Compression of quantum shallow-circuit states
- URL: http://arxiv.org/abs/2404.11177v1
- Date: Wed, 17 Apr 2024 08:48:07 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 $O(n log N)$ (qu)bits.
- Score: 11.305910458469098
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Shallow quantum circuits feature not only computational advantage 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 in the NISQ era.
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