The 5th and 14th amendments provide that no person shall "be deprived of life, liberty, or property, without due process of law". He was convicted of a crime. The punishment can include random searches, drug tests, ankle monitors, etc., as long as it is provided for by law.
When I read the parent comment, I didn't see someone surprised that it CAN be done, but someone surprised at where the line of when it is an appropriate remedy had been drawn.
That horribly low standard for a justice system. Especially that due process of law basically boils down to judge deciding what tickles him the right way.
In this case the value of his life and liberty given his lack of background is probably worth more than the protection the state gains by being able to search his house at will. Which is the entire purpose of the 4th amendment.