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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.