Fig. 1: The ab initio DMET-QiankunNet (DMET-NNQS) framework.

a The complex solid-state material is divided into an impurity along with its corresponding environment, and DMET embedding constructs an embedding Hamiltonian that encompasses the impurity orbitals and the bath orbitals. The impurity problem is subsequently solved for the many-body wave function with QiankunNet. b The mapping between orbital and qubit. c QiankunNet: The autoregressive language model takes qubits as tokens, and outputs the conditional probability p(xi∣x < i) of the next token in the sequence. The conditional probabilities can be combined with additional parameterizations of phase information to output the complex quantum state or wave function.