Benchmarking a heuristic Floquet adiabatic algorithm for the Max-Cut problem
摘要
According to the adiabatic theorem of quantum mechanics, a system initially in the ground state of a Hamiltonian remains in the ground state if one slowly changes the Hamiltonian. This can be used in principle to solve hard problems on quantum computers. Generically, however, implementation of this Hamiltonian dynamics on digital quantum computers requires scaling Trotter step size with system size and simulation time, which incurs a large gate count. In this work, we argue that for classical optimization problems, the adiabatic evolution can be performed with a fixed, finite Trotter step. This “Floquet adiabatic evolution” reduces by several orders of magnitude the gate count compared to the usual, continuous-time adiabatic evolution. We give numerical evidence using matrix-product-state simulations that it can optimally solve the