Quantum Algorithm for Reversing Unknown Unitary Evolutions

• URL: http://arxiv.org/abs/2403.04704v2
• Date: Tue, 22 Apr 2025 16:42:33 GMT
• Title: Quantum Algorithm for Reversing Unknown Unitary Evolutions
• Authors: Yu-Ao Chen, Yin Mo, Yingjian Liu, Lei Zhang, Xin Wang,
• Abstract summary: Reversing an unknown quantum evolution is of central importance to quantum information processing and fundamental physics.<n>We introduce the Quantum Unitary Reversal Algorithm (QURA), a deterministic and exact approach to universally reverse arbitrary unknown unitary transformations.
• Score: 8.630679964089696
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reversing an unknown quantum evolution is of central importance to quantum information processing and fundamental physics, yet it remains a formidable challenge as conventional methods necessitate an infinite number of queries to fully characterize the quantum process. Here 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 quantum algorithm resolves a fundamental problem of time-reversal simulations for closed quantum systems by confirming 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 many quantum algorithm frameworks, such as quantum singular value transformation. It notably reveals a sharp boundary between the quantum and classical computing realms and unveils a quadratic quantum advantage in computational complexity for this foundational task.

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