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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.23687 |
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| _version_ | 1866913128261877760 |
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| author | Kagamihara, Daichi Tsuchiya, Shunji |
| author_facet | Kagamihara, Daichi Tsuchiya, Shunji |
| contents | Nonstabilizerness, also known as magic, plays a central role in universal quantum computation. Hypergraph states are nonstabilizer generalizations of graph states and constitute a key class of quantum states in various areas of quantum physics, such as the demonstration of quantum advantage, measurement-based quantum computation, and the study of topological phases. In this work, we investigate nonstabilizerness of 3-uniform hypergraph states, which are solely generated by controlled-controlled-Z gates, in terms of the stabilizer Rényi entropy (SRE). We find that the SRE of 3-uniform hypergraph states can be expressed using the matrix rank, which reduces computational cost from $\mathcal{O}(2^{3N})$ to $\mathcal{O}(N^3 2^{N})$ for $N$-qubit states. Based on this result, we exactly evaluate SREs of one-dimensional hypergraph states. We also present numerical results of SREs of several large-scale 3-uniform hypergraph states. Our results would contribute to an understanding of the role of nonstabilizerness in a wide range of physical settings where hypergraph states are employed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23687 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stabilizer Rényi entropy of 3-uniform hypergraph states Kagamihara, Daichi Tsuchiya, Shunji Quantum Physics Nonstabilizerness, also known as magic, plays a central role in universal quantum computation. Hypergraph states are nonstabilizer generalizations of graph states and constitute a key class of quantum states in various areas of quantum physics, such as the demonstration of quantum advantage, measurement-based quantum computation, and the study of topological phases. In this work, we investigate nonstabilizerness of 3-uniform hypergraph states, which are solely generated by controlled-controlled-Z gates, in terms of the stabilizer Rényi entropy (SRE). We find that the SRE of 3-uniform hypergraph states can be expressed using the matrix rank, which reduces computational cost from $\mathcal{O}(2^{3N})$ to $\mathcal{O}(N^3 2^{N})$ for $N$-qubit states. Based on this result, we exactly evaluate SREs of one-dimensional hypergraph states. We also present numerical results of SREs of several large-scale 3-uniform hypergraph states. Our results would contribute to an understanding of the role of nonstabilizerness in a wide range of physical settings where hypergraph states are employed. |
| title | Stabilizer Rényi entropy of 3-uniform hypergraph states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.23687 |