Abstract:
Recently, a new quantum algorithm has been proposed to determine the parity of cyclic permutations of arbitrary number of objects [1]. The algorithm makes use of a single quantum object with finite number of discrete levels in pure state and hence there are no correlations in the system. Soon after its proposal, the algorithm has been demonstrated experimentally in nuclear magnetic resonance systems for three [2] and four [3] levels, respectively. The origin of the quantum speed-up has not been clarified yet but since it works starting from three levels, contextuality is a possible candidate [4]. In this talk, the algorithm will be presented starting from the motivations originated from contextual nature of quantum mechanics and experimental systems will be explained.

[1] Z. Gedik, arXiv:1403.5861 [quant-ph]

[2] S. Dogra, Arvind, and K. Dorai, Physics Letters A 378, 3452 (2014)

[3] I. A. Silva, B. Çakmak, G. Karpat, E. L. G. Vidoto, D. O. Soares-Pinto, E. R. deAzevedo, F. F. Fanchini, and Z. Gedik, arXiv:1406.3579 [quant-ph]

[4] M. Howard, J. Wallman, V. Veitch, and J. Emerson, Nature 510, 351 (2014)