I'm not a lawyer or anything; I just wanted to say I also signed a contract which I very much regret having signed. What I did was I have tendered my resignation and gave 30 days' notice (which the contract I signed (and the HR) says I should do). I'm entering what should be my 4th and last month with this job.
Unfortunately (as I've posted elsewhere in this forum) my boss won't accept my resignation (which is why I find myself asking for advice in my post elsewhere). Anyway just wanted to say I know how you feel and I hope you won't have any problems like mine in backing out of your contract.