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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 evolve to their 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 the 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-hard problems. The scalability of the silicon PIC-OPA and its compatibility with monolithic integration with CMOS electronics further promise the realization of a powerful hybrid photonic/electronic non-Von Neumann compute engine. [ABSTRACT FROM AUTHOR]

Photonic integrated circuit based optical phased arrays (PIC-OPAs) are emerging as promising programmable processors and spatial light modulators, combining the best of planar and free-space optics. Their implementation on silicon photonic platforms has been especially fruitful. Despite much progress in this field, demonstrating steerable two-dimensional (2D) OPAs that are scalable to a large number of array elements and operate with a single wavelength has proven a challenge. In addition, the phase shifters used in the array for programming the far-field beam are either power hungry or have a large footprint, preventing the implementation of large scale 2D arrays. Here, we demonstrate a two-dimensional silicon photonic phased array with high-speed (∼330 kHz) and ultralow power microresonator phase-shifters with a compact radius (∼3 µm) and 2π phase shift ability. Each phase-shifter consumes an average of ∼250 µW of static power for resonance alignment and ∼50 µW of power for far-field beamforming, a more than one order of magnitude improvement compared to prior OPA works based on waveguide-based thermo-optic phase shifters. Such PIC-OPA devices can enable a new generation of compact and scalable low power processors and sensors. [ABSTRACT FROM AUTHOR]