The Impact of Logical Errors on Quantum Algorithms via Jump Formalism

In this paper, we first study the quantum jump formalism and its equivalence to the Lindblad master equation in describing the evolution of open quantum systems. Second, we evaluate the impact of logical Pauli and coherent Z-rotation errors on six quantum algorithms and their algorithmic resilience to these errors by performing the Monte Carlo simulations dictated by the quantum jump method. The results suggest that the resilience of the studied quantum algorithms decreases as the number of qubits and the depth of the algorithms' circuits increase for single Pauli and Z-rotation errors. Moreover, when two Pauli errors occur, the success of the algorithms becomes significantly unlikely. As per two Z-rotations errors, the success rate of the algorithms vanishes.