QuimP depends on several external Java libraries (jar files, see here for full list). All they are included in default Fiji installation, so QuimP should run smootly on latest Fiji versions. If you faced a problem with missing libraries with message similar to this:

Exception in thread "AWT-EventQueue-0" java.lang.NoClassDefFoundError: org/scijava/vecmath/Tuple2d
Caused by: java.lang.ClassNotFoundException: org.scijava.vecmath.Tuple2d
at java.net.URLClassLoader.findClass(URLClassLoader.java:381)
at java.lang.ClassLoader.loadClass(ClassLoader.java:424)
at sun.misc.Launcher$AppClassLoader.loadClass(Launcher.java:331)
at java.lang.ClassLoader.loadClass(ClassLoader.java:357)
... 26 more

please check:

1. For Fiji
   1. If you have latest Fiji installed
   2. If you have Java-8 update site enabled (Help->Update Fiji->Manage update sites)
2. For ImageJ
   1. Download missing dependencies manually and copy them to ImageJ/plugins/jars folder