  The topological state of matter is a potential resource to realize long-term
fault-tolerant quantum computers beyond the near-term noisy intermediate-scale
quantum devices. To achieve the realization, we need a deep understanding of
topological behaviors in real quantum computers. However, quantum-circuit
algorithms to analyze topological properties have still been insufficient. Here
we propose three quantum-circuit algorithms, (i) to find the ground state in
the selected parity subspace, (ii) to determine the many-body topological
invariant, and (iii) to visualize the zero-energy edge mode. To demonstrate
these algorithms, we adopt the interacting Kitaev chain as a typical model of
many-body topological superconductors in one dimension. The algorithms are
applicable to not only one-dimensional topological superconductors but other
topological states including higher-dimensional systems.
