On-chip photonic-neural-network processors have potential benefits in both speed and energy efficiency but have not yet reached the scale to compete with electronic processors. The dominant paradigm is to build integrated-photonic processors using relatively bulky discrete components connected by single-mode waveguides. A far more compact alternative is to avoid explicitly defining any components and instead sculpt the continuous substrate of the photonic processor to directly perform the computation using waves freely propagating in two dimensions. In this talk, I will present our recent work [1] on experimentally realizing this approach with a device whose refractive index as a function of space, n(x,z), can be rapidly reprogrammed. This device combines photoconductive gain with the electro-optic effect in a lithium niobate slab waveguide. Using this device, we performed neural-network inference with up to 49-dimensional input vectors in a single pass.
[1]: T. Onodera*, M.M. Stein*, et al. arXiv:2402.17750 (2024)
On-chip photonic-neural-network processors promise benefits in both speed and energy efficiency but have not yet reached the scale to compete with electronic processors. The dominant paradigm is to build integrated-photonic processors using discrete components connected by single-mode waveguides. A far more compact alternative is to avoid discrete components and instead sculpt a complex and continuous microphotonic medium in which computations are performed by multimode waves controllably propagating in two dimensions. We show our realization of this approach with a device whose refractive index as a function of space can be rapidly reprogrammed. We demonstrate optical computations much larger and more error-resilient than previous photonic chips relying on discrete components. We argue that beyond photonic-neural-network processors, devices with such arbitrarily programmable index distributions enable the realization of a wide range of photonic functionality.
We report on the realization of an on-chip waveguide platform capable of creating arbitrary two-dimensional refractive index profiles in situ and in real-time. The device exhibits complex multimode dynamics which we train to perform machine learning. We tune the refractive index profile in situ using a backpropagation algorithm to perform audio and image classification with up to 50-dimensional inputs. The two-dimensional programmability is realized by sandwiching a photoconductive film and a lithium niobate slab waveguide between two flat electrodes. While applying voltage between the electrodes, we program the effective index of the waveguide by projecting different light patterns onto the photoconductive film. The effective index increases by 10^-3 in illuminated regions via the electro-optic effect, free from any measurable memory effects or cyclic degradation. In conclusion, we developed a photonics platform with versatile spatial programmability that opens new avenues for optical computing and photonic inverse-design.
Extremizing a quadratic form can be computationally straightforward or difficult depending on the feasible domain over which variables are optimized. For example, maximizing E = xTVx for a real-symmetric matrix 𝑉 with 𝑥 constrained to a unit ball in 𝑅𝑁 can be performed simply by finding the maximum (principal) eigenvector of 𝑉, but can become computationally intractable if the domain of 𝑥 is limited to corners of the ±1 hypercube in 𝑅𝑁 (i.e., 𝑥 is constrained to be a binary vector). Many gain-loss physical systems, such as coherently coupled arrays of lasers or optical parametric oscillators, naturally solve minimum/maximum eigenvector problems (of a matrix of coupling coefficients) in their equilibration dynamics. In this paper we discuss recent case studies on the use of added nonlinear dynamics and real-time feedback to enforce constraints in such systems, making them potentially useful for solving difficult optimization problems. We consider examples in both classical and quantum regimes of operation.
Coherent Ising machines (CIMs) are an experimentally promising class of physics-based computational architectures that embed hard combinatorial optimization problems into systems of coupled nonlinear optical oscillators. The solution-finding mechanisms employed by CIMs feature complicated dynamical bifurcations occurring on a network scale, posing significant challenges to the development of theory and models for their underlying principles of operation. These difficulties are especially pronounced in the ultra-low-power or quantum regimes where the benefits in computational efficiency over conventional optimization algorithms are expected to be largest. We discuss some of our recent approaches and results at this intersection of dynamical systems theory and quantum model reduction, which have highlighted some potentially useful architectures and applications on the horizon for CIMs.
Coherent Ising Machines (CIMs) are an emerging class of computational architectures that embed hard combinatorial optimization problems in the continuous dynamics of a physical system with analog degrees of freedom. While crisp theoretical results on the ultimate performance and scaling of such architectures are lacking, large-scale experimental prototypes have begun to exhibit promising results in practice. Our team at Stanford has begun to study the fundamental properties of CIM dynamics using a combination of techniques from statistical physics, random matrices, and dynamical systems theory. Many connections to recent work in neuroscience and deep learning are noted. Our work focuses specifically on CIMs that utilize the nonlinear threshold behavior of optical parametric oscillators to effect a soft (potentially glassy) transition between linear and binary dynamical regimes.
The advent of dispersion-engineered and highly nonlinear nanophotonics is expected to open up an all-optical path towards the strong-interaction regime of quantum optics by combining high transverse field confinement with ultra-short-pulse operation. Obtaining a full understanding of photon dynamics in such broadband devices, however, poses major challenges in the modeling and simulation of multimode non-Gaussian quantum physics, highlighting the need for sophisticated reduced models that facilitate efficient numerical study while providing useful physical insight. In this manuscript, we review our recent efforts in modeling broadband optical systems at varying levels of abstraction and generality, ranging from multimode extensions of quantum input-output theory for sync-pumped oscillators to the development of numerical methods based on a field-theoretic description of nonlinear waveguides. We expect our work not only to guide ongoing theoretical and experimental efforts towards next-generation quantum devices but also to uncover essential physics of broadband quantum photonics.
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