Baiyi Yu

The exponential growth of many-body Hilbert space presents a fundamental barrier to quantum technology, obscuring the search for physically significant states within an astronomically vast landscape. Consequently, resources for quantum-enhanced metrology have been largely confined to the symmetric subspace whose dimensionality scales only polynomially with the particle number-leaving the vast majority of the Hilbert space largely unexplored and poorly understood. Here we challenge this paradigm by demonstrating that metrological advantage can arise as a ubiquitous feature across exponential-dimensional manifolds. By tailoring the first-moment structure of random unitaries, we uncover dense manifolds of engineered random states (ERSs) where Heisenberg-limited scaling emerges as a statistically generic property. This ubiquity endows these resource states with inherent resilience against parameter disorder. We experimentally validate this framework on a trapped-ion processor, achieving a metrological enhancement of $6.98 \pm 0.38$ dB beyond the standard quantum limit. Potential applications extend to diverse platforms, ranging from superconducting circuits and waveguide QED to solid-state spins and polar molecules. Our results establish a powerful paradigm where quantum-enhanced precision can be harvested from the exponential vastness of the Hilbert space.

Ion-ion coupling over long distances represents a highly useful resource for quantum technologies, for example, to sympathetically cool or interconnect qubits in ion-based quantum-computing architectures. In this respect, the recently demonstrated wire-mediated ion-ion coupling stands due to the simplification of its trap layout and its prospects for deterministic entanglement. However, the strength of such coherent ion-wire-ion coupling is typically weak, hindering its practical utilization. Here, we propose a wire-mediated scheme for coherent ion-electron coupling. The scheme not only enables the sympathetic cooling of electrons via advanced ion-cooling techniques, but also allows to promote the effective ion-ion coupling strength by orders of magnitudes via electron mediation. Our work thus paves a way toward quantum information processing in ion-electron hybrid quantum systems.