QuarkXpress documents (.qxd) might be simply exported as PDF documents with either QuarkXpress itself or programs that support QXD format (typically other professional desktop publishing apps). Except for that, your choices for qxd to pdf conversion are somewhat limited as professional proprietary formats are rarely supported in freeware apps.
Convert QuarkXPress document file to Adobe Portable document format.
We found 4 software records in the database related to .qxd to .pdf file format conversion.
Microsoft Windows software - convert qxd to pdf on Windows
A design software used to create rich documents for web or print
Convert from qxd file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned qxd to pdf. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Professional desktop document publishing software from Adobe
Apple macOS / Mac OS X software - convert qxd to pdf on OS X
Software fro document design and publishing
Mac version od Adobe's popular document designing and publishing software