Work

Anticoncentration and state design of doped real Clifford circuits and tensor networks

Year: 2026

Type: article

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.

Source: Physical Review A

DOI: 10.1103/w6l4-mh6k

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

Institutions: University of Cologne, University of Salerno, Freie Universität Berlin

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: G3356704239, G3826674488, TRR 183: Verschränkte Materiezustände, EXC 2004: Materie und Licht für Quanteninformation (ML4Q)