Classical optimization with imaginary time block encoding on quantum computers: The MaxCut problem

Optimization problems in finance, physics and computer science are typically very hard to tackle in classical computing and quantum computing could help speed up computations and provide efficient methods for tackling large problems. Typically, to treat the problem with a quantum computer, the optimal solution is cast as the ground state of a diagonal Hamiltonian. We develop a new method, called ITE-BE, based on a recent imaginary time algorithm, which requires no variational parameter optimization as all parameters can be derived analytically from the target Hamiltonian. We also demonstrate that our method can be successfully combined with other quantum algorithms such as quantum approximate optimization algorithm (QAOA). For illustration, here we study the MaxCut problem. We find that the QAOA ansatz increases the post-selection success of ITE-BE, and shallow QAOA circuits, when boosted with ITE-BE, achieve better performance than deeper QAOA circuits. For the special case of the transverse initial state, we adapt our block encoding scheme to allow for a deterministic application of the first layer of the circuit.