Fault-tolerant discrete time quantum walks

Název anglicky / Title English: Fault-tolerant discrete time quantum walks
Osnova / Outline:

Quantum walks are a promising platform for quantum simulators and quantum algorithms [1]. In a discrete time quantum walk the walker hops along edges of a graph from one vertex to the other depending on its internal coin state. If we allow the coin state, as well as the walker's position, to assume arbitrary superpositions the resulting process exhibits a quadratic speedup over the classical random walk. Algorithmic applications of the discrete time quantum walk rely on this speedup.

Up to date there are several experimental implementations of quantum walks [2], including on lattice topologies in 2 dimensions [3]. Crucial limiting factor preventing applications of quantum information to real-world problems are experimental imperfections and decoherence. Error correcting codes, formulated within the standard model of quantum computing, provide means to combat these effects [4]. Recently, examples of quantum error correction improving robustness of quantum walks have been proposed in the scientific literature [5,6].

The aim of this assigment is to familiarize with the notion of quantum walks, quantum error correcting codes and existing proposals for their application to quantum walks, and eventually design new error correction schemes applicable to real-world implementations.

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. K. Manouchehri, J.B. Wang: "Physical Implementation of Quantum Walks," Springer, 2014
  3. A. Schreiber, A. Gábris, P. P. Rohde, K. Laiho, M. Štefaňák, V. Potoček, C. Hamilton, I. Jex, and Ch. Silberhorn: "A 2D Quantum Walk Simulation of Two-Particle Dynamics." Science 336, 55 (2012)
  4. M. A. Nielsen & I. L. Chuang: "Quantum Computation and Quantum Information," Cambridge University Press (2011)
  5. S. D. Freedman, Y. H. Tong, J. B. Wang: Fault-tolerant quantum walks, arXiv:1408.1250 (2014)
  6. X. Qiang, T. Loke, A. Montanaro, K. Aungskunsiri, X. Zhou, J. L. O’Brien, J. B. Wang & J. C. F. Matthews: "Efficient quantum walk on a quantum processor," Nature Communications 7, 11511 (2016)


Jméno vedoucího / Supervisor name: Aurél Gábris, PhD
Pracoviště vedoucího / Supervisor office: KF FJFI, BR 13b
Email vedoucího / Supervisor email: gabris.aurel@fjfi.cvut.cz
Datum zadání / Date of creation: 20/03/2017
Jazyk / Language:
  • Anglicky / English
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