- MRL 2053
- Special Physics Colloquium
We present recent advances in our understanding of (i) exotic quantum phases of matter in three dimensions, and (ii) robust mechanisms for storing and processing quantum information, that have been enabled by new techniques to study highly-entangled quantum states. First, we introduce new kinds of quantum phases which are characterized by the presence of gapped, point-like excitations that are strictly immobile. These states of matter -- termed "fracton" phases -- provide a remarkable alternative to the conventional Bose or Fermi statistics of point-like excitations in three dimensions, as well as a gateway for studying "slow" dynamical behavior in the absence of disorder. We then apply the same tools used to discover these phases in order to construct entangled states of fermions that can be used to robustly store and process quantum information; our efforts are inspired by recent interest in encoding physical qubits in the fermion occupation number. We introduce the first quantum error-correcting codes that can recover from fermion parity-violating (quasiparticle poisoning) errors, and propose their realizations in experiments on mesoscopic superconductors that host Majorana zero modes.