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In this paper, we study the localization of an electron in a binary quantum system formed by a pair of quantum dots (QDs). The traditional theoretical consideration of such systems is limited to the symmetrical case when QDs in such double quantum dot (DQD) are assumed identical in all respects. In this paper, we model the effects of breaking QD similarities in a DQD by studying two-dimensional (2D) DQDs as a double quantum well (DQW). This is done by solving the Schrödinger equation, with parameters chosen to describe an InAs/GaAs heterostructure. We calculate the energy spectrum of the electron confinement and the spectral distribution of localized/delocalized spatial states. Both symmetric and asymmetric QW shapes are considered and their effects are compared. The effects of symmetry breaking are explained within the framework of the two-level system theory. We delineate the QW weak and strong coupling cases in DQW. In particular, we show that the coherence in ideal DQW is unstable in the case of a weak QW coupling. Within the framework of the proposed approach, a charge qubit realized on a DQD is discussed and, as an example, a qubit based on an almost ideal DQD is proposed. 

We study electron tunneling in binary quantum systems as double quantum dot (DQD) and double quantum well (DQW), considered as two-level systems. The Schrodinger equation for this system is reduced using single band kp-effective Hamiltonian, and is solved numerically. We calculate full electron spectrum E, n = 1,2 ... in the bi-confinement potential. The tunneling in DQD is studied in relation to two factors, a coupling coefficient W and an asymmetry factor A of the potential. The ratio W/A defines the electron localization in DQD. The cases of ideal and almost ideal DQD are examined and compared. We are modeling the effects of environmental influence and fluctuations of electrical pulse on the coherence of DQD based charge qubit. In particular, we show that the coupling in the ideal DQD (A=0) is unstable for any small fluctuations of A.