TL;DR
This paper explores the Grover quantum search algorithm through a topological framework, offering new insights and proofs of correctness that enhance understanding and potential generalizations.
Contribution
It introduces a topological perspective to analyze the multi-step Grover algorithm, providing novel proofs and insights into its structure.
Findings
Topological approach offers new proofs of algorithm correctness
Provides clearer understanding of Grover algorithm structure
Facilitates potential generalizations of quantum algorithms
Abstract
It has been shown in recent years that quantum information has a topological nature (\cite{AC}, \cite{Co}, \cite{Co2}). In \cite{V}, Vicary undergoes the study of quantum algorithms using this new topological approach. The advantage of this new formalism is that it allows new proofs of correctness of the algorithms such as Deutsch-Jozsa, hidden subgroup and single-shot Grover algorithms. It also provide more clear insight to the generalizations of these algorithms. In this paper, we consider (multi-step) Grover algorithm from this new perspective.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Mechanics and Applications · Quantum Information and Cryptography