Anticoncentration and state design of doped real Clifford circuits and tensor networks
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.
Fields of Study & Subjects
Quantum Computing Algorithms and Architecture
Matrix Theory and Algorithms
Quantum many-body systems
Publication details
- Journal / source
- Physical Review A
- Publisher
- American Physical Society (APS)
- Volume
- 113
- Issue
- 6
- Publication date
- 27 May 2026
- Language
- EN