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| Format: | Recurso digital |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17274756 |
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Table of Contents:
- <h3><strong>Description:</strong></h3> This work presents a novel computational framework for simulating open quantum systems, addressing two fundamental limitations of traditional Matrix Product State (MPS) methods: exponential entanglement growth and fidelity degradation under decoherence. <strong>Background & Problem:</strong> Tensor network simulations, particularly using Matrix Product States (MPS), are powerful tools for quantum many-body systems. However, their application to open quantum systems is severely hampered by runaway entanglement, which leads to prohibitive computational costs, and by an inherent sensitivity to noise that rapidly destroys quantum information. <strong>Proposed Solution:</strong> We introduce a <strong>Pre-decoherence MPS (Pre-MPS)</strong> model. Our key innovation is the integration of a tunable <strong>pre-decoherence operator</strong> directly into the Lindblad master equation. This operator acts as a controlled mechanism to actively suppress the generation of excessive entanglement <em>before</em>it destabilizes the simulation, while aiming to preserve the coherent dynamics of the system. <strong>Key Contributions:</strong> <ol> <li> <strong>Theoretical Foundation:</strong> A modified Lindblad master equation incorporating a dedicated pre-decoherence term. </li> <li> <strong>Entanglement Control:</strong> Derivation of an entanglement entropy bound condition (<span><span><span><span><span><span>S</span><span><span><span><span><span><span><span>v</span><span>N</span></span></span></span><span></span></span></span></span></span><span>≤</span></span><span><span>α</span><span>log</span><span><span>(</span><span><span>χ</span><span><span><span><span><span><span><span>eff</span></span></span></span><span></span></span></span></span></span><span>)</span></span></span></span></span></span>) to ensure computational tractability. </li> <li> <strong>Algorithmic Implementation:</strong> A full numerical validation pipeline implemented using the QuTiP (Quantum Toolbox in Python) framework. </li> <li> <strong>Performance Gains:</strong> Demonstrated improvements in entanglement control, noise robustness, and computational compression efficiency. </li> </ol> <strong>Numerical Validation:</strong> The method was rigorously tested on a transverse-field Ising model. The numerical results, summarized in Figure 1 below, confirm that our Pre-MPS model consistently achieves superior performance compared to traditional MPS, showing significantly lower entanglement entropy, higher state fidelity under noise, and favorable computational scaling. <div> <div> <div> </div> </div> </div> <strong>Impact and Applications:</strong> This work provides a scalable and robust approach for the simulation of open quantum systems. The Pre-MPS model offers a practical pathway to simulate larger and more complex quantum dynamics that were previously limited by entanglement-induced computational bottlenecks, with potential applications in quantum information processing, condensed matter physics, and quantum thermodynamics.