Memory-minimal quantum generation of stochastic processes

Stochastic processes underlie many natural phenomena, and modeling them efficiently is crucial across the sciences. Hidden Markov models (HMMs) and their quantum counterparts (QHMMs) describe these processes through interactions between an observed system and an unobserved memory. While many models can generate a given process, their memory requirements vary, making it essential—but challenging—to identify memory-minimal representations. In this talk, I introduce spectral invariants that provide strict bounds on the quantum generative complexity of a process. We show that these bounds increase quadratically when restricted to classical operations, a fundamentally quantum-coherent effect. Finally, we demonstrate that quantum models can surpass classical memory limits, highlighting the advantages of quantum information processing.

NOTE PLACE: room 215