Unifying the Clifford Hierarchy

Narayanan Rengaswamy, Robert Calderbank, and Henry Pfister have posted to the arXiv their recent paper on Unifying the Clifford Hierarchy via Symmetric Matrices over Rings.  The Clifford hierarchy is a way to classify operations on a quantum computer.  The hierarchy is especially useful in the context of error correction where position in the hierarcy can be related to the difficulty of constructing the desired operation from a simple set of instructions. By connecting the Clifford hierarchy to symmetric matrices over rings, Narayanan, Robert, and Henry provide both insight into the mathematics and new possiblities for the construction of quantum compilers.