## Thursday, August 22, 2013

### Frequency Multiplexed Magnetometry via Compressive Sensing / Compressing measurements in quantum dynamic parameter estimation

The keyword today is Magnetometry.

Frequency Multiplexed Magnetometry via Compressive Sensing by Graciana Puentes, Gerald Waldherr, Philipp Neumann, Jörg Wrachtrup

Quantum sensors based on single Nitrogen-Vacancy (NV) defects in diamond are state-of-the-art tools for nano-scale magnetometry with precision scaling inversely with total measurement time $\sigma_{B} \propto 1/T$ (Heisenberg scaling) rather than as the inverse of the square root of $T$, with $\sigma_{B} =1/\sqrt{T}$ the Shot-Noise limit. This scaling can be achieved by means of phase estimation algorithms (PEAs) using adaptive or non-adaptive feedback, in combination with single-shot readout techniques. Despite their accuracy, the range of applicability of PEAs is limited to periodic signals involving single frequencies with negligible temporal fluctuations. In this Letter, we propose an alternative method for precision magnetometry in frequency multiplexed signals via compressive sensing (CS) techniques. We show that CS can provide for precision scaling approximately as $\sigma_{B} \approx 1/T$, both in the case of single frequency and frequency multiplexed signals, as well as for a 5-fold increase in sensitivity over dynamic-range gain, in addition to reducing the total number of resources required.

Compressing measurements in quantum dynamic parameter estimation by Easwar Magesan, Alexandre Cooper, Paola Cappellaro

We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control methods to efficiently estimate time-dependent parameters in the system Hamiltonian. We show that incoherent measurement bases and, more generally, suitable random measurement matrices can be created by performing simple control sequences on the quantum system. Since random measurement matrices satisfying the restricted isometry property can be used to reconstruct any sparse signal in an efficient manner, and many physical processes are approximately sparse in some basis, these methods can potentially be useful in a variety of applications such as quantum sensing and magnetometry. We illustrate the theoretical results throughout the presentation with various practically relevant numerical examples.

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