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Published on: April 19, 2018
The Riemann Hypothesis manifested in dynamical quantum phase transitions
Shijie Wei1, Yue Zhai2,3, Quanfeng Lu4
1Beijing Academy of Quantum Information Sciences, Beijing, China. weisj@baqis.ac.cn.
Nature Communications
|June 30, 2026
Summary
Researchers link the Riemann Hypothesis (RH) to quantum phase transitions. This discovery recasts the RH as a phase transition and suggests quantum computing can explore this mathematical problem.
Area of Science:
- Quantum Physics
- Number Theory
- Condensed Matter Physics
Background:
- The Riemann Hypothesis (RH) is a major unsolved problem in mathematics concerning the zeros of the Riemann zeta function.
- Connecting mathematical concepts to physical phenomena can provide novel insights and verification methods.
Purpose of the Study:
- To establish a direct correspondence between the nontrivial zeros of the Riemann zeta function and dynamical quantum phase transitions.
- To explore the potential of quantum computing in investigating the Riemann Hypothesis.
Main Methods:
- Engineering two complementary quantum many-body systems.
- Characterizing these systems using the average accumulated phase factor and the Loschmidt amplitude.
- Conducting a proof-of-principle experiment on a quantum processor.
Main Results:
- A direct correspondence was established between Riemann zeta function zeros and quantum phase transitions.
- The Riemann Hypothesis was recast as a phase transition occurring at a specific temperature.
- A proof-of-principle experiment successfully demonstrated this correspondence.
Conclusions:
- The study bridges nonequilibrium quantum dynamics and number theory.
- Quantum computing offers a powerful platform for exploring the Riemann Hypothesis and other mathematical conjectures.
- The identified transition mechanism provides a new perspective on the Riemann Hypothesis.
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