Exact simulation of coined quantum walks with the continuous-time model
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The connection between coined and continuous-time quantum walk models has been addressed in a number of papers. In most of those studies, the continuous-time model is derived from coined quantum walks by employing dimensional reduction and taking appropriate limits. In this work, we produce the evolution of a coined quantum walk on a generic graph using a continuous-time quantum walk on a larger graph. In addition to expanding the underlying structure, we also have to switch on and off edges during the continuous-time evolution to accommodate the alternation between the shift and coin operators from the coined model. In one particular case, the connection is very natural, and the continuous-time quantum walk that simulates the coined quantum walk is driven by the graph Laplacian on the dynamically changing expanded graph.
KeywordsQuantum walks Quantum walk on graphs Coined quantum walk Continuous-time quantum walk
P.P. would like to thank CNPq for its financial support (Grant Nos. 400216/2014-0 and 150726/2015-5). R.P. acknowledges financial support from Faperj (Grant No. E-26/102.350/2013) and CNPq (Grant Nos. 303406/2015-1 and 474143/2013-9).
- 2.Aharonov, D., Ambainis, A., Kempe, J., Vazirani, U.: Quantum walks on graphs. In: Proceedings of the Thirty-third Annual ACM Symposium on Theory of Computing, STOC ’01, pp. 50–59. ACM, New York (2001)Google Scholar
- 9.Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing, STOC ’96, pp. 212–219. ACM, New York (1996)Google Scholar
- 11.Ambainis, A., Kempe, J., Rivosh, A.: Coins make quantum walks faster. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’05, pp. 1099–1108. Society for Industrial and Applied Mathematics, Philadelphia (2005)Google Scholar
- 16.Mallick, A., Mandal, S., Chandrashekar, C.M.: Simulation of neutrino oscillations using discrete-time quantum walk. ArXiv e-prints, April (2016)Google Scholar
- 22.di Molfetta, G., Debbasch, F.: Discrete-time quantum walks: continuous limit and symmetries. J. Math. Phys. 53(12), 123302 (2012)Google Scholar
- 24.Szegedy, M.: Quantum speed-up of Markov chain based algorithms. In: 45th Annual IEEE symposium on foundations of computer science, 2004. Proceedings, pp. 32–41, Oct (2004)Google Scholar
- 26.Oliveira, A.C., Portugal, R., Donangelo, R.: Decoherence in two-dimensional quantum walks. Phys. Rev. A 74(012312), 012312 (2006)Google Scholar