Is it permissible for me to obtain a loan with annual interest from a bank to purchase a house, given that the state, the bank, and the beneficiary each contribute a third of the cost?

The described scenario is impermissible because it involves forbidden usury (riba). Your payment of one-third of the amount and the state's payment of the other third does not alter the ruling, as long as you will be borrowing an amount from the bank with an usurious interest. You should seek someone to lend you one-third of the amount as a benevolent loan (qard hasan (definition)). If the bank is the only option, then it is not permissible for you to engage in this transaction.