The project investigates the applicability and performance of fault-tolerant quantum computers in solving stochastic and partial differential equations motivated by generative modelling in artificial intelligence (AI). These differential equations arise as models of non-equilibrium dynamics in dissipative physical systems and provide the foundations of recent revolutionary AI models such as diffusion models. More generally, the project views the associated computational tasks as transports of ensemble states in stochastic thermodynamics and compares the performance of quantum algorithms with the fundamental limits of efficient generation of target ensembles by any machine, whether they are unitary and closed, or dissipative and open, quantum or classical, and artificial or biological.
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