Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information

• URL: http://arxiv.org/abs/2401.04672v2
• Date: Mon, 22 Jul 2024 04:51:28 GMT
• Title: Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information
• Authors: Chengkai Zhu, Yin Mo, Yu-Ao Chen, Xin Wang,
• Abstract summary: We show that virtual combs can reverse unitary operations and investigate the trade-off between the slot number and the sampling overhead. We also show that virtual combs can universally reverse unitary operations and investigate the trade-off between the slot number and the sampling overhead.
• Score: 4.656320930335616
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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