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Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.11 n.4 México Apr./Jun. 2008

 

Qubits Structure as an Enhancement Factor of Coherence in a One–Way Quantum Computer

 

Estructura de Qubits como un Factor de Realce de Coherencia en una Computadora Cuántica de un Solo Camino

 

Isidro Valentín Rodríguez1, Magally Martínez Reyes1 and Manuel Ávila Aoki1

 

1 Centro Universitario UAEM Valle de Chalco, Universidad Autónoma del Estado de México. María Isabel, CP 56615, Valle de Chalco, Estado de México, México. E–mails: nnervio@gmail.com, mmreyes@cinvestav.mx, manvlk@uaemex.mx.

 

Article received on July 05, 2007
Accepted on January 24, 2008

 

Abstract

Present day's efforts for building up an operative quantum computer soon will take shape. One of the main challenges to this task is to implement qubit coherence in a practical way. We make emphasis on the structure of the nuclear qubits in a one–way quantum computer as a source of coherence enhancement. The form factor, accounting for the nuclear qubit structure of the model, is the magnetogyric ratio γ (more commonly called the gyromagnetic ratio). We collect experimental values for y and calculate the respective times of coherence Th , for a number of materials. A parametrization is also given for γ, in terms of the atomic number, whose agreement with the experiment is very good. We also calculate, accurately enough, bounds to the corrections to Th due to spurious dipolar coupling between nuclei because this has not been done in the past. Such corrections are negligible for nearby planes whereas for remote planes they might be of considerable size. It is concluded that the nuclei states last longer than their electronic counterpart. However, this stability of nuclei qubits limits the speed at which the computer can carry out instructions and process the information.

Keywords: Qubit, structure, form factors, dipolar coupling, spurious, decoherence time.

 

Resumen

Esfuerzos presentes para construir una computadora cuántica operativa, pronto tomarán forma. Uno de los principales retos de esta tarea es el de implementar coherencia de qubits de una manera práctica. Hacemos énfasis en la estructura de los qubits nucleares en una computadora cuántica de un solo camino como fuente de realce de coherencia. El factor de forma, que explica la estructura del qubit nuclear, del modelo es la razón magnetogírica y (más comúnmente llamada la razón giromágnetica). Colectamos valores experimentales para γ y calculamos los respectivos tiempos de coherencia, Th, para diferentes materiales. Es también dada una parametrización para γ en términos del número atómico cuyo acuerdo con el experimento es bastante bueno. También calculamos cotas suficientemente exactas para las correcciones a Th debidas a acoplamientos espurios dipolares en tanto que en el pasado no se les ha tratado con suficiente atención. Tales correcciones son despreciables para planos cercanos mientras que para planos remotos, ellas podrían ser de tamaño considerable. Es concluido que los estados nucleares duran más que su contraparte electrónica. No obstante, esta estabilidad de los qubits nucleares limita la rapidez a la cual la computadora puede efectuar las instrucciones y procesar la información.

Descriptores: Qubit, estructura, factores de forma, acoplamiento dipolar, espurio, tiempo de deco–herencia.

 

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Acknowledgments

We wish to thank SNI grant.

 

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Glossary

Qubit: The logic register of a quantum processor. It can take the values q = α 0 > + β 1> where 0 > and 1 > are the basic logic blocks and α2 + β 2 = 1.

Qubit structure: The qubit (nucleon) size.

Form factors: The mathematical functions accounting for the qubit size.

Dipolar coupling: Energy of interaction between the nuclei magnetic dipole.

Decoherence time: Time during which superposition of the states does not suffer quantum perturbation.

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