Diamond as a Solid State Quantum Computer with a Linear Chain of Nuclear Spins System

G V López

doi:10.4236/jmp.2014.51009

Abstract

By removing a 12C atom from the tetrahedral configuration of the diamond, replacing it by a 13C atom, and repeating this in a linear direction, it is possible to have a linear chain of nuclear spins one half and to build a solid state quantum computer. One qubit rotation, controlled-not (CNOT) and controlled-controlled-not (CCNOT) quantum gates are obtained immediately from this configuration. CNOT and CCNOT quantum gates are used to determined the design parameters of this quantum computer.

Highlights

The idea of having a working quantum computer with enough number of qubits has faced two main problems: the decoherence [1,2,3,4,5,6,7,8] due the interaction of the environment with the quantum system, and technological limitations
It was shown that by removing a 12C atom, replacing it by a 13C atom in the tetrahedral configuration of the diamond, and doing this process periodically in a linear direction, one could get a linear chain of nuclear spins one half which can work as a quantum computer
The interaction between 13C atoms is governed by the magnetic dipole-dipole interaction, and the parameters of a possible quantum computer design were determined by studying the quantum CNOT and CCNOT gates with two and three qubits respectively

Summary

Introduction

The idea of having a working quantum computer with enough number of qubits (at least 1000) has faced two main problems: the decoherence [1,2,3,4,5,6,7,8] due the interaction of the environment with the quantum system, and technological limitations (pick up signal from NMR quantum computer [9,10], laser control capability in ion trap quantum computer [11,12], physical build up for more than two qubits like in photons cavities [13], atoms traps [14,15], Josephson’s joint ions [16], Aronov-Bhom devices [17], diamond NV device [18], or high field and high field gradients in linear chain of paramagnetic atoms with spin one half [19]). One put together the ideas of using the diamond stable structure and the linear chain of spin one half nucleus. On the tetrahedral 12C (with nuclear spin zero) configuration of the diamond main structure, one removes a 12C element of this configuration and replace it by a 13C (with nuclear spin one half) atom, and one repeats this replacement along a linear direction of the crystal. By doing this replacement, one obtains a linear chain of atoms of nuclear spin one half which is protected from the environment by the crystal structure and the electrons cloud. Aligning the chain of 13C nucleus along the x-axis of the reference system and assuming Ising interaction between 13C nucleus, this energy can be written as

Hamiltonian of the System

Analysis of the System

Conclusion and Discussion