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Spin systems are an attractive candidate for quantum-enhanced metrology. Here we develop a variational method to generate metrological states in small dipolar-interacting ensembles with limited qubit controls and unknown spin locations. The generated states enable sensing beyond the standard quantum limit (SQL) and approaching the Heisenberg limit (HL). Depending on the circuit depth and the level of readout noise, the resulting states resemble Greenberger-Horne-Zeilinger (GHZ) states or Spin Squeezed States (SSS). Sensing beyond the SQL holds in the presence of finite spin polarization and a non-Markovian noise environment. 

Quantum metrology enables some of the most precise measurements. In the life sciences, diamond-based quantum sensing has led to a new class of biophysical sensors and diagnostic devices that are being investigated as a platform for cancer screening and ultrasensitive immunoassays. However, a broader application in the life sciences based on nanoscale NMR spectroscopy has been hampered by the need to interface highly sensitive quantum bit (qubit) sensors with their biological targets. Here, we demonstrate an approach that combines quantum engineering with single-molecule biophysics to immobilize individual proteins and DNA molecules on the surface of a bulk diamond crystal that hosts coherent nitrogen vacancy qubit sensors. Our thin (sub–5 nm) functionalization architecture provides precise control over the biomolecule adsorption density and results in near-surface qubit coherence approaching 100 μs. The developed architecture remains chemically stable under physiological conditions for over 5 d, making our technique compatible with most biophysical and biomedical applications. 

Quantum metrology enables some of the most precise measurements. In the life sciences, diamond-based quantum sensing has enabled a new class of biophysical sensors and diagnostic devices that are being investigated as a platform for cancer screening and ultra-sensitive immunoassays. However, a broader application in the life sciences based on nanoscale nuclear magnetic resonance spectroscopy has been hampered by the need to interface highly sensitive quantum bit (qubit) sensors with their biological targets. Here, we demonstrate a new approach that combines quantum engineering with single-molecule biophysics to immobilize individual proteins and DNA molecules on the surface of a bulk diamond crystal that hosts coherent nitrogen vacancy qubit sensors. Our thin (sub-5 nm) functionalization architecture provides precise control over protein adsorption density and results in near-surface qubit coherence approaching 100 {\mu}s. The developed architecture remains chemically stable under physiological conditions for over five days, making our technique compatible with most biophysical and biomedical applications.