Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915683942531072 |
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| author | Magni, Beatrice Heinrich, Markus Leone, Lorenzo Turkeshi, Xhek |
| author_facet | Magni, Beatrice Heinrich, Markus Leone, Lorenzo Turkeshi, Xhek |
| contents | We investigate the statistical properties of orthogonal, or real, Clifford circuits doped with magic and imaginary resources. By developing the Weingarten calculus for the real Clifford group, we derive the exact overlap distribution of real stabilizer states, identifying a new universality class: the orthogonal Clifford Porter-Thomas distribution. We prove that local real architectures recover this global statistic in logarithmic depth. Furthermore, we uncover a sharp hierarchy in resource requirements: while retrieving Haar statistics necessitates a polylogarithmic amount of magic states, recovering the full unitary Clifford statistics requires only a single phase gate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks Magni, Beatrice Heinrich, Markus Leone, Lorenzo Turkeshi, Xhek Quantum Physics Statistical Mechanics We investigate the statistical properties of orthogonal, or real, Clifford circuits doped with magic and imaginary resources. By developing the Weingarten calculus for the real Clifford group, we derive the exact overlap distribution of real stabilizer states, identifying a new universality class: the orthogonal Clifford Porter-Thomas distribution. We prove that local real architectures recover this global statistic in logarithmic depth. Furthermore, we uncover a sharp hierarchy in resource requirements: while retrieving Haar statistics necessitates a polylogarithmic amount of magic states, recovering the full unitary Clifford statistics requires only a single phase gate. |
| title | Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2512.15880 |