A research team led by Tao Xin at the International Quantum Academy, working with collaborators, has made significant progress in exploring the physical interpretation and quantum simulation of the Riemann Hypothesis. For the first time, the researchers established a direct correspondence between the nontrivial zeros of the Riemann zeta function and dynamical quantum phase transitions, suggesting a possible physical origin for the mathematical structure of the hypothesis in quantum many-body dynamics. They also developed a quantum-simulation framework with the potential for quantum computational advantage, opening a new avenue for investigating problems in number theory. The findings were published online in Nature Communications on July 1, 2026, in a paper titled “The Riemann Hypothesis manifested in dynamical quantum phase transitions.”

The Riemann Hypothesis is one of the central unsolved problems in modern number theory. The distribution of the nontrivial zeros of the Riemann zeta function has long fascinated mathematicians and physicists alike. Yet important questions remain: Is there a physical mechanism behind this mathematical structure? Could quantum technologies eventually help probe the hypothesis or locate its zeros more efficiently?

Figure 1. Physical correspondence between the Riemann Hypothesis and quantum many-body spin dynamics.

To explore these questions, the team developed a quantum many-body dynamical model that can be simulated efficiently. In this model, the nontrivial zeros of the Riemann zeta function are mapped directly onto dynamical quantum phase transitions. This connection suggests a promising way to approach the Riemann Hypothesis, and potentially other fundamental mathematical problems, through quantum physics.

The researchers designed an efficiently implementable quantum many-body system whose dynamics exhibits a precise correspondence with the nontrivial zeros of the Riemann zeta function. Their analysis shows how coherence and correlation dynamics in engineered spin systems can encode information about the zeta function. At evolution times corresponding to its nontrivial zeros, the relevant dynamical signals vanish, providing measurable signatures of dynamical quantum phase transitions.

By translating the abstract distribution of mathematical zeros into observable features of quantum dynamics, the work offers a physical perspective on the Riemann Hypothesis. In particular, the hypothesis can be reformulated in terms of whether the associated quantum phase transitions occur at a specific temperature. The team also proposed a resource-efficient digital quantum simulation framework, providing a scalable route for studying this connection on universal gate-based quantum computers.

Figure 2. The Riemann Hypothesis can be interpreted in terms of quantum phase transitions in a spin system at a particular temperature.

The team then tested the theoretical prediction on a five-qubit nuclear-spin quantum processor by implementing the corresponding quantum many-body spin system. Using precise control of the nuclear spins, they drove the system under an engineered interaction Hamiltonian and observed the predicted dynamical signatures. In particular, the measured coherence signals exhibited clear features consistent with the first five nontrivial zeros of the Riemann zeta function.

These experimental results provide a proof-of-principle demonstration of the proposed connection between number theory and nonequilibrium quantum many-body physics. They also highlight the potential of quantum computing as a tool for investigating fundamental mathematical conjectures.

The paper’s co-first authors are Shijie Wei, an associate researcher at the Beijing Academy of Quantum Information Sciences who also serves as a corresponding author; Yue Zhai, a doctoral student affiliated with the International Quantum Academy and the Southern University of Science and Technology; and Quanfeng Lu, a doctoral student at Tsinghua University. Tao Xin of the International Quantum Academy and Professor Guilu Long of Tsinghua University are also corresponding authors.

Other coauthors include Professor Franco Nori of RIKEN in Japan and Wentao Yang, a doctoral student at Tsinghua University. The work received support from the National Natural Science Foundation of China, the Beijing Nova Program, Shenzhen science and technology funding programs, and Guangdong provincial science and technology funding programs.

Paper link: https://www.nature.com/articles/s41467-026-74935-8