Generating Fault-Tolerant Cluster States from Crystal Structures

Quantum information is delicate.  To preserve it, we must constantly interact  with our system in order to remove errors.  However, not all patterns of interaction are made equal; some strategies for removing errors are more robust than others.

In this work (arXiv:1909.11817),  Michael Newman, Leonardo de Castro, and Kenneth Brown use a different perspective on processing quantum information known as 'measurement-based quantum computing on graph states' to choose interaction patterns that are good for removing errors.  These patterns can be described by crystal structures that tile space in interesting ways.  Using an algebraic language for this geometric problem, we construct various interaction patterns, including some that only require our qubits to talk to their three nearest neighbors.  These systematically generated space tilings provide a static language for improving the dynamics of quantum error-correction.