Direct Probe of Topology and Geometry of Quantum States on IBM Q
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916276737146880 |
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| author | Chen, Tianqi Ding, Hai-Tao Shen, Ruizhe Zhu, Shi-Liang Gong, Jiangbin |
| author_facet | Chen, Tianqi Ding, Hai-Tao Shen, Ruizhe Zhu, Shi-Liang Gong, Jiangbin |
| contents | The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe of topological and geometric properties on a universal quantum computer even for a minimum model is still in vain. In this work, we first show that a density matrix form of the quantum geometric tensor (QGT) can be explicitly re-constructed from Pauli operator measurements on a quantum circuit. We then propose two algorithms, suitable for IBM quantum computers, to directly probe QGT. The first algorithm is a variational quantum algorithm particularly suitable for Noisy Intermediate-Scale Quantum (NISQ)-era devices, whereas the second one is a pure quantum algorithm based on quantum imaginary time evolution. Explicit results obtained from IBM Q simulating a Chern insulator model are presented and analysed. Our results indicate that transmon qubit-based universal quantum computers have the potential to directly simulate and investigate topological and geometric properties of a quantum system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14249 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Direct Probe of Topology and Geometry of Quantum States on IBM Q Chen, Tianqi Ding, Hai-Tao Shen, Ruizhe Zhu, Shi-Liang Gong, Jiangbin Quantum Physics Mesoscale and Nanoscale Physics The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe of topological and geometric properties on a universal quantum computer even for a minimum model is still in vain. In this work, we first show that a density matrix form of the quantum geometric tensor (QGT) can be explicitly re-constructed from Pauli operator measurements on a quantum circuit. We then propose two algorithms, suitable for IBM quantum computers, to directly probe QGT. The first algorithm is a variational quantum algorithm particularly suitable for Noisy Intermediate-Scale Quantum (NISQ)-era devices, whereas the second one is a pure quantum algorithm based on quantum imaginary time evolution. Explicit results obtained from IBM Q simulating a Chern insulator model are presented and analysed. Our results indicate that transmon qubit-based universal quantum computers have the potential to directly simulate and investigate topological and geometric properties of a quantum system. |
| title | Direct Probe of Topology and Geometry of Quantum States on IBM Q |
| topic | Quantum Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2403.14249 |