This example was suggested to our writers by Edward Witten of the Institute for Advanced Study.

One of the surprising ways pure mathematics has shaped modern technology is through something called topological quantum field theory (TQFT). Originally developed to study the properties of shapes and spaces, TQFT focuses not on precise measurements like lengths and angles, but on broader questions like: Does this object have a hole? How many holes? If you stretch or bend it without tearing, does it stay the same? These large-scale, or topological, features turn out to be incredibly stable — resistant to noise and small imperfections — and physicists realized that the same ideas could apply to certain exotic materials.

This realization led to the discovery of topological superconductors. These materials behave like normal superconductors deep inside, but along their edges or around defects, they host strange new types of quantum states. In particular, they can support Majorana fermions — exotic particles that are their own antiparticles. What makes Majorana fermions special is that they are not localized to a single point: they are spread out over a region, with two Majorana “halves” often living at opposite ends of a material. Because of this non-local nature, if you poke or disturb one end, you can’t easily change the overall state. The information they carry is tied to the topology — the “global” structure — rather than anything local. This makes them remarkably stable against the kinds of errors that plague ordinary quantum bits (qubits).

Today, scientists are racing to harness these properties to build topological quantum computers. In these systems, information would be stored not in fragile states that can be disrupted by every tiny bump or vibration, but in the “braids” formed by moving Majorana fermions around each other. Because these braids depend only on the order and structure of the paths taken — not on the exact timing or microscopic details — they offer a way to perform quantum computations that are naturally protected from errors. In fact, as of 2025, scientists and engineers have been able to design chips that can store and measure 8 qubits, with the ability to scale to a million qubits over time.

Quantum computer operating on million qubit chips could solve many problems that classical computers can not, which would completely revolutionize our daily lives. For example, they could simulate the behavior of complex molecules and quantum materials in ways that current supercomputers cannot — revolutionizing drug discovery, catalyst design, and materials science. They could also solve certain types of optimization problems exponentially faster, such as improving logistics and scheduling, or cracking encryption schemes based on number theory — a prospect that has national security implications.