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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.22311 |
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| _version_ | 1866918379315527680 |
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| author | Shao, Yuguo Cheng, Song Liu, Zhengwei |
| author_facet | Shao, Yuguo Cheng, Song Liu, Zhengwei |
| contents | Simulating real-time quantum dynamics in interacting spin systems is a fundamental challenge, where exact diagonalization suffers from exponential Hilbert-space growth and tensor-network methods face entanglement barriers. Recently, Pauli-propagation-based methods have emerged as a promising alternative. In this work, we bridge operator complexity and the complexity of Pauli-propagation-based methods in simulating real-time dynamics of quantum spin systems. Specifically, we derive a priori error bounds governed by the Operator Stabilizer Rényi entropy (OSE) $\mathcal{S}^α(O)$, which explicitly links the truncation accuracy to operator complexity. For the 1D Heisenberg model with $J_z = 0$, we prove the number of non-zero Pauli coefficients scales quadratically in Trotter steps, establishing the compressibility of Heisenberg-evolved operators. We then consider a Pauli propagation instance with a Top-$K$ truncation strategy, and benchmark the method numerically on XXZ Heisenberg chain benchmarks, showing high accuracy with small truncation number $K$ in free regimes ($J_z = 0$) and competitive performance against tensor-network methods (e.g., TDVP) in interacting cases ($J_z = 0.5$). Analogous to the role of entanglement entropy in tensor networks, these results establish a new perspective on using OSE to quantify the computational complexity of Pauli-propagation-based methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22311 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizing Pauli Propagation via Operator Complexity in Quantum Spin Systems Shao, Yuguo Cheng, Song Liu, Zhengwei Quantum Physics Statistical Mechanics Simulating real-time quantum dynamics in interacting spin systems is a fundamental challenge, where exact diagonalization suffers from exponential Hilbert-space growth and tensor-network methods face entanglement barriers. Recently, Pauli-propagation-based methods have emerged as a promising alternative. In this work, we bridge operator complexity and the complexity of Pauli-propagation-based methods in simulating real-time dynamics of quantum spin systems. Specifically, we derive a priori error bounds governed by the Operator Stabilizer Rényi entropy (OSE) $\mathcal{S}^α(O)$, which explicitly links the truncation accuracy to operator complexity. For the 1D Heisenberg model with $J_z = 0$, we prove the number of non-zero Pauli coefficients scales quadratically in Trotter steps, establishing the compressibility of Heisenberg-evolved operators. We then consider a Pauli propagation instance with a Top-$K$ truncation strategy, and benchmark the method numerically on XXZ Heisenberg chain benchmarks, showing high accuracy with small truncation number $K$ in free regimes ($J_z = 0$) and competitive performance against tensor-network methods (e.g., TDVP) in interacting cases ($J_z = 0.5$). Analogous to the role of entanglement entropy in tensor networks, these results establish a new perspective on using OSE to quantify the computational complexity of Pauli-propagation-based methods. |
| title | Characterizing Pauli Propagation via Operator Complexity in Quantum Spin Systems |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2510.22311 |