Study of Decoherence of Elementary Gates Implemented in a Chain of Few Nuclear Spins Quantum Computer Model

Abstract

We study the phenomenon of decoherence during the operation of one qubit transformation, controlled-not (CNOT) and controlled-controlled-not (C 2 NOT) quantum gates in a quantum computer model formed by a linear chain of three nuclear spins system. We make this study with different type of environments, and we determine the associated decoherence time as a function of the dissipative parameter. We found that the dissipation parameter to get a well defined quantum gates (without significant decoherence) must be within the range of . We also study the behavior of the purity parameter for these gates and different environments and found linear or quadratic decays of this parameter depending on the type of environments.

Study of Decoherence on the Teleportation Algorithm in a Chain of Three Nuclear Spins System

“…The environment is now at a certain finite temperature, and it can be thought as field radiation modes contained in a cavity where the central system lies. The Lindblad term has the following form [11,24] …”

“…In our case, one has that , the dimensionality of our Hilbert space is eight, and the explicit equations for the dynamical system of each case be see in the appendix of reference [24,25]. We have considered that it is not necessary to repeat those equations in this manuscript.…”

Study of Decoherence of Entangled States Made up of Two Basic States in a Linear Chain of Three Qubits

“…In this work, we are interested in determining the decoherence of several entangled states formed by two states of three qubits, and we will use the above mentioned Markovian-Lindblad master type of equation [4] [12]. On the other hand, even this model for solid state quantum computer has not been built; it has been very useful for theoretical studies about implementation of quantum gates and quantum algorithms [13]- [16] which can be extrapolated to other solid state quantum computers. The main idea is to explore the possible sensitivity of the decay of an entangled state with respect to the energy-difference of its two states involved; we establish four cases to be considered with the quantum-environment system: independent environment interaction, pure dephasing interaction, correlated dissipation interaction, and dephasing correlated interaction.…”

Quasi non-Markovian Approach to the Study of Decoherence of a Controlled-Not Quantum Gate in a Chain of Few Nuclear Spins Quantum Computer

“…Kelvins, the master equation takes the form as 0 T  0 T described in [28] for the A-Independent environment cases, and we still have the time dependent terms on the non diagonal elements of the master equation, referring to the quasi-non Markovian case. Figure 3 shows the behavior of the diagonal elements of the CNOT quantum gate at  Kelvins.…”

“…This type of master equations generates no-correlated thermalized cases which describes spontaneous and thermally induced emission-absorption process [3,28,29]. The environment generates excitations or de-excitations in the closed system by absorbing-emitting photons of the thermal bath.…”