Quantum Simulation of Lindbladian Dynamics via Repeated Interactions

Understand

The Lindblad equation generalizes the Schr\"{o}dinger equation to quantum systems that undergo dissipative dynamics.

• The quantum simulation of Lindbladian dynamics is therefore non-unitary, preventing a naive application of state-of-the-art quantum algorithms.
• Here, we make use of an approximate correspondence between Lindbladian dynamics and evolution based on Repeated Interaction (RI) CPTP maps to write down a Hamiltonian formulation of the Lindblad dynamics and derive a rigorous error bound on the master equation.
• Specifically, we show that the number of interactions needed to simulate the Liouvillian $e^{t\mathcal{L}}$ within error $\epsilon$ scales in a weak coupling limit as $\nu\in O(t^2\|\mathcal{L}\|_{1\rightarrow 1}^2/\epsilon)$.