Black hole qubit correspondence from quantum circuits

Abstract

We consider the black hole qubit correspondence (BHQC) from quantum circuits, taking into account the use of gate operations with base in the formulation of wrapped brane qubits. We interpret these quantum circuits with base on the BHQC classification of entanglement classes and apply in specific examples as the generation of Bell, GHZ states, quantum circuit teleportation and consider the implementation of interchanges in SUSY, black hole configurations, Freudenthal and rank system constructions. These results are discussed from the superstring viewpoint showing that the importance of the construction of the physical states formed by the entanglement of geometrical entities by cohomological operations automatically allows the preservation of different amounts of SUSY in the compactification process given an alternative to the case when fluxes are introduced in the game: the generalized Calabi-Yau of Hitchin.

Peccei–Quinn Transformations and Black Holes: Orbit Transmutations and Entanglement Generation

“…However, in order to generate entanglement in EBH systems through PQ symplectic transformations and thus realize "EBH quantum circuits" and "EBH quantum gates" in the context of BHQC [45], one can employ simpler composed PQ operators, namely:…”

“…As observed, e.g., in [28], this is a crucial step in order to implement a quantum mechanical computation (such as the ones exploited by the "EBH quantum circuits" and "EBH quantum gates" [45]), since in QIT, all parameters are generally complex and not real (as instead, the electric and magnetic charges of an EBH are). This clearly implies that the PQ symplectic transformations themselves should be considered on a complex ground field C, since they act on the complex vector space R C , on which G 4 (C) acts linearly, but non-transitively.…”

“…Moreover, the Hilbert space for qubits was traced back to wrapped branes inside the cohomology of the extra dimensions [32,42], and exceptional groups E 7 and E 6 were respectively related to the tripartite entanglement of seven qubits [43] and to the bipartite entanglement of three qutrits [44]. Recently, "BH quantum gates" were formulated within the BHQC in [45].…”

“…Going beyond the SLOCC paradigm within the BHQC, [45] investigated the possibility of establishing quantum circuits (realizing certain classes of quantum gate operations) capable of switching, within the same FTS, from one rank class to another one. On the BH (supergravity) side of BHQC, this essentially amounts to switching from one U-duality orbit to another one; in the present treatment, this phenomenon will be named orbit transmutation.…”

“…In FTS terms, this amounts to switching from an FTS element with a definite rank to another FTS element with another rank, lying in another orbit of the FTS automorphism group. In this context, specific quantum circuits generating Bell states, quantum teleportation and GHZ states can be clearly associated with the protocols of actions on the charge state configurations of EBHs [45].…”