based quantum computation, namely the blind quantum computation. Blind quantum computation is the following secure delegated quantum computation: Alice who does not have any quantum computer asks Bob who has a fully-fledged quantum computer to perform her algorithm on his quantum computer in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. Such a blind protocol is difficult for the circuit model. However, recently it was shown that if we use the cluster model, such a protocol can be easily done[6]. We have recently shown that such a blind quantum computation is also possible on other MBQC models such as the AKLT states [7] and the Raussendorf's topological MBQC [8], by using the above general scheme.

[1] D. Gross and J. Eisert, PRL98, 220503 (2007).
[2] TM, Phys. Rev. A 83, 042337 (2011)
[3] TM, arXiv:1012.1000
[4] K. Fujii and TM, arXiv:1106.3377
[5] TM and K. Fujii, arXiv:1106.3720
[6] A. Broadbent, J. Fitzsimons, and E. Kashefi FOCS2009
[7] TM, V. Dunjko, and E. Kashefi, arXiv: 1009.3486
[8] TM and K. Fujii, arXiv:1110.5460

Summary of our results are also available at the following url.(in Japanese)