Quantum-Trajectory-Inspired Lindbladian Simulation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909871898624000 |
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| author | Peng, Sirui Sun, Xiaoming Zhao, Qi Zhou, Hongyi |
| author_facet | Peng, Sirui Sun, Xiaoming Zhao, Qi Zhou, Hongyi |
| contents | Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the dynamics of open quantum systems governed by Lindbladians. We introduce a new approximation channel for short-time evolution, inspired by the quantum trajectory method, which underpins the efficiency of our algorithms. The first algorithm achieves a gate complexity independent of the number of jump operators, $m$, marking a significant improvement in efficiency. The second algorithm achieves near-optimal dependence on the evolution time $t$ and precision $ε$ and introduces only an additional $\tilde{O}(m)$ factor, which strictly improves upon state-of-the-art gate-based quantum algorithm that has an $\tilde O(m^2)$ factor. The improvement stems from the integration of the new approximation channel with a novel structured linear combination of unitaries method. In both our algorithms, the reduction of dependence on $m$ significantly enhances the efficiency of simulating practical dissipative processes characterized by a large number of jump operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10505 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum-Trajectory-Inspired Lindbladian Simulation Peng, Sirui Sun, Xiaoming Zhao, Qi Zhou, Hongyi Quantum Physics Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the dynamics of open quantum systems governed by Lindbladians. We introduce a new approximation channel for short-time evolution, inspired by the quantum trajectory method, which underpins the efficiency of our algorithms. The first algorithm achieves a gate complexity independent of the number of jump operators, $m$, marking a significant improvement in efficiency. The second algorithm achieves near-optimal dependence on the evolution time $t$ and precision $ε$ and introduces only an additional $\tilde{O}(m)$ factor, which strictly improves upon state-of-the-art gate-based quantum algorithm that has an $\tilde O(m^2)$ factor. The improvement stems from the integration of the new approximation channel with a novel structured linear combination of unitaries method. In both our algorithms, the reduction of dependence on $m$ significantly enhances the efficiency of simulating practical dissipative processes characterized by a large number of jump operators. |
| title | Quantum-Trajectory-Inspired Lindbladian Simulation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2408.10505 |