You can use static functions of the class JlCompress. It's very easy to use.
Static Public Member Functions
static bool compressFile (QString fileCompressed, QString file)
static bool compressFiles (QString fileCompressed, QStringList files)
static bool compressDir (QString fileCompressed, QString dir=QString(), bool recursive=true)
static QString extractFile (QString fileCompressed, QString fileName, QString fileDest=QString())
static QStringList extractFiles (QString fileCompressed, QStringList files, QString dir=QString())
static QStringList extractDir (QString fileCompressed, QString dir=QString())
static QStringList getFileList (QString fileCompressed)
Source: http://quazip.sourceforge.net/classJlCompress.html