Geodesic
Computing with the Square Root of NOT
Serdica Journal of Computing, Tome 3 (2009) no. 4, pp. 359-370.

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To the two classical reversible 1-bit logic gates, i.e. the identity gate (a.k.a. the follower) and the NOT gate (a.k.a. the inverter), we add an extra gate, the square root of NOT. Similarly, we add to the 24 classical reversible 2-bit circuits, both the square root of NOT and the controlled square root of NOT. This leads to a new kind of calculus, situated between classical reversible computing and quantum computing.
Keywords: Reversible Computing, Square Root of NOT, Discrete Group 
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De Vos, Alexis; De Beule, Jan; Storme, Leo. Computing with the Square Root of NOT. Serdica Journal of Computing, Tome 3 (2009) no. 4, pp. 359-370. http://geodesic.mathdoc.fr/item/SJC_2009_3_4_a1/