  Ising annealer is a promising quantum-inspired computing architecture for
combinatorial optimization problems. In this paper, we introduce an Ising
annealer based on the Hamiltonian Monte Carlo, which updates the variables of
all dimensions in parallel. The main innovation is the fusion of an approximate
gradient-based approach into the Ising annealer which introduces significant
acceleration and allows a portable and scalable implementation on the
commercial FPGA. Comprehensive simulation and hardware experiments show that
the proposed Ising annealer has promising performance and scalability on all
types of benchmark problems when compared to other Ising annealers including
the state-of-the-art hardware. In particular, we have built a prototype
annealer which solves Ising problems of both integer and fraction coefficients
with up to 200 spins on a single low-cost FPGA board, whose performance is
demonstrated to be better than the state-of-the-art quantum hardware D-Wave
2000Q and similar to the expensive coherent Ising machine. The sub-linear
scalability of the annealer signifies its potential in solving challenging
combinatorial optimization problems and evaluating the advantage of quantum
hardware.
