Jacob Miller and Akimasa Miyake have recently published a paper in Physical Review Letters giving strong evidence that certain forms of symmetric topological quantum matter can be utilized ubiquitously to power quantum computation. Their work is carried out within measurement-based quantum computation, where computation is extracted from a fixed quantum “resource state” using local measurements. In this setting, the power of computation attributes the physical properties of the resource state, but the properties which guarantee a state can carry out universal quantum computation are still unknown.
In their work, the authors study a model of symmetric topological matter and identify special states in each phase which enable universal quantum computation precisely when they possess nontrivial quantum order. This gives an infinite family of new universal resource states whose structure perfectly mirrors a recent classification of symmetric quantum order coming from condensed matter physics. These special resource states are distinguished by their “fractional symmetry”, a property already noticed in previous universal resource states, but which hadn’t been investigated systematically. Overall, the work provides a concrete research program for identifying phases of universal quantum computation within the setting of symmetric quantum matter.
The full article can be found online at Phys. Rev. Lett. 120, 170503 (2018).
Classification of special resource states with fractional symmetry.