One-Dimensional Coinless Quantum Walks
arXiv:1408.5166 · doi:10.1103/PhysRevA.91.052319
Abstract
A coinless, discrete-time quantum walk possesses a Hilbert space whose dimension is smaller compared to the widely-studied coined walk. Coined walks require the direct product of the site basis with the coin space, coinless walks operate purely in the site basis, which is clearly minimal. These coinless quantum walks have received considerable attention recently because they have evolution operators that can be obtained by a graphical method based on lattice tessellations and they have been shown to be as efficient as the best known coined walks when used as a quantum search algorithm. We argue that both formulations in their most general form are equivalent. In particular, we demonstrate how to transform the one-dimensional version of the coinless quantum walk into an equivalent extended coined version for a specific family of evolution operators. We present some of its basic, asymptotic features for the one-dimensional lattice with some examples of tessellations, and analyze the mixing time and limiting probability distributions on cycles.
16 pages, 6 figs, added a reference
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- Relation between Random Walks and Quantum Walks
- Quantum walks with a one-dimensional coin
- Quantum search on the two-dimensional lattice using the staggered model with Hamiltonians
- Discrete-Time Quantum-Walk & Floquet Topological Insulators via Distance-Selective Rydberg-Interaction
- Dynamics of Rydberg excitations and quantum correlations in an atomic array coupled to a photonic crystal waveguide
- Staggered quantum walks with superconducting microwave resonators
- Moments of Coinless Quantum Walks on Lattices
- Virtually Abelian Quantum Walks
- Chirality from quantum walks without quantum coin
- Second-order topological insulator in a coinless discrete-time quantum walk
- Boundary-induced coherence in the staggered quantum walk on different topologies
- Transient temperature and mixing times of quantum walks on cycles
- A new type of quantum walks based on decomposing quantum states
- Discrete-Time Quantum Walks on Oriented Graphs
- Transport and Localization in Quantum Walks on a Random Hierarchy of Barriers