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arXiv · 2512.24685

A fast and exact approach for stabilizer R\'enyi entropy via the XOR-FWHT algorithm

Xuyang Huang·Han-Ze Li·Ching Hua Lee·Jian-Xin Zhong
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Abstract

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 R\'enyi 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.

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Xuyang Huang, Han-Ze Li, Ching Hua Lee, Jian-Xin Zhong. 2025-12-31. A fast and exact approach for stabilizer R\'enyi entropy via the XOR-FWHT algorithm. https://arxiv.org/abs/2512.24685

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