  In quantum computing, the computation is achieved by linear operators in or
between Hilbert spaces. In this work, we explore a new computation scheme, in
which the linear operators in quantum computing are replaced by (higher)
functors between two (higher) categories. If from Turing computing to quantum
computing is the first quantization of computation, then this new scheme can be
viewed as the second quantization of computation. The fundamental problem in
realizing this idea is how to realize a (higher) functor physically. We provide
a theoretical idea of realizing (higher) functors physically based on the
physics of topological orders.
