Study of Quantum Walk over a Square Lattice
arXiv:1803.05152 · doi:10.1103/PhysRevA.98.032104
Abstract
Quantum random walk finds application in efficient quantum algorithms as well as in quantum network theory. Here we study the mixing time of a discrete quantum walk over a square lattice in presence percolation and decoherence. We consider bit-flip and phase damping noise, and evaluate the instantaneous mixing time for both the cases. Using numerical analysis we show that in case of phase damping noise probability distribution of walker's position is sufficiently close to the uniform distribution after infinite time. However, during the action of bit-flip noise, even after infinite time the total variation distance between the two probability distributions is large enough.
arXiv commentInitial draft, 8 pages, 4 figures
References in corpus (20)
- A Quantum Random Walk Search Algorithm
- Quantum information can be negative
- An example of the difference between quantum and classical random walks
- Decoherence in quantum walks - a review
- Decoherence can be useful in quantum walks
- Quantum random walks with decoherent coins
- Hitting time for quantum walks on the hypercube
- Quantum walks on general graphs
- Quantum speedup of classical mixing processes
- Continuous-time Quantum Walks on a Cycle Graph
- Quantum random walk on the line as a markovian process
- Decoherence vs entanglement in coined quantum walks
- Decoherence in Quantum Walks on the Hypercube
- Almost uniform sampling via quantum walks
- Asymptotic dynamics of coined quantum walks on percolation graphs
- Analysis of Absorbing Times of Quantum Walks
- Mixing Times in Quantum Walks on the Hypercube
- Decoherence and Quantum Walks: anomalous diffusion and ballistic tails
- Asymptotic Evolution of Random Unitary Operations
- Decoherence on a two-dimensional quantum walk using four- and two-state particle
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- Two-particle Hadamard walk on dynamically percolated line and circle