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<p>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 is 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 challenge by enabling efficient simulation of the time evolution operator. 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 <i>via</i> 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 the factorized form. The new algorithm is applied to simulating longtime Green’s functions for the Fermi-Hubbard and transverse-field Ising models, extracting the spectral functions through Fourier transformation.</p>

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Calculation of the Green’s Function on Near-term Quantum Computers via Cartan Decomposition

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • Lingyun Wan,
  • Jie Liu,
  • Jinlong Yang

摘要

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 is 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 challenge by enabling efficient simulation of the time evolution operator. 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 the factorized form. The new algorithm is applied to simulating longtime Green’s functions for the Fermi-Hubbard and transverse-field Ising models, extracting the spectral functions through Fourier transformation.