The U.S. Bureau of Industry and Security (BIS) has issued an Advanced Notice of Proposed Rulemaking (ANPRM) proposing to add Quantum Information and Sensing Technology to the Commerce Control List (CCL). CCL items are typically considered dual-use items which may have a military in addition to a commercial use. Items on this list are then subject to Export Administration Regulations (EAR) administered by the BIS which governs whether an item can be exported or re-exported to a foreign country.
Quantum information and sensing technology is one of fourteen items proposed to be added to the CCL and BIS will be accepting comments on this ANPRM until December 19, 2018. For more details you can view the text of the ANPRM here, details on the EAR regulations including a country chart (Part 738 supplement 1) here, and the home page of the Bureau of Industry and Security here.