This is as small as this can go:
'xs:dateTime(sql:variable("@stringDate"))'
It needs to be a literal string for the Value() function.

Xml Datatype
http://msdn2.microsoft.com/en-us/library/ms189887.aspx

Sql:Variable() Function
http://msdn2.microsoft.com/en-us/library/ms188254.aspx

'xs:dateTime( val )'
http://www.w3schools.com/xpath/xpath_functions.asp#datetime

Xml Datatype Methods
http://msdn2.microsoft.com/en-us/library/ms190798.aspx