We propose a quantum algorithmic approach to metrology and its implementation using trapped-ion qubits. Active decoherence suppression methods such as decoherence-free subspaces, Quantum error-correction codes and dynamic decoupling will be used to reduce the effect of noise while amplifying a measured signal, thus improving on the measurement signal-to-noise ratio. An ion trap architecture that best suits this approach will be designed and realized. Several metrology protocols will be demonstrated. Finally, we propose to apply these methods in actual precision measurements, including the detection of magnetic interaction between ions at large distances, optical frequency metrology, the measurement of parity violation in atomic transitions, and the detection of correlations in an ultra-cold gas of neutral atoms. The implications of scaling-up to large numbers of probe-qubits will be investigated as well.
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