How Long Can Passive Quantum Memories Withstand Depolarizing Noise?

Abstract: Existing fault tolerance theorems state that robust quantum
computation and in particular, quantum memories may be achieved by
growing the number of dedicated resources. Such theorems assume the
availability of fresh ancillas (qubits in a predefined state) and the
possibility of periodically applying recovery operations. Experimentally
however, these requirements have shown to be hard to meet. In an attempt
to provide a simpler path, many body Hamiltonians have been proposed with
the hope that they could through their dynamics alone provide long
protection times to quantum information. I will explain recent results
which show that under a depolarizing noise model, protection times may not
exceed O(log N) and such scaling is achievable by many body non-local
Hamiltonians. I will go on to mention existing proposals for protecting
Hamiltonians and describe some limitations we have found for the
information lifetime under comparatively weak Hamiltonian perturbations.