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Peer-reviewedCC BY-NC-NDNature Communications

The Riemann Hypothesis manifested in dynamical quantum phase transitions

  • Shijie Wei1
  • Yue Zhai2,3
  • Quanfeng Lu4
  • Wentao Yang4
  • Pan Gao5
  • Chao Wei2,3
  • Junda Song2,3
  • Franco Nori6,7
  • Tao Xin8
  • Gui‐Lu Long9,10,11
11 affiliations
  1. 1Beijing Academy of Quantum Information Sciences, Beijing, China. [email protected]
  2. 2International Quantum Academy, Shenzhen, 518048, China
  3. 3Southern University of Science and Technology, Shenzhen, 518055, China
  4. 4Department of Physics, Tsinghua University, Beijing, China
  5. 5Beijing Academy of Quantum Information Sciences, Beijing, China
  6. 6Center for Quantum Computing, RIKEN, Wakoshi, Saitama, Japan
  7. 7Quantum Research Institute, The University of Michigan, Ann Arbor, MI, USA
  8. 8International Quantum Academy, Shenzhen, 518048, China. [email protected]
  9. 9Beijing Academy of Quantum Information Sciences, Beijing, China. [email protected]
  10. 10Department of Physics, Tsinghua University, Beijing, China. [email protected]
  11. 11Tsinghua National Laboratory for Information Science and Technology, Beijing, China. [email protected]
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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 quantum many-body systems, characterized by the average accumulated phase factor and the Loschmidt amplitude respectively. This precise correspondence recasts the RH as the emergence 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.

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Cite

BibTeXRIS
BibTeX
@article{wei2026riemann,
  title = {{The Riemann Hypothesis manifested in dynamical quantum phase transitions}},
  author = {Shijie Wei and Yue Zhai and Quanfeng Lu and Wentao Yang and Pan Gao and Chao Wei and Junda Song and Franco Nori and Tao Xin and Gui‐Lu Long},
  journal = {Nature Communications},
  year = {2026},
  month = jun,
  doi = {10.1038/s41467-026-74935-8},
  url = {https://doi.org/10.1038/s41467-026-74935-8},
  note = {CC BY-NC-ND},
}
RIS
TY  - JOUR
TI  - The Riemann Hypothesis manifested in dynamical quantum phase transitions
AU  - Shijie Wei
AU  - Yue Zhai
AU  - Quanfeng Lu
AU  - Wentao Yang
AU  - Pan Gao
AU  - Chao Wei
AU  - Junda Song
AU  - Franco Nori
AU  - Tao Xin
AU  - Gui‐Lu Long
PY  - 2026
DA  - 2026/06/30
JO  - Nature Communications
DO  - 10.1038/s41467-026-74935-8
UR  - https://doi.org/10.1038/s41467-026-74935-8
AB  - 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 quantum many-body systems, characterized by the average accumulated phase factor and the Loschmidt amplitude respectively. This precise correspondence recasts the RH as the emergence 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.
SN  - 2041-1723
ER  -