Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910536200880128 |
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| author | Zhu, Chengkai Mo, Yin Chen, Yu-Ao Wang, Xin |
| author_facet | Zhu, Chengkai Mo, Yin Chen, Yu-Ao Wang, Xin |
| contents | The inherent irreversibility of quantum dynamics for open systems poses a significant barrier to the inversion of unknown quantum processes. To tackle this challenge, we propose the framework of virtual combs that exploit the unknown process iteratively with additional classical post-processing to simulate the process inverse. Notably, we demonstrate that an $n$-slot virtual comb can exactly reverse a depolarizing channel with one unknown noise parameter out of $n+1$ potential candidates, and a 1-slot virtual comb can exactly reverse an arbitrary pair of quantum channels. We further explore the approximate inversion of an unknown channel within a given channel set. A worst-case error decay of $\mathcal{O}(n^{-1})$ is unveiled for depolarizing channels within a specified noise region. Moreover, we show that virtual combs can universally reverse unitary operations and investigate the trade-off between the slot number and the sampling overhead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04672 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information Zhu, Chengkai Mo, Yin Chen, Yu-Ao Wang, Xin Quantum Physics The inherent irreversibility of quantum dynamics for open systems poses a significant barrier to the inversion of unknown quantum processes. To tackle this challenge, we propose the framework of virtual combs that exploit the unknown process iteratively with additional classical post-processing to simulate the process inverse. Notably, we demonstrate that an $n$-slot virtual comb can exactly reverse a depolarizing channel with one unknown noise parameter out of $n+1$ potential candidates, and a 1-slot virtual comb can exactly reverse an arbitrary pair of quantum channels. We further explore the approximate inversion of an unknown channel within a given channel set. A worst-case error decay of $\mathcal{O}(n^{-1})$ is unveiled for depolarizing channels within a specified noise region. Moreover, we show that virtual combs can universally reverse unitary operations and investigate the trade-off between the slot number and the sampling overhead. |
| title | Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.04672 |