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

Quantum-circuit algorithms for many-body topological invariant and Majorana zero mode