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

## Abstract

On thinking up a Grover-type quantum search algorithm for an ordered tuple of multiqubit states, a gradient system associated with the negative von Neumann entropy is studied on the space of regular relative configurations of multiqubit states (SR{sup 2}CMQ). The SR{sup 2}CMQ emerges, through a geometric procedure, from the space of ordered tuples of multiqubit 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{sup 2}CMQ, of that system.

- Authors:

- Future University-Hakodate, School of Systems Information Sciences (Japan), E-mail: uwano@fun.ac.jp
- Kyoto University, Department of Applied Mathematics and Physics (Japan)

- Publication Date:

- OSTI Identifier:
- 21075886

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Atomic Nuclei; Journal Volume: 70; Journal Issue: 4; Other Information: DOI: 10.1134/S1063778807040217; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CONFIGURATION; ENTROPY; INTEGRAL CALCULUS; MATHEMATICAL SPACE; QUANTUM INFORMATION

### Citation Formats

```
Uwano, Y., Hino, H., and Ishiwatari, Y..
```*Certain integrable system on a space associated with a quantum search algorithm*. United States: N. p., 2007.
Web. doi:10.1134/S1063778807040217.

```
Uwano, Y., Hino, H., & Ishiwatari, Y..
```*Certain integrable system on a space associated with a quantum search algorithm*. United States. doi:10.1134/S1063778807040217.

```
Uwano, Y., Hino, H., and Ishiwatari, Y.. Sun .
"Certain integrable system on a space associated with a quantum search algorithm". United States.
doi:10.1134/S1063778807040217.
```

```
@article{osti_21075886,
```

title = {Certain integrable system on a space associated with a quantum search algorithm},

author = {Uwano, Y. and Hino, H. and Ishiwatari, Y.},

abstractNote = {On thinking up a Grover-type quantum search algorithm for an ordered tuple of multiqubit states, a gradient system associated with the negative von Neumann entropy is studied on the space of regular relative configurations of multiqubit states (SR{sup 2}CMQ). The SR{sup 2}CMQ emerges, through a geometric procedure, from the space of ordered tuples of multiqubit 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{sup 2}CMQ, of that system.},

doi = {10.1134/S1063778807040217},

journal = {Physics of Atomic Nuclei},

number = 4,

volume = 70,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}

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