Quantum Algorithm for Reversing Unknown Unitary Evolutions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918156763660288 |
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| author | Chen, Yu-Ao Mo, Yin Liu, Yingjian Zhang, Lei Wang, Xin |
| author_facet | Chen, Yu-Ao Mo, Yin Liu, Yingjian Zhang, Lei Wang, Xin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_04704 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Algorithm for Reversing Unknown Unitary Evolutions Chen, Yu-Ao Mo, Yin Liu, Yingjian Zhang, Lei Wang, Xin Quantum Physics 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. |
| title | Quantum Algorithm for Reversing Unknown Unitary Evolutions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2403.04704 |