Topological Computation and Generative Artificial Intelligence

A fresh look is taken at what is commonly called "quantum" computation, from the purely topological perspective; for this reason we prefer to call it simply topological computation. Instead of arithmetic computation, where the inputs are numbers, encoded as bits, and the output are also numbers encoded as bits, after a series of arithmetic functions (addition, subtraction, multiplication, and division) have been done; topological computation is done, where the inputs are analytic functions, encoded as qubits, and the output are also analytic functions, encoded as qubits, after a series of functional (group addition, group subtraction, group multiplication, and group division) operations have been done. The analytic functions specify topologies or Lie groups. It will be discussed how a new Generative Artificial Intelligence, based on topological characterization and control, removes the three roadblocks to topological computation: (1) tying the system in the topological knots, that is encoding the input analytic functions into qubits, (2) identifying the output topological knots, that is decoding the output analytic function from qubits, and (3) stabilizing the system from disruptions, that is cooling the system.