Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits, Part 2: Modeling Decoherence from Lossy Drive Ports

Noise entering through drive ports is an important source of decoherence in superconducting circuits. Building on the Hamiltonian construction techniques presented in Part 1, we develop a framework for modeling decoherence from lossy drive ports for a given circuit layout and port specification. Using classical microwave simulations, we extract the susceptibility that maps port-voltage fluctuations to perturbations to the system Hamiltonian, enabling modeling of decoherence from a given spectral density of the voltage noise, e.g., those arising from port resistance or from the input signal. Combined with Fermi's golden-rule calculations (extended through the Floquet–Markov formalism for driven systems), this framework allows efficient computation of decoherence rates, accurately capturing correlations among perturbations originating from the same noise source. As a demonstration of these advantages, we compute drive-induced Purcell decay and dephasing rates for a circuit coupled to a complex filter network. We show that the method successfully estimates these decoherence rates under correlated noise, with much lower computational cost than solving Lindblad master equations. These rates are useful for estimating infidelities of quantum operations due to lossy drive ports.