Coupled Lindblad pseudomode theory is a promising approach for simulating non-Markovian quantum dynamics on both classical and quantum platforms, with dynamics that can be realized as a quantum channel. We provide theoretical evidence that the number of coupled pseudomodes only needs to scale as $\text{polylog}(T/ϵ)$ in the simulation time $T$ and precision $ϵ$. Inspired by the realization problem in control theory, we also develop a robust numerical algorithm for constructing the coupled modes that avoid the nonconvex optimization required by existing approaches. We demonstrate the effectiveness of our method by computing population dynamics and absorption spectra for the spin-boson model. This Letter provides a significant theoretical and computational improvement to the coupled Lindblad framework, which impacts a broad range of applications from classical simulations of quantum impurity problems to quantum simulations on near-term quantum platforms.

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• Light-matter interaction
• Open quantum systems
• Quantum transport
• Quantum many-body systems
• Anderson impurity model
• Dynamical mean field theory
• Non-Markovian processes
• Spin-boson model