In a recent paper (Mod. Phys. Lett. A 2015, 30, 1550104), the black-hole/qubit correspondence (BHQC) was exploited to deﬁne “black hole quantum circuits” allowing for a change of the supersymmetry-preserving features of electromagnetic charge conﬁgurations supporting the black hole solution. This resulted in switching from one U-duality orbit to another, or equivalently, from an element of the corresponding Freudenthal triple system with a deﬁnite rank to another one. On the supergravity side of BHQC, such quantum gates are related to particular symplectic transformations acting on the black hole charges; namely, such transformations cannot belong to the U-duality group, otherwise switching among orbits would be impossible. In this paper, we consider a particular class of such symplectic transformations, namely the ones belonging to the so-called Peccei–Quinn symplectic group, introduced some time ago within the study of very special Kähler geometries of the vector multiplets’ scalar manifolds in N = 2 supergravity in D =4 spacetime dimensions.
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