  The photonic Ising machine is a new paradigm of optical computing that takes
advantage of the unique properties of light wave propagation, parallel
processing, and low-loss transmission. Thus, the process of solving
combinatorial optimization problems can be accelerated through
photonic/optoelectronic devices, but implementing photonic Ising machines that
can solve arbitrary large-scale Ising problems with fast speed remains
challenging. In this work, we have proposed and demonstrated the Phase Encoding
and Intensity Detection Ising Annealer (PEIDIA) capable of solving arbitrary
Ising problems on demand. The PEIDIA employs the heuristic algorithm and
requires only one step of optical linear transformation with simplified
Hamiltonian calculation by encoding the Ising spins on the phase term of the
optical field and performing intensity detection during the solving process. As
a proof of principle, several 20 and 30-spin Ising problems have been solved
with high ground state probability (>0.97/0.85 for the 20/30-spin Ising model).
