Engineered Randomness for Ubiquitous Quantum-Enhanced Metrology in Exponential-Dimensional Manifolds
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866916066457812992 |
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| author | Chu, Yaoming Yu, Baiyi Häffner, Hartmut Heyl, Markus Goldman, Nathan Cai, Jianming |
| author_facet | Chu, Yaoming Yu, Baiyi Häffner, Hartmut Heyl, Markus Goldman, Nathan Cai, Jianming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31442 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Engineered Randomness for Ubiquitous Quantum-Enhanced Metrology in Exponential-Dimensional Manifolds Chu, Yaoming Yu, Baiyi Häffner, Hartmut Heyl, Markus Goldman, Nathan Cai, Jianming Quantum Physics 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. |
| title | Engineered Randomness for Ubiquitous Quantum-Enhanced Metrology in Exponential-Dimensional Manifolds |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.31442 |