\section{Acknowledgements}
We thank Luming Duan, Zhe-Xuan Gong, Tarun Grover, Chris Laumann, Shengtao Wang, Norman Yao, and Jiehang Zhang for helpful discussions. This work is supported by the ARO Atomic and Molecular Physics Program, the AFOSR MURI on Quantum Measurement and Verification, the IARPA MQCO program, and the NSF Physics Frontier Center at JQI. PH and MH acknowledge  the Deutsche Akademie der Naturforscher Leopoldina (grant No.~LPDS 2013-07), the EU IP SIQS, the SFB FoQuS (FWF Project No.~F4016-N23) and the ERC synergy grant UQUAM.




