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

• URL: http://arxiv.org/abs/2304.13408v2
• Date: Fri, 22 Nov 2024 08:45:48 GMT
• Title: Quantum-circuit algorithms for many-body topological invariant and Majorana zero mode
• Authors: Takanori Sugimoto,
• Abstract summary: Topological states of matter are promising resources for composing fault-tolerant quantum computers. Existing quantum-circuit algorithms to examine topological properties remain limited. 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.
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• 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.

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