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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.09248 |
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| _version_ | 1866915489422245888 |
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| author | Wan, Lingyun Liu, Jie Yang, Jinlong |
| author_facet | Wan, Lingyun Liu, Jie Yang, Jinlong |
| contents | Accurate computation of the Green's function is crucial for connecting experimental observations to the underlying quantum states. A major challenge in evaluating the Green's function in the time domain lies in the efficient simulation of quantum state evolution under a given Hamiltonian-a task that becomes exponentially complex for strongly correlated systems on classical computers. Quantum computing provides a promising pathway to overcome this barrier by enabling efficient simulation of quantum dynamics. However, for near-term quantum devices with limited coherence times and fidelity, the deep quantum circuits required to implement time-evolution operators present a significant challenge for practical applications. In this work, we introduce an efficient algorithm for computing Green's functions via Cartan decomposition, which requires only fixed-depth quantum circuits for arbitrarily long time simulations. Additionally, analytical gradients are formulated to accelerate the Cartan decomposition by leveraging a unitary transformation in a factorized form. The new algorithm is applied to simulate long-time Green's functions for the Fermi-Hubbard and transverse-field Ising models, extracting the spectral functions through Fourier transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09248 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Special Issue: Commemorating the 110th Anniversary of TANG Au-chin's Birthday Calculation of the Green's function on near-term quantum computers via Cartan decomposition Wan, Lingyun Liu, Jie Yang, Jinlong Quantum Physics Accurate computation of the Green's function is crucial for connecting experimental observations to the underlying quantum states. A major challenge in evaluating the Green's function in the time domain lies in the efficient simulation of quantum state evolution under a given Hamiltonian-a task that becomes exponentially complex for strongly correlated systems on classical computers. Quantum computing provides a promising pathway to overcome this barrier by enabling efficient simulation of quantum dynamics. However, for near-term quantum devices with limited coherence times and fidelity, the deep quantum circuits required to implement time-evolution operators present a significant challenge for practical applications. In this work, we introduce an efficient algorithm for computing Green's functions via Cartan decomposition, which requires only fixed-depth quantum circuits for arbitrarily long time simulations. Additionally, analytical gradients are formulated to accelerate the Cartan decomposition by leveraging a unitary transformation in a factorized form. The new algorithm is applied to simulate long-time Green's functions for the Fermi-Hubbard and transverse-field Ising models, extracting the spectral functions through Fourier transformation. |
| title | Special Issue: Commemorating the 110th Anniversary of TANG Au-chin's Birthday Calculation of the Green's function on near-term quantum computers via Cartan decomposition |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.09248 |