While the team did its experiment using an NMR machine, they expect that their approach could also work in other physical systems for quantum computers, such as superconductors, and that it could serve as a potential system for quantum memory.
Each matrix plots out “Anyonic” statistics that represent the behaviour of anyons in a system: the S matrix shows what happens when a quantum system that is mapped onto a torus is rotated; the T matrix defines that same toric system when it is sheared.
Theory told them that the system they were simulating – a particular kind of topological code called a Z2 toric code, which is the simplest example of topological order – has four ground states, but they didn’t know what quantum phase those states belonged to.
Quantum systems are described using something called a Hamiltonian. The ground state of a quantum system is the lowest energy it can have while still maintaining its particular Hamiltonian.
They designed an experiment using the “Adiabetic method,” which posits that, if you move slowly enough, you can manipulate a quantum system without disrupting its quantum-ness.
At each quantum phase, a topological system obeys specific rules or symmetries.