The paper establishes a correspondence between nontrivial zeros of the Riemann zeta function and dynamical quantum phase transitions in engineered quantum systems. The authors emphasize that, despite extensive numerical evidence, the Riemann Hypothesis is still unproven. Their results provide a physical pathway for probing the hypothesis via measurable quantum dynamics and quantum simulation frameworks, potentially enabling scalable numerical verification of zeros on large instances.
This problem remains central to analytic number theory because the distribution of zeros governs deep properties of the prime numbers and underpins many mathematical results and applications. The authors’ work positions the RH as a statement about the emergence of dynamical quantum phase transitions at a specific inverse temperature in certain constructed quantum systems, thereby offering an alternative viewpoint and experimental route to examine the hypothesis.