  Solving large-scale computationally hard optimization problems using existing
computers has hit a bottleneck. A promising alternative approach uses
physics-based phenomena to naturally solve optimization problems wherein the
physical phenomena evolves to its minimum energy. In this regard, photonics
devices have shown promise as alternative optimization architectures,
benefiting from high-speed, high-bandwidth and parallelism in the optical
domain. Among photonic devices, programmable spatial light modulators (SLMs)
have shown promise in solving large scale Ising model problems to which many
computationally hard problems can be mapped. Despite much progress, existing
SLMs for solving the Ising model and similar problems suffer from slow update
rates and physical bulkiness. Here, we show that using a compact silicon
photonic integrated circuit optical phased array (PIC-OPA) we can simulate an
XY Hamiltonian, a generalized form of Ising Hamiltonian, where spins can vary
continuously. In this nanophotonic XY Hamiltonian solver, the spins are
implemented using analog phase shifters in the optical phased array. The far
field intensity pattern of the PIC-OPA represents an all-to-all coupled XY
Hamiltonian energy and can be optimized with the tunable phase-shifters
allowing us to solve an all-to-all coupled XY model. Our results show the
utility of PIC-OPAs as compact, low power, and high-speed solvers for
nondeterministic polynomial (NP)-hard problems. The scalability of the silicon
PIC-OPA and its compatibility with monolithic integration with CMOS electronics
further promises the realization of a powerful hybrid photonic/electronic
non-Von Neumann compute engine.
