Measurement-based interaction of quantum walkers

Název anglicky / Title English: Measurement-based interaction of quantum walkers
Osnova / Outline:

Discrete time quantum walks can be regarded as a quantum mechanical generalization of random walks. The process consists of a single walker hopping along edges of a graph from one vertex to the other depending on its internal coin state, allowing the coin state as well as the walker's position to assume arbitrary superpositions [1]. Discrete time quantum walks can be efficiently implemented using passive linear optical networks, i.e. using only beam-splitters (partially reflecting mirrors) and phase shifters, or equivalently polarization beam-splitters and wave-plates [2]. Quantum walks provide an efficient platform for simulating single-particle dynamics, which in some not very distant future could be turned into a practical device solving problems presently unsolvable using conventional computers. To unleash the full power of the platform it should include many quantum walkers with controlled interactions between them. There is yet no technology available to realize deterministic strong interaction between photons representing quantum walkers in a quantum optical implementation. The KLM protocol [3], however, offers a scheme to realize these non-linear interactions probabilistically, exploiting the projective nature of measurement in quantum mechanics, while retaining scalability [4,5]. The idea is to extend photonic implementations of discrete quantum walks to simulate interacting walker dynamics by applying probabilistic gate schemes, possibly including feed-forward [6].

The aim of this assigment is to familiarize with the notion of quantum walks, probabilistic non-linear gate schemes, and to devise schemes that implement probabilistic gates to simulate interactions in discrete time quantum walks.

The assigment is suitable both as a bachelors and as a masters thesis. In case of a bachelor thesis the emphasis will be on the study of existing literature, with the possibility to continue the research as master's thesis.

Literatura / reference:
  1. Renato Portugal: "Quantum Walks and Search Algorithms," Springer, (2013)
  2. Th. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen and Ch. Silberhorn: "Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer," New J. Phys. 18, 063017 (2016)
  3. E. Knill, R. Laflamme & G. J. Milburn: "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001)
  4. S. Scheel, K. Nemoto, W. J. Munro, and P. L. Knight: "Measurement-induced nonlinearity in linear optics," Phys. Rev. A 68, 032310 (2003)
  5. S. Scheel and K. M. R. Audenaert: "Scaling of success probabilities for linear optics gates," New J. Phys. 7, 149 (2005)
  6. S. Scheel, W. J. Munro, J. Eisert, K. Nemoto, and P. Kok: "Feed-forward and its role in conditional linear optical quantum dynamics," Phys. Rev. A 73, 034301 (2006)
Jméno vedoucího / Supervisor name: Aurél Gábris, PhD
Pracoviště vedoucího / Supervisor office: KF FJFI, BR 13b
Email vedoucího / Supervisor email:
Datum zadání / Date of creation: 21/03/2017
Jazyk / Language:
  • Anglicky / English
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