Quantum Error Correction in Loop Quantum Gravity

Abstract

Previous works (by Almiehri, Dong, Harlow, Pastakawski, Preskill, Yoshida and others) have established that quantum error correction plays an important role in understanding how the bulk degrees of freedom of an Anti-deSitter spacetime are encoded in the degrees of freedom of the boundary Conformal Field Theory. In previous work [1] I have argued that the Bilson-Thompson model [2,3] of elementary particles allows us to view elementary particles as gates for universal quantum computation. In the present work I show that the Bilson-Thompson model, where elementary particles are represented by elements of the framed braid group on three strands, provides an explicit model for the generation of qutrit (three-qubit) states which are the ingredients of Shor's quantum error correcting code. This allows, for the first time, to connect in a concrete manner the proposals of Almheiri, Pastawski, Preskill and others regarding the role of quantum error correction in quantum gravity, to a viable model of elementary particles. Loop Quantum Gravity (LQG), the theory of quantum gravity in which such topological excitations exist, can thus serve as the glue which can connect AdS/CFT based approaches to quantum gravity to the well understood physics of the Standard Model.