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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.24685 |
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| _version_ | 1866914420820541440 |
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| author | Huang, Xuyang Li, Han-Ze Lee, Ching Hua Zhong, Jian-Xin |
| author_facet | Huang, Xuyang Li, Han-Ze Lee, Ching Hua Zhong, Jian-Xin |
| contents | Quantum advantage is widely understood to rely on key quantum resources beyond entanglement, among which nonstabilizerness (quantum ``magic'') plays a central role in enabling universal quantum computation. However, the exact evaluation of the second-order stabilizer Rényi entropy for generic many-body quantum states remains computationally challenging, with brute-force methods scaling as $\mathcal O(8^N)$ for an $N$-qubit state. Here we develop a deterministic and exact algorithm that reduces this cost to $\mathcal{O}(N4^N)$ while retaining natural parallelism. This advance enables high-precision exact calculations for generic state vectors at medium system sizes, and provides a practical tool for investigating the scaling, phase structure, and nonequilibrium dynamics of quantum magic in many-body systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24685 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A fast and exact approach for stabilizer Rényi entropy via the XOR-FWHT algorithm Huang, Xuyang Li, Han-Ze Lee, Ching Hua Zhong, Jian-Xin Quantum Physics Quantum advantage is widely understood to rely on key quantum resources beyond entanglement, among which nonstabilizerness (quantum ``magic'') plays a central role in enabling universal quantum computation. However, the exact evaluation of the second-order stabilizer Rényi entropy for generic many-body quantum states remains computationally challenging, with brute-force methods scaling as $\mathcal O(8^N)$ for an $N$-qubit state. Here we develop a deterministic and exact algorithm that reduces this cost to $\mathcal{O}(N4^N)$ while retaining natural parallelism. This advance enables high-precision exact calculations for generic state vectors at medium system sizes, and provides a practical tool for investigating the scaling, phase structure, and nonequilibrium dynamics of quantum magic in many-body systems. |
| title | A fast and exact approach for stabilizer Rényi entropy via the XOR-FWHT algorithm |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.24685 |