Quantum Walks on Quantum Cellular Automata Lattices: Towards a New Model for Quantum Computation
Many physical problems cannot be easily formulated as quantum circuits, which are a successful universal model for quantum computation. Because of this, new models that are closer to the structure of physical systems must be developed. Discrete and continuous quantum walks have been proven to be a universal quantum computation model, but building quantum computing systems based on their structure is not straightforward. Although classical cellular automata are models of universal classical computation, this is not the case for their quantum counterpart, which is limited by the no-coning theorem and the no-go lemma. Here we combine quantum walks, which reproduce unitary evolution in space with quantum cellular automata, which reproduce unitary evolution in time, to form a new model of quantum computation. Our results show that such a model is possible.
KeywordsQuantum cellular automata Quantum walks Quantum computing
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