Engineered Randomness for Ubiquitous Quantum-Enhanced Metrology in Exponential-Dimensional Manifolds

• URL: http://arxiv.org/abs/2605.31442v1
• Date: Fri, 29 May 2026 15:39:00 GMT
• Title: Engineered Randomness for Ubiquitous Quantum-Enhanced Metrology in Exponential-Dimensional Manifolds
• Abstract summary: We show that quantum-enhanced precision can be harvested from the exponential vastness of the Hilbert space.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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