Special PME Quantum Seminar - Chao Yin

Physics in infinite dimensions

Many quantum platforms are able to host effectively infinite-dimensional interactions among the quantum particles, which challenges conventional physical ideas based on spatial locality. In the first part of my talk, I will introduce an all-to-all Hamiltonian protocol that provides an asymptotic speed-up, over the usual quantum-circuit protocols of processing digital information. On the other hand, certain finite-dimensional theories may generalize: I will show in the second part that many quantum low-density parity-check codes with powerful error correction properties are stable against local perturbations, justifying them as topological ordered phases of matter in infinite dimensions.