Congrats on the job. My wife worked for HP about 35 years ago. It was a pretty decent company.
California, the state I live in, (home of HP corporate headquarters) has what is referred to as "at will" employment. The company can let you go at any time without notice and you are free to leave a position at any time without notice. Most people still give 2 weeks notice as a courtesy unless they really dislike the employer.