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Trapped Ion Quantum Computing

Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks

arXiv

Authors: Beatrice Magni, Markus Heinrich, Lorenzo Leone, Xhek Turkeshi

Year

2025

Paper ID

5966

Status

Preprint

Abstract Read

~2 min

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Abstract

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.

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We investigate the statistical properties of orthogonal, or real, Clifford circuits doped with magic and imaginary resources.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2512.15880 [2] arXiv https://arxiv.org/abs/2512.15880 [3] Publisher https://arxiv.org/abs/2512.15880

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