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arXiv · 2404.11177

Compression of quantum shallow-circuit states

Yuxiang Yang
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Abstract

Shallow quantum circuits feature not only computational advantages over their classical counterparts but also cutting-edge applications. Storing quantum information generated by shallow circuits is a fundamental question of both theoretical and practical importance that remained largely unexplored. In this work, we show that $N$ copies of an unknown $n$-qubit state generated by a fixed-depth circuit can be compressed into a hybrid memory of $O(n \log_2 N)$ (qu)bits, which achieves the optimal scaling of memory cost. Our work shows that the computational complexity of resources can significantly impact the rate of quantum information processing, offering a unique and unified view of quantum Shannon theory and quantum computing.

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Yuxiang Yang. 2025-01-11. Compression of quantum shallow-circuit states. https://doi.org/10.1103/physrevlett.134.010603

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