Universität zu Köln

Magni, Beatrice ORCID: 0009-0009-8577-0525, Christopoulos, Alexios ORCID: 0000-0003-4857-5922, De Luca, Andrea and Turkeshi, Xhek ORCID: 0000-0003-1093-3771 (2025). Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudomagic States. Physical Review X, 15 (3). pp. 1-16. American Physical Society (APS). ISSN 2160-3308

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Abstract

[Artikel-Nr. 031071] Anticoncentration describes how an ensemble of quantum states spreads over the allowed Hilbert space, leading to statistically uniform output probability distributions. In this work, we investigate the anticoncentration of random Clifford circuits toward the overlap distribution of random stabilizer states. Using exact analytical techniques and extensive numerical simulations based on Clifford replica tensor networks, we demonstrate that random Clifford circuits fully anticoncentrate in logarithmic circuit depth; namely, higher-order moments of the overlap distribution converge to those of random stabilizer states. Moreover, we investigate the effect of introducing a controlled number of non-Clifford (magic) resources into Clifford circuits. We show that inserting a polylogarithmic in qudit number of T states is sufficient to drive the overlap distribution toward the Porter-Thomas statistics, effectively recovering full quantum randomness. In short, this fact presents doped tensor networks and shallow Clifford circuits as pseudomagic quantum states. Our results clarify the interplay between Clifford dynamics, magic-state injection, and quantum complexity, with implications for quantum circuit sampling, many-body quantum physics, and the benchmarking of quantum computational advantage.

Item Type:	Article
Creators:	Creators Email ORCID ORCID Put Code Magni, Beatrice UNSPECIFIED https://orcid.org/0009-0009-8577-0525 UNSPECIFIED Christopoulos, Alexios UNSPECIFIED https://orcid.org/0000-0003-4857-5922 UNSPECIFIED De Luca, Andrea UNSPECIFIED UNSPECIFIED UNSPECIFIED Turkeshi, Xhek UNSPECIFIED https://orcid.org/0000-0003-1093-3771 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-798290
Identification Number:	10.1103/p8dn-glcw
Journal or Publication Title:	Physical Review X
Volume:	15
Number:	3
Page Range:	pp. 1-16
Date:	15 September 2025
Publisher:	American Physical Society (APS)
ISSN:	2160-3308
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	Natural sciences and mathematics Physics
['eprint_fieldname_oa_funders' not defined]:	Publikationsfonds UzK
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/79829