The Riemann Hypothesis manifested in dynamical quantum phase transitions.

Authors

Shijie Wei, Yue Zhai, Quanfeng Lu, Wentao Yang, Pan Gao, Chao Wei, Junda Song, Franco Nori, Tao Xin, Guilu Long

Published in

Nature communications. Jul 01, 2026. Epub Jul 01, 2026.

Abstract

The Riemann Hypothesis (RH), one of the most profound unsolved problems in mathematics, concerns the nontrivial zeros of the Riemann zeta function. Linking these zeros to physical phenomena offers new perspectives on their origin and verification. Here we establish a direct correspondence between these zeros and dynamical quantum phase transitions in two complementary engineered quantum many-body systems, characterized by the average accumulated phase factor and the Loschmidt amplitude, respectively. This precise correspondence recasts the RH as the occurrence of phase transitions at a unique temperature and identifies it as a previously unknown transition mechanism. We demonstrate this correspondence in a proof-of-principle experiment on a quantum processor. Moreover, we propose a quantum computational framework that implements both systems with polynomial resources, suggesting quantum advantage in probing the hypothesis. Our work bridges nonequilibrium quantum dynamics and number theory, positioning quantum computing as a powerful platform for exploring mathematical conjectures, phase transitions and beyond.

PMID:
42380166
Bibliographic data and abstract were imported from PubMed on 01 Jul 2026.

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