Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations

Wepresent a quantum algorithm based on the generalized quantummaster equation (GQME) approach to simulate open quantum system dynamicson noisy intermediate-scale quantum (NISQ) computers. This approachovercomes the limitations of the Lindblad equation, which assumesweak system-bath coupling and Markovity, by providing a rigorousderivation of the equations of motion for any subset of elements ofthe reduced density matrix. The memory kernel resulting from the effectof the remaining degrees of freedom is used as input to calculatethe corresponding non-unitary propagator. We demonstrate how the Sz.-Nagydilation theorem can be employed to transform the non-unitary propagatorinto a unitary one in a higher-dimensional Hilbert space, which canthen be implemented on quantum circuits of NISQ computers. We validateour quantum algorithm as applied to the spin-boson benchmark modelby analyzing the impact of the quantum circuit depth on the accuracyof the results when the subset is limited to the diagonal elementsof the reduced density matrix. Our findings demonstrate that our approachyields reliable results on NISQ IBM computers.