Quantum speed limits (QSLs) define the minimum time required for a quantum system to evolve between distinguishable states, placing fundamental bounds on control, sensing, and information processing. In this project, we advance the theory of QSLs across multiple physical regimes.

We begin by incorporating relativistic corrections and higher-order energy-momentum expansions to explore how coherent and squeezed quantum states evolve under modified dynamics. These refinements have direct implications for high-precision quantum metrology, particularly in scenarios where Doppler and gravitational redshifts are significant, such as gravitational wave detectors (e.g., LIGO and LISA) and satellite-based quantum communication systems.

We further extend the QSL framework to irreversible quantum systems, including the inverted harmonic oscillator, uncovering novel bounds on evolution speed that are intrinsically linked to entropy production and the exponential divergence of trajectories. These findings provide valuable insights into fundamental processes such as information scrambling in black holes, particle production in cosmology, and strong-field quantum phenomena.

We also demonstrate the operational realization of QSLs in classical wave systems. By emulating quantum-limited evolution through classical optics, we enable analog simulations of unstable quantum dynamics, ultrafast beam shaping, and high-sensitivity parameter estimation.

In addition, we investigate quantum gravimetry using optically levitated nanoparticles. By explicitly incorporating gravitational acceleration and time into the Hamiltonian framework, we derive two-parameter quantum Fisher information bounds, thereby improving the theoretical sensitivity limits of inertial quantum sensors.

Lastly, we also examine QSLs in the context of quantum reference frames (QRFs), where the reference frame itself is treated as a quantum system. This line of inquiry seeks to understand how QRF-dependent descriptions constrain evolution speed and impact the calibration of relativistic quantum sensors.

Intelligent Transportation Systems (ITS) are critical to modern mobility, enhancing traffic efficiency, reducing congestion, enabling autonomous vehicle deployment, and improving road safety. However, despite their growing relevance, ITS still faces several technical challenges. These include the need for real-time processing of large-scale sensor data, accurate and adaptive traffic prediction, robust vehicle-to-infrastructure coordination, and reliable object detection under complex environmental conditions such as noise, shadows, or low visibility. Among the most pressing issues is anomaly detection—identifying irregular or potentially hazardous behavior in traffic flow, including unexpected vehicle movements and cyber-physical threats. Traditional machine-learning approaches often struggle to meet these demands due to inherent scalability, adaptability, and resilience limitations in dynamic and uncertain environments.

This project proposes the use of quantum machine learning (QML) and hybrid quantum-classical computing to enhance the performance, adaptability, and security of ITS. Quantum neural networks (QNNs) will be explored for advanced perception tasks, including traffic signal recognition and context-aware image analysis. Quantum-based anomaly detection models will be developed to identify atypical patterns in vehicle behavior and system interactions, even under noisy or adversarial conditions. Additionally, quantum optimization algorithms will be employed to solve complex routing and traffic coordination problems more efficiently than classical methods. Quantum generative models will also be used to enrich training datasets and improve simulation fidelity.

Together, these quantum-enabled techniques aim to significantly improve the responsiveness, reliability, and intelligence of next-generation transportation systems, paving the way for more secure, efficient, and autonomous mobility infrastructures.