# History dependent quantum random walks as quantum lattice gas automata

@article{Shakeel2014HistoryDQ,
title={History dependent quantum random walks as quantum lattice gas automata},
author={Asif Shakeel and David A. Meyer and Peter J. Love},
journal={Journal of Mathematical Physics},
year={2014},
volume={55},
pages={122204}
}
• Published 5 May 2014
• Physics
• Journal of Mathematical Physics
Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified…
6 Citations

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## References

SHOWING 1-10 OF 49 REFERENCES

• Mathematics, Physics
• 2003
Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum
• Physics
Science
• 2013
The construction of a scalable quantum computer architecture based on multiple interacting quantum walkers could, in principle, be used as an architecture for building a scaled quantum computer with no need for time-dependent control.
• Physics
Physical review letters
• 2003
The position variance is used as an indicator of classical behavior and it is seen that the multicoin walk retains the "quantum" quadratic growth of the variance except in the limit of a new coin for every step, while the walk with decoherence exhibits "classical" linear growth ofThe variance even for weakDecoherence.
• Computer Science
• 2003
It will be shown that this algorithm performs an oracle search on a database of N items with $O(\sqrt{N})$ calls to the oracle, yielding a speedup similar to other quantum search algorithms.
A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, we begin an investigation of exactly unitary cellular automata. After
• Physics
• 2014
Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical
• Mathematics
Scientific reports
• 2014
A quantum walk in one dimension with tunable levels of self-avoidance is complemented with a memory register that records where the walker has previously resided and can be made to reproduce ideal quantum or classical random walk statistics, or a plethora of more elaborate diffusive phenomena.
• Mathematics, Physics
STOC '01
• 2001
A quantum analog of the symmetric random walk, which the authors call the Hadamard walk, is analyzed, which has position that is nearly uniformly distributed in the range after steps, in sharp contrast to the classical random walk.
• Physics
• 2013
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model
I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum