From quantum cellular automata to quantum lattice gases
TLDR
In this paper, it was shown that there is no nontrivial, homogeneous, local, unitary, scalar cellular automata in one dimension, and that the homogeneity condition can be overcome by a quantum cellular automaton with exactly unitary partitioning.Abstract:
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 proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial, exactly unitary, partitioning cellular automata. We find a one-parameter family of evolution rules which are best interpreted as those for a one-particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second, of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.read more
Citations
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Exactly Solved Models in Statistical Mechanics
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Quantum random walks: an introductory overview
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Environment-assisted quantum walks in photosynthetic energy transfer.
TL;DR: A theoretical framework for studying the role of quantum interference effects in energy transfer dynamics of molecular arrays interacting with a thermal bath within the Lindblad formalism is developed and an effective interplay between the free Hamiltonian evolution and the thermal fluctuations in the environment is demonstrated.
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Quantum walks: a comprehensive review
TL;DR: This paper has reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.
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Exponential algorithmic speedup by a quantum walk
TL;DR: A black box graph traversal problem that can be solved exponentially faster on a quantum computer than on a classical computer is constructed and it is proved that no classical algorithm can solve the problem in subexponential time.
References
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Proceedings ArticleDOI
Algorithms for quantum computation: discrete logarithms and factoring
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