Probabilistic eigensolver with a trapped-ion quantum processor

Preparing the eigenstate, especially the ground state, of a complex Hamiltonian is of great importance in quantum simulations. Many proposals have been introduced and experimentally realized, among which are quantum variational eigensolver and heat-bath algorithmic cooling, with the former hindered by local minima and the latter lacking of complex system Hamiltonians. Here we introduce a dissipative quantum-classical hybrid scheme, the probabilistic eigensolver. The scheme repeatedly uses an ancilla qubit to acquire information on the system, based on which it postselectively lowers the average energy of the system. The optimal reduction is achieved through classical optimization with a single variational parameter. We describe the implementation of the probabilistic eigensolver with trapped-ion systems and demonstrate the performance by numerically simulating the ground-state preparation of several paradigmatic models, including the Rabi and the Hubbard models. We believe the scheme would enrich the functionalities of universal quantum simulators and be useful as a module for various quantum-computation tasks.