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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.04620 |
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| _version_ | 1866909993619423232 |
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| author | Rahman, Salahuddin Abdul Karabacak, Özkan Wisniewski, Rafal |
| author_facet | Rahman, Salahuddin Abdul Karabacak, Özkan Wisniewski, Rafal |
| contents | Recently, feedback-based quantum algorithms have been introduced to calculate the ground states of Hamiltonians, inspired by quantum Lyapunov control theory. This paper aims to generalize these algorithms to the problem of calculating an eigenstate of a given Hamiltonian, assuming that the lower energy eigenstates are known. To this aim, we propose a new design methodology that combines the layer-wise construction of the quantum circuit in feedback-based quantum algorithms with a new feedback law based on a new Lyapunov function to assign the quantum circuit parameters. We present two approaches for evaluating the circuit parameters: one based on the expectation and overlap estimation of the terms in the feedback law and another based on the gradient of the Lyapunov function. We demonstrate the algorithm through an illustrative example and through an application in quantum chemistry. To assess its performance, we conduct numerical simulations and execution on IBM's superconducting quantum computer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04620 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Feedback-Based Quantum Algorithm for Excited States Calculation Rahman, Salahuddin Abdul Karabacak, Özkan Wisniewski, Rafal Quantum Physics Recently, feedback-based quantum algorithms have been introduced to calculate the ground states of Hamiltonians, inspired by quantum Lyapunov control theory. This paper aims to generalize these algorithms to the problem of calculating an eigenstate of a given Hamiltonian, assuming that the lower energy eigenstates are known. To this aim, we propose a new design methodology that combines the layer-wise construction of the quantum circuit in feedback-based quantum algorithms with a new feedback law based on a new Lyapunov function to assign the quantum circuit parameters. We present two approaches for evaluating the circuit parameters: one based on the expectation and overlap estimation of the terms in the feedback law and another based on the gradient of the Lyapunov function. We demonstrate the algorithm through an illustrative example and through an application in quantum chemistry. To assess its performance, we conduct numerical simulations and execution on IBM's superconducting quantum computer. |
| title | Feedback-Based Quantum Algorithm for Excited States Calculation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.04620 |