Chinese Quantum Team Maps Riemann Zeta Zeros onto Atomic Phase Transitions

A research group at the Beijing Academy of Quantum Information Sciences has built a quantum simulator that mirrors the Riemann zeta function, the mathematical object at the heart of the centuries-old Riemann hypothesis. In the device, the temperature of a set of interacting atomic nuclei encodes the real part of a zeta-function input, while the evolution time encodes its imaginary part. A sharp phase transition occurs only when those inputs would make the zeta function equal zero. By preparing the system at a temperature different from the critical value ½ and watching for a transition, the team can test whether any non-trivial zeros lie off the critical line, which would falsify the hypothesis.

Scientific American

The idea that the zeros of the zeta function might correspond to quantum energy levels dates back to 1972, when mathematician Hugh Montgomery and physicist Freeman Dyson noted a surprising similarity between the statistical distribution of zeta zeros and the spectra of atomic nuclei. Their observation sparked a long-standing speculation that a physical quantum system could reveal the hidden order of prime numbers.

Scientific American

The demonstration employed five interacting atoms, the quantum analogue of bits (qubits). The researchers showed that the system’s phase-transition behavior reproduces the zeta function’s zeros and that the quantum algorithm scans for zeros faster than conventional classical methods. No previously unknown zeros have been observed yet, but the authors argue that scaling the simulator to about 100 qubits would allow it to probe far more of the critical line than any existing computer.

Scientific American

Co-lead author Shijie Wei says the work illustrates how quantum computing can become a powerful avenue for investigating major mathematical conjectures. Senior author Guilu Long suggests that the Riemann hypothesis and dynamical quantum phase transitions may be two aspects of a deeper underlying principle.

Scientific American

• “It provides a new perspective on the Riemann hypothesis,” — Shijie Wei, of the Beijing Academy of Quantum Information Sciences, the study’s co-lead author — Shijie Wei, of the Beijing Academy of Quantum Information Sciences, the study’s co-lead author.

Scientific American