Quantum computing topological invariants of two-dimensional quantum matter
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913614971011072 |
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| author | Niedermeier, Marcel Nairn, Marc Flindt, Christian Lado, Jose L. |
| author_facet | Niedermeier, Marcel Nairn, Marc Flindt, Christian Lado, Jose L. |
| contents | Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials, and a variety of numerical approaches for this purpose have been developed. However, the complexity of quantum many-body Hamiltonians makes calculations of topological invariants challenging for interacting systems. Here, we present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. Both circuits combine a gate-based adiabatic time-evolution over the discretized Brillouin zone with particular phase estimation techniques. The first algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. The second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits. Our results establish a method for computing topological invariants with quantum circuits, taking a step towards characterizing interacting topological quantum matter using quantum computers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum computing topological invariants of two-dimensional quantum matter Niedermeier, Marcel Nairn, Marc Flindt, Christian Lado, Jose L. Quantum Physics Mesoscale and Nanoscale Physics Strongly Correlated Electrons Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials, and a variety of numerical approaches for this purpose have been developed. However, the complexity of quantum many-body Hamiltonians makes calculations of topological invariants challenging for interacting systems. Here, we present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. Both circuits combine a gate-based adiabatic time-evolution over the discretized Brillouin zone with particular phase estimation techniques. The first algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. The second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits. Our results establish a method for computing topological invariants with quantum circuits, taking a step towards characterizing interacting topological quantum matter using quantum computers. |
| title | Quantum computing topological invariants of two-dimensional quantum matter |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2404.06048 |