Grover's Algorithm and the Secant Varieties
Fr\'ed\'eric Holweck, Hamza Jaffali, Isma\"el Nounouh
TL;DR
This paper explores the entanglement properties of quantum states produced by Grover's algorithm using algebraic geometry, linking entanglement to algebraic varieties and providing new qualitative insights.
Contribution
It introduces a novel algebraic geometric framework to analyze entanglement in Grover's algorithm, connecting it to secant varieties and offering interpretative tools.
Findings
Established a link between entanglement and algebraic varieties.
Provided qualitative interpretations of previous numerical results.
Analyzed specific examples in detail.
Abstract
In this paper we investigate the entanglement nature of quantum states generated by Grover's search algorithm by means of algebraic geometry. More precisely we establish a link between entanglement of states generated by the algorithm and auxiliary algebraic varieties built from the set of separable states. This new perspective enables us to propose qualitative interpretations of earlier numerical results obtained by M. Rossi et al. We also illustrate our purpose with a couple of examples investigated in details.
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