The Riemann Hypothesis Emerges in Dynamical Quantum Phase Transitions

TL;DR

This paper links the Riemann Hypothesis to dynamical quantum phase transitions in quantum systems, demonstrating experimental verification and proposing a quantum simulation framework to explore this profound mathematical conjecture.

Contribution

It establishes a direct correspondence between the zeros of the zeta function and DQPTs, and introduces a quantum simulation approach for studying the RH.

Findings

Experimental demonstration on a five-qubit system

Proposed universal quantum simulation framework

Quantum advantage in numerical verification of RH

Abstract

The Riemann Hypothesis (RH), one of the most profound unsolved problems in mathematics, concerns the nontrivial zeros of the Riemann zeta function. Establishing connections between the RH and physical phenomena could offer new perspectives on its physical origin and verification. Here, we establish a direct correspondence between the nontrivial zeros of the zeta function and dynamical quantum phase transitions (DQPTs) in two realizable quantum systems, characterized by the averaged accumulated phase factor and the Loschmidt amplitude, respectively. This precise correspondence reveals that the RH can be viewed as the emergence of DQPTs at a specific temperature. We experimentally demonstrate this correspondence on a five-qubit spin-based system and further propose an universal quantum simulation framework for efficiently realizing both systems with polynomial resources, offering a quantum advantage for numerical verification of the RH. These findings uncover an intrinsic link between nonequilibrium critical dynamics and the RH, positioning quantum computing as a powerful platform for exploring one of mathematics' most enduring conjectures and beyond.