Quantum Regression Theory and Efficient Computation of Response Functions for Non-Markovian Open Systems

Explore quantum regression theory and efficient computation methods for response functions in non-Markovian open quantum systems through this 50-minute conference presentation. Learn how linear response functions serve as fundamental tools in physics for efficiently estimating dynamical properties, predicting electric conductivity, magnetic susceptibility, and dielectric constants without requiring full system resimulation. Discover the challenges of estimating two-time correlation functions in open quantum systems, where traditional quantum master equations only provide one-point observables. Examine a breakthrough memoryless, system-only formulation that extends the standard quantum regression theorem beyond the Markov limit by incorporating spectral properties of the bath and expressing time propagators as memoryless generators in Lindblad-type forms. Understand how this approach recasts total response functions into evolutions generated by time-dependent Hamiltonian and Lindblad primitives, along with the propagation of commutators and anti-commutators. Investigate quantum algorithms for these primitives that achieve poly-logarithmic scaling in system dimension and 1/ϵ^1.25 scaling in target accuracy ϵ for two-time correlation estimators. Gain insights into how this framework eliminates the separability (Born-Markov) assumption and provides efficient pathways for computing nonequilibrium properties from open quantum systems, presented at IPAM's New Frontiers in Quantum Algorithms for Open Quantum Systems Workshop.