Computation in Quantum Space-time Could Lead to a Super-polynomial Speedup

In theoretical computer science, researchers usually distinguish between feasible problems (that can be solved in polynomial time) and problems that require more computation time. A natural question is: can we use new physical processes, processes that have not been used in modern computers, to make computations drastically faster -- e.g., to make intractable problems feasible? Such a possibility would occur if a physical process provides a super-polynomial (= faster than polynomial) speed-up.

In this direction, the most active research is undertaken in quantum computing. It is well known that quantum processes can drastically speed up computations; however, there are no proven super-polynomial quantum speedups of the overall computation time.