Universal quantum computation using the discrete-time quantum walk

By Neil B. Lovett, S. Cooper, Matthew S. Everitt, M. Trevers, V. Kendon. 2009

466 citations recorded by the source corpus.

A proof that continuous-time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by A. M. Childs [Phys. Rev. Lett. 102, 180501 (2009)]. We present a version based instead on the discrete-time quantum walk. We show that the discrete-time quantum walk is able to implement the same universal gate set and thus both discrete and continuous-time quantum walks are computational primitives. Additionally, we give a set of components on which the discrete-time quantum walk provides perfect state transfer.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8bf62965c6c0a0e49c62d895cf79f2c912c55f7e

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Citations in the corpus

Simulating chemistry using quantum computers. (2010, background): “Although we focus on the adiabatic and circuit models, these are not the only universal models of quantum computation, and it may be possible to make further algorithmic progress with models such as topological quantum computing (8,9), one-way quantum computing (10, 11), and quantum walks (12, 135, ”
Boson Sampling on a Photonic Chip (2012, background): “They also require qubit-speciﬁc state initialization, measurement, and the generation of quantum correlations across the system [1–5].”
Quantum walks: a comprehensive review (2012, methodology): “the propagation method proposed in [301] in the following lines.”