Experimental noise filtering by quantum control
  Instabilities due to extrinsic interference are routinely faced in systems engineering, and a common solution is to rely on a broad class of $\textit{filtering}$ techniques in order to afford stability to intrinsically unstable systems. For instance, electronic systems are frequently designed to incorporate electrical filters composed of, $\textit{e.g.}$ RLC components, in order to suppress the effects of out-of-band fluctuations that interfere with desired performance. Quantum coherent systems are now moving to a level of complexity where challenges associated with realistic time-dependent noise are coming to the fore. Unfortunately, standard control solutions involving feedback are generally impossible due to the strictures of quantum mechanics, and existing error-suppressing gate constructions generally rely on unphysical bang-bang controls or quasi-static error models that do not reflect realistic laboratory environments. In this work we use the theory of quantum control engineering and experiments with trapped $^{171}$Yb$^{+}$ ions to demonstrate the construction of novel $\textit{noise filters}$ which are specifically designed to mitigate the effect of realistic time-dependent fluctuations on qubits \emph{during useful operations}. Starting with desired filter characteristics and the Walsh basis functions, we use a combination of analytic design rules and numeric search to construct time-domain noise filters tailored to a desired state transformation. Our results validate the generalized filter-transfer function framework for arbitrary quantum control operations, and demonstrate that it can be leveraged as an effective and efficient tool for developing novel robust control protocols. 
A. Soare, H. Ball, D. Hayes, J. Sastrawan, M. C. Jarratt, J. J.   McLoughlin, X. Zhen, T. J. Green, M. J. Biercuk
quant-ph