Quantum computers store information in qubits, and qubits are fragile. Heat, stray fields and imperfections in materials disturb them, and the information they carry decays in a short time. The dominant strategy is quantum error correction, in which many physical qubits are combined to protect a smaller number of reliable logical ones, at a heavy overhead in hardware. Topological quantum computing proposes a different route. If information could be stored in a property of a system that is robust against local disturbance, in the way that a knot in a rope is not undone by shaking it, qubits could be inherently more stable. Topological insulators are among the materials studied as ingredients for realising that idea.
What makes topological insulators unusual?
A topological insulator is a material that behaves as an insulator in its interior and conducts electricity along its surface or edges. This is not a matter of surface contamination. It follows from the way the electron states of the whole crystal are organised, and the conducting surface states are protected by symmetry, so they persist despite small imperfections. In the surface states, an electron's spin is locked to its direction of motion, which makes backscattering from non-magnetic impurities strongly suppressed. These properties first attracted attention for low-dissipation electronics and spintronics. Their relevance to quantum computing arises from what happens when such a material is placed in contact with a superconductor.
How could this lead to protected qubits?
Theory predicts that the combination of a topological insulator surface and a superconductor can host exotic excitations called Majorana zero modes. Information can be encoded in the shared state of a pair of such modes that are far apart, so a local disturbance affecting one end does not reveal or alter the stored value. Operations would be performed by moving the modes around each other, a process called braiding, whose outcome depends only on the path's topology. In principle, this offers qubits with error rates far lower than conventional ones, which would reduce the overhead of error correction. This is the appeal of the approach, and it should be stressed that it is a theoretical promise that experiments have yet to fully deliver.
Materials and the state of the evidence
Materials studied include bismuth selenide, bismuth telluride and antimony telluride, along with quantum wells of mercury telluride and related compounds. Making them is demanding, since crystals tend to contain defects that put the interior into a conducting state and obscure the surface physics, and interfaces with superconductors must be clean. Experimental claims of Majorana signatures have been made by several groups, and some have been questioned or withdrawn when alternative explanations were found, so the field treats individual results with caution. Competing approaches, including superconducting circuits and trapped ions, have advanced steadily meanwhile, and topological hardware would need to demonstrate a clear advantage to compete.
Why it matters
Reliable quantum computation is likely to require qubits and error correction of a quality that is still some way off, and any approach that reduces the burden is worth investigating. Topological insulators illustrate how an advance in basic materials science can open a path to new computing hardware, as well as the care needed to separate a compelling theory from a demonstrated device. Progress will depend on cleaner materials, reproducible measurements and independent confirmation of the key signatures.
A protected qubit is a beautiful idea. The work is proving that the material really behaves the way the theory says.
