Compression of quantum shallow-circuit states

• URL: http://arxiv.org/abs/2404.11177v2
• Date: Mon, 30 Sep 2024 09:53:27 GMT
• Title: Compression of quantum shallow-circuit states
• Authors: Yuxiang Yang,
• Abstract summary: Storing quantum information generated by shallow circuits is a fundamental question of both theoretical and practical importance. We show that $N$ copies of an unknown $n$-qubit state can be compressed into a hybrid memory of $O(nlog N)$ (qu)bits.
• Score: 11.305910458469098
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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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