Non-Stationary Long-Term Dynamics via Selected Incomplete Dual Bases

• URL: http://arxiv.org/abs/2306.07407v2
• Date: Tue, 22 Oct 2024 17:00:36 GMT
• Title: Non-Stationary Long-Term Dynamics via Selected Incomplete Dual Bases
• Authors: Hsiao-Han Chuang, Abhijit Pendse,
• Abstract summary: We propose an SU(2) coherent state basis and deriving equations of motion for both time-independent and time-dependent Hamiltonian. We evaluate this method through numerical simulations of a seven-qubit system. Our conclusion suggests that the selected incomplete dual basis method can efficiently capture both short-term and long-term dynamics.
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• Abstract: Simulating the dynamics of non-stationary, long-term many-body quantum systems poses significant challenges due to the large size of the state space. We are examining how traditional basis sets struggle to accurately represent long-term dynamics when using incomplete sets. To address this issue, we propose using an SU(2) coherent state basis and deriving equations of motion for both time-independent and time-dependent Hamiltonian. This methodology involves a sampling approach, where a subset of relevant configurations is chosen based on energy criteria, and a projection method is used to enhance the accuracy of wavefunction propagation while reducing computational cost. We evaluate this method through numerical simulations of a seven-qubit system, calculating key physical observables such as state probabilities and domain-wall densities. Our results indicate that while complete basis sets offer accurate dynamics, selected incomplete sets can recover essential features, especially with the assistance of a projector. Our conclusion suggests that the selected incomplete dual basis method can efficiently capture both short-term and long-term dynamics.

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