Single-ancilla ground state preparation via Lindbladians

In this talk, I will introduce a new quantum algorithm for the quantum ground state preparation problem. Different from previous algorithms, our method is based on the simulation of a specific Lindblad dynamics that contains only one jump operator and fixes the ground state as an equilibrium. Under some conditions, the ground state is the unique fix point of the Lindblad dynamics with polynomial mixing time. Furthermore, the dynamics can be efficiently simulated with only one ancilla qubits and its discrete version can be simulated with almost optimal complexity.