Achieving accurate, efficient, and consistent localization within an a priori environment map remains a fundamental challenge in robotics and computer vision. Conventional map-based keyframe localization often suffers from sub-optimal viewpoints due to limited field of view (FOV), thus degrading its performance. To address this issue, in this paper, we design a real-time tightly-coupled Neural Radiance Fields (NeRF)-aided visual-inertial navigation system (VINS), termed NeRF-VINS. By effectively leveraging NeRF's potential to synthesize novel views, essential for addressing limited viewpoints, the proposed NeRF-VINS optimally fuses IMU and monocular image measurements along with synthetically rendered images within an efficient filter-based framework. This tightly coupled integration enables 3D motion tracking with bounded error. We extensively compare the proposed NeRF-VINS against the state-of-the-art methods that use prior map information, which is shown to achieve superior performance. We also demonstrate the proposed method is able to perform real-time estimation at 15 Hz, on a resource-constrained Jetson AGX Orin embedded platform with impressive accuracy.

We formulate the first differentiable analog quantum computing framework with a specific parameterization design at the analog signal (pulse) level to better exploit near-term quantum devices via variational methods. We further propose a scalable approach to estimate the gradients of quantum dynamics using a forward pass with Monte Carlo sampling, which leads to a quantum stochastic gradient descent algorithm for scalable gradient-based training in our framework. Applying our framework to quantum optimization and control, we observe a significant advantage of differentiable analog quantum computing against SOTAs based on parameterized digital quantum circuits by orders of magnitude.