  Quantum annealers, coherent Ising machines and digital Ising machines for
solving quantum-inspired optimization problems have been developing rapidly due
to their near-term applications. The numerical solvers of the digital Ising
machines are based on traditional computing devices. In this work, we propose a
fast and efficient solver for the Ising optimization problems. The algorithm
consists of a pruning method that exploits the graph information of the Ising
model to reduce the computational complexity, and a domain selection method
which introduces significant acceleration by relaxing the discrete feasible
domain into a continuous one to incorporate the efficient gradient descent
method. The experiment results show that our solver can be an order of
magnitude faster than the classical solver, and at least two times faster than
the quantum-inspired annealers including the simulated quantum annealing on the
benchmark problems. With more relaxed requirements on hardware and lower cost
than quantum annealing, the proposed solver has the potential for near-term
application in solving challenging optimization problems as well as serving as
a benchmark for evaluating the advantage of quantum devices.
