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

Abstract

Topological states of matter are promising resources for composing fault-tolerant quantum computers, advancing beyond the limitations of current noisy intermediate-scale quantum devices. To enable this progress, a deep understanding of topological phenomena within actual quantum computing platforms is essential. However, existing quantum-circuit algorithms to examine topological properties remain limited. Here we introduce three quantum-circuit algorithms designed to (i) determine the ground state within a specified parity subspace, (ii) identify the many-body topological invariant, and (iii) visualize zero-energy edge modes. We illustrate these algorithms with the interacting Kitaev chain, a typical model of one-dimensional topological superconductors. These approaches are versatile, extending beyond one-dimensional systems to various topological states, including those in higher dimensions.