Correction to: Int J Theor Phys (2017) 56:2990–3004

https://doi.org/10.1007/s10773-017-3466-8

The authors want to add two references in the original version of this article. The references are as follows.

27. Angizi, S., Sarmadi, S., Sayedsalehi, S., Navi, K.: Design and evaluation of new majority gate-based RAM cell in quantum-dot cellular automata, Microelectron. J. 46 (2015) 43–51 (Elsevier)

28. Chabi, A.M., et al.: Towards ultra-efficient QCA reversible circuits. Microprocessors and Microsystems, 2017. 49: pp. 127–138.

Reference [27] is cited in the first full sentence following equation (4) as below:

The structure of this gate is shown in Fig. 7 [20–24, 27].

Reference [28] is cited in the first full sentence following Table 1 as below:

This structure is constructed from one two-input AND gate and one two-input XOR gate [28].

Everything else remain unchanged.