Quantum Advantage in Reversing Unknown Unitary Evolutions

Reversing an unknown unitary with finite calls of the unitary evolution.

Abstract

We introduce the Quantum Unitary Reversal Algorithm (QURA), a deterministic and exact approach to universally reverse arbitrary unknown unitary transformations using $\mathcal{O}(d^2)$ calls of the unitary, where $d$ is the system dimension. Our construction resolves a fundamental problem of time-reversal simulations for closed quantum systems by affirming the feasibility of reversing any unitary evolution without knowing the exact process. The algorithm also provides the construction of a key oracle for unitary inversion in quantum algorithm frameworks such as quantum singular value transformation. Notably, our work demonstrates that compared with classical methods relying on process tomography, reversing an unknown unitary on a quantum computer holds a quadratic quantum advantage in computation complexity. QURA ensures an exact unitary inversion while the classical counterpart can never achieve exact inversion using a finite number of unitary calls.

Publication
arXiv:2403.04704
Yu-Ao Chen
Yu-Ao Chen
Research Associate

I obtained my BS in Mathematics and Applied Mathematics from University of Science and Technology of China. I obtained my PhD degree in Applied Mathematics from University of Chinese Academy of Sciences under the supervision of Prof. Xiao-Shan Gao. My research interests include quantum computing, symbolic computation and cryptanalysis.

Yin Mo
Yin Mo
Research Associate

I obtained my BS in Fundamental Science in Physics and Mathematics from Tsinghua University. I obtained my PhD degree in Computer Science from the University of Hong Kong. My research interests include quantum information theory, quantum supermaps and quantum machine learning.

Yingjian Liu
Yingjian Liu
Research Assistant

I obtained my BS in Electronics at Shandong University, China. Then I obtained my MS degree in Optics and Photonics from Karlsruhe Institute of Technology in Germany and finished my master’s thesis at ICFO in Spain. My research interests include quantum computation, quantum information and quantum many-body physics.

Lei Zhang
Lei Zhang
PhD Student

I obtained my BMath in AMath, CO & joint PMath from the University of Waterloo. My research interests include quantum information theory and quantum machine learning.

Xin Wang
Xin Wang
Associate Professor

The main focus of my research is to better understand the limits of information processing with quantum systems and the power of quantum artificial intelligence.