A digital processor simulates a quantum computing system by implementing a QPU model including a set of representation models and a device connectivity representation to simulate a quantum processor design or a physical quantum processor. The digital processor receives an analog waveform and generates a digital waveform representation comprising a set of waveform values that correspond to biases applied to programmable devices in a quantum processor. The digital processor selects a subset of waveform values based on channels in the device connectivity representation. The digital processor implements a representation model to compute a response based on the waveform values and a plurality of physical parameter values, the physical parameters characterizing a programmable device in a quantum processor. The device connectivity representation can be generated from a design implementation, validated against a set of rules, and adjusted to change the device connectivity representation until all of the rules are passed.