Compression of Quantum Shallow-Circuit States
Yuxiang Yang · Physical Review Letters · 2025
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 Letter, 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(nlog_{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.