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We present an essentially exact numerical method for modelling flux qubitchains subject to charge and flux noise. We define an essentially exact methodas one that introduces errors that are completely controlled such that they canbe made arbitrarily small by tuning the simulation parameters. The methodadopts the quasi-adiabatic path integral formalism to express the system'sreduced density matrix as a time-discretized path integral, comprising a seriesof influence functionals that encode the non-Markovian dynamics of the system.We present a detailed derivation of the path integral expression for thesystem's reduced density matrix and describe in detail the tensor networkalgorithm used to evaluate the path integral expression. We have implementedour method in an open-sourced Python library called "spinbosonchain". Whenappropriate, we draw connections between concepts covered in this manuscriptand the library's code.

Essentially exact numerical modelling of flux qubit chains subject to charge and flux noise