Grover's Algorithm and Many-Valued Quantum Logic
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As the engineering endeavour to realise quantum computers progresses, we consider that such machines need not rely on binary as their de facto unit of information. We investigate Grover's algorithm under a generalised quantum circuit model, in which the information and transformations can be expressed in any arity, and analyse the structural and behavioural properties while preserving the semantics; namely, searching for the unique preimage to an output a function. We conclude by demonstrating that the generalised procedure retains O(√(N)) time complexity.
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