QuimP depends on several external Java libraries (jar files, see hereLink opens in a new window 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