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Learn rigorous methods for characterizing time-dependent quantum systems through this 48-minute conference talk that addresses the critical gap in Hamiltonian learning protocols for time-dependent Hamiltonians and Lindbladians. Discover a novel protocol for learning the time-dependent evolution of locally interacting n-qubit systems on graphs using only product Pauli eigenstate preparation, time-dependent evolution, and product Pauli basis measurements. Explore how the method assumes time-dependent parameters can be approximated by functions in known spaces admitting stable interpolation, such as polynomials, and outputs coefficient-approximating functions with controlled accuracy and success probability while requiring only polynomial scaling in the function space dimension rather than exponential scaling of previous methods. Understand the innovative approach that combines Lieb-Robinson bounds, process shadows, and semidefinite programs to efficiently recover coefficients at constant times, along with extensions of state-of-the-art Lieb-Robinson bounds to time-dependent, dissipative dynamics on general graphs. Gain insights into practical applications for verifying state-preparation procedures like adiabatic protocols and characterizing time-dependent noise in quantum devices, providing essential tools for benchmarking quantum computers and simulators in realistic time-dependent scenarios.
