Approximating open quantum system dynamics in a controlled and efficient way: A microscopic approach to decoherence

Abstract

We demonstrate that the dynamics of an open quantum system can be calculated efficiently and with predefined error, provided a basis exists in which the system-environment interactions are local and hence obey the Lieb-Robinson bound. We show that this assumption can generally be made. Defining a dynamical renormalization group transformation, we obtain an effective Hamiltonian for the full system plus environment that comprises only those environmental degrees of freedom that are within the effective light cone of the system. The reduced system dynamics can therefore be simulated with a computational effort that scales at most polynomially in the interaction time and the size of the effective light cone. Our results hold for generic environments consisting of either discrete or continuous degrees of freedom.

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• Efficient simulation of non-Markovian system-environment interaction
• Rate operator unravelling for open quantum system dynamics
• Convergence guarantees for discrete mode approximations to non-Markovian quantum baths
• Non-perturbative analytical diagonalization of Hamiltonians with application to coupling suppression and enhancement in cQED
• Rise and fall of entanglement between two qubits in a non-Markovian bath
• Optimized Sampling of Mixed-State Observables