Topological quantum computing is based on a different approach to making qubits, compared to other qubit technologies, that can be protected against decoherence by a non-trivial topology. At first, the primary strategy for making topological qubits is based on a new type of quantum state known as a Majorana mode, also sometimes known as a Majorana fermion.
Conventional qubits avoid decoherence by interacting weakly with the environment, but the need to control and measure the qubits in the course of a quantum operation means that that coupling cannot be too weak, and decoherence remains the primary stumbling block for most existing qubit technologies.
An alternative approach to qubits is to encode the quantum 1’s and 0’s in a degree of freedom that is invisible to the environment at a local level, but can be seen and controlled by a clever experimentalist (or ultimately, by a quantum computer) by looking at the system as a whole. An analogy to this approach would be to encode “0” in a normal loop of paper, and “1” by adding a twist in that loop, as in a Mobius strip. If you look at any one place on the loop of paper, you can’t tell whether or not there is a twist, but by looking at the loop as a whole you can easily distinguish Mobius from normal.
This approach to quantum computing technologies is referred to as topological quantum computing, and is being pursued by Microsoft Research in collaboration with several research groups around the world. The Quantum Devices group is joining this effort in collaboration with the Microsoft approach, and at a more fundamental level by trying to better understand the mysterious states that could host such topological qubits, starting from so-called Majorana modes and ultimately moving on to a broader family of similar states (with names like “parafermions” and “Fibonnaci anyons”).
Quantum Devices Group: https://phas.ubc.ca/~qdev/