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Certain integrable system on a space associated with a quantum search algorithm

Yoshio Uwano·Hideitsu Hino·Yasue Ishiwatari
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Abstract

On thinking of a Grover-type quantum search algorithm for an ordered tuple of multi-qubit states, a gradient system associated with the negative von-Neumann entropy is studied on the space of regular relative-configurations of multi-qubit states (SR${}^2$CMQ). The SR${}^2$CMQ emerges, through a geometric procedure, from the space of ordered tuples of multi-qubit states for the quantum search. The aim of this paper is to give a brief report on the integrability of the gradient dynamical system together with quantum information geometry of the underlying space, SR${}^2$CMQ, of that system.

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Yoshio Uwano, Hideitsu Hino, Yasue Ishiwatari. 2005-12-02. Certain integrable system on a space associated with a quantum search algorithm. https://arxiv.org/abs/nlin/0512004

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