Ground state preparation via unitary time evolution with time-dependent classical fields

Ground-state preparation is one of the most important problems in quantum computation and in computational many-body physics. Because time-dependent Hamiltonians can change their energy as a function of time, we can optimize the reduction of energy at each time step within a pool of allowed classical fields coupled to quantum operators of the system. In this fashion, we can prepare ground states with unitary circuits. The optimization step also helps the algorithm to be robust and work for a wide range of different initial states. Often, we can find ground-state fidelities of 0.99 or higher with relatively shallow unitary circuits. This approach is an alternative to Kraus-map approaches, which are robust for essentially all initial states, but become difficult to formulate with shallow circuits for interacting models. Our examples study the Hubbard model for a wide range of interactions, and show that this unitary method has a good likelihood of working, even on near-term quantum computers.